Physics Papers Collection

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ATOMIC NUCLEI 1. In an atom, two electrons moves around the nucleus in circular orbit of radius R and

4R.Calculate the ratio of time taken to complete one revolution around the nucleus.

2. The spectrum of hydrogen atom has many lines although hydrogen atom contains only one electron.Why?

3. The energy level of an atom of an element ’X’ are shown in the diagram. A photon of wavelength 620 nm is emitted . This corresponds to which of the transition A,B,C,D or E.

4. Calculate the speed of electron revolving around the nucleus of a hydrogen atom in order that it may not be pulled into the nucleus by the electrostatic attraction ?

5. The spectrum of a star in the visible and the uv region was observed and the wavelength of some of the line that could be identified found to be : 824Å, 970 Å,1120 Å,2504 Å,5173 Å,6100 Å.Which of these lines cannot belong to hydrogen spectrum? R=1.03*107m-1

1/R=960 Å.Support the answer with suitable calculation.

6. Prove that Intanstaneous rate of change of change of the activity of a radioactive substance is inversely proportional to the square of its half life.

7. A radio active nuclei decays to form a stable nucleide. Its half life is 3 min.What fraction of its 1gm will remain radioactive after 9 minutes?

8. 8.How much mass has to be converted to energy to produce electric power 500 MW for one hour?

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9.A certain radioactive substance disintegrates for an interval of time equal to its mean life. A)What fraction of element remains undecayed? B)What fraction of element has disintegrated?

�� ?

11.Explain why heavy water is preferred as a moderator to ordinatory water in a nuclear reactor having uranium as a fuel?

12.The isotope 92U238 decays successively to form 90 Th234 ,91 Pa234 ,92 U234 , 90 Th230 , 88 Ra226.

What are the radiations emitted in these 5 steps?

13.Binding energy of Lithium(39.22 meV)is greater than binding energy of helium(27.22 meV).Even then Helium is more stable than lithium. Explain.

14.4 nuclei of an element fuse together to form a heavier nucleus .If the process is accompanied by release of energy ,which of the two –the parent or the daughter nuclei would have higher binding energy per nucleon.

15. Two different radioactive elements with half lives T1 & T2 have N1 & N2 atoms respectively present at a given instant .Determine the ratio of their activities at this instant.

16. A radioactive material is reduced to 1/16 of its original amount in 4 days .How much material should one begin with so that 4x10-3 of the material left after 6 days.

17. What do you understand by the term mirror isobars?

18.Show that the decay rate R of a sample of radio nuclei is related to the number of radioactive nuclei N at sam ��

�� 92U238 changes to 90Th230

20.Draw a graph showing variation of P.E of a pair of nucleons as a function of their separation b.Indicate the reason in which nuclear force is

a)Attractive (b)Repulsive

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22.You are given two nuclei 3X7 and 3Y4 .Explain giving reasons as to which one of the two nuclei is more stable?

23.If the nucleons bound in the nucleus are separated apart from each other ,the sum of their masses is greater than the mass of the nucleus.Where does this mass difference come from.Explain.

24.The wavelength of the first line of Lymann series for Hydrogen is identical to that of second line of Balmer series for some hydrogen like ion x.Calculate the energies of the first 4 levels of x.

25.At time t=0 activity of a radioactive substance is 1600 Bq. At t =8s activity remains 100 Bq . Find the activity at 2 seconds.

26. A radioactive nucleus undergoes a series of decay according to the scheme. A A1�A2�A3�A4 .If the mass number and atomic number of A are 180 and 72

respectively.What are these numbers A4

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26. A gas of monoatomic hydrogen is bombarded with a stream of electrons that have been accelerated from rest through a potential difference of 12.75 V. Which spectral lines should be emitted?

27. An electron and anti particle, the positron, can form a bound system, called Positronium. What should be the ionization potential of positronium.

28. Estimate the energy needed to eject from a lead atom the electron with n = 1. What wavelength X ray would be required to do this ( Z = 82 ).

29. An alpha particle comes to with in 80 fm of gold nucleus . Assuming gold nucleus and the alpha particle are point charges, find the maximum repulsive force.

30. Show that if two ions of the same charge and velocity but of different mass pass through a uniform transverse magnetic field, the radii of the path are proportional to the masses. Find an expression for dm if dr is change in radius.

31. A nucleus X initially at rest, undergoes alpha decay according to the equation 92 X A

-----> z Y 228 + Alpha particle. ( a ) find the values of A and Z. (b ) the alpha particle in the above process is found to move in a circular track of radius 1.1 X 10 2 m in a uniform field 3 X 10 3 T , find the energy during process and binding energy of parent nucleus ?

32. In experiment angles of scattering of alpha particle is 180. What is its impact parameter.

33. What will happen if electron revolving around the nucleus comes to rest. 34. By what factor must the mass number A change for the nuclear radius to double. 35. Initial amount of a radioactive substance is N0 . How much amount of the substance

is left after 10 half lifes ? 36. Half life of a radioactive element A is same as mean life time of another radioactive

element B. Initially both have same no of atoms. Explain why Beta decay faster than A.

37. Half life of radioactive substance A is two times the half life of another substance B. Initially the no of nuclei of A and B are NA and NB . After three half lives of A number of nuclei of both are equal. What is ratio of NA and NB

38. 92U 238 changes to 85 At 210 by series of alpha , Beta decays. How many alpha , beta decay underwent?

39. Find the ratio between total acceleration of electron in singly ionized helium atom and hydrogen atom when both are in ground state.

40. The shortest wavelength of Brackett series of a hydrogen atom is the same as the shortest wavelength of Balmer series of hydrogen . Find the atomic no?

41. Find the maximum angular velocity of a electron of hydrogen atom in stationary orbit?

42. Find the ratio of maximum wavelength of Lymann series in hydrogen spectrum to the maximum wavelength in Paschen Series?

43. A electron and photon have same wavelength . If P is the momentum and E is energy of photon . Find the ratio of P/E.

44. B.E. per nucleon of hydrogen and helium are 1.1 eV and 7 MeV. Find the energy released in the process?

45. Find the probability of survival of a radioactive nucleus for one mean life? 46. The ratio of molecular mass of two radio active substances is 3/2 and ratio of their

decay constant is 4/3. Find the ratio of their initial activity per mole? 47. A freshly prepared radio active substance of half life 2 hours emits radiation of

intensity which is 64 times the permissible safe level. Find the minimum time after which it would possible to work with this source safely.

48. A star can convert all He nuclei completely into oxygen nuclei. Find the energy released per oxygen nuclei?

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49. A beam of electron is used in YDS experiment. The slit width is d. What happens to fringe width?

50. A nucleus disintegrates in to two nuclear parts which have their velocities in the ratio 2 : 1. Find the ratio of their sizes

51. When a uranium originally at rest decays by emitting alpha particle having speed u. Find the recoil speed of residual nucleus?

52. The activity of a radioactive sample diminishes from 1024 to 128 in 2 min. Find how much activity diminishes in 6 min.

53. The activity of a radioactive element decreased to 1/3 of the original activity I0 in a period of 9 years. What its activity after further lapse of 9 years?

54. Half life of two substances A and B are 20 min and 40 min. Initially the sample have equal no of nuclei. Find after 80 min the ratio of remaining no of A and B nucleii?

1 [P.T.O.55/1/1

PHYSICS (Theory)HkkSfrd foKku ¼lS)kfUrd½HkkSfrd foKku ¼lS)kfUrd½HkkSfrd foKku ¼lS)kfUrd½HkkSfrd foKku ¼lS)kfUrd½HkkSfrd foKku ¼lS)kfUrd½

Time allowed : 3 hours ] [ Maximum Marks: 70fu/kkZfjr le; % 3 ?k.Vs ] [ vf/kdre vad % 70

General Instructions :

(i) All questions are compulsory.

(ii) There is no overall choice. However, an internal choice has been provided in onequestion of two marks, one question of three marks and all three questions of fivemarks. You have to attempt only one of the choice in such questions.

(iii) Question numbers 1 to 5 are very short answer type questions, carrying one markeach.

(iv) Question numbers 6 to 12 are short answer type questions, carrying two markseach.

(v) Question numbers 13 to 24 are also short answer type questions, carrying threemarks each.

(vi) Questions numbers 25 to 27 are long answer type questions, carrying five markseach.

Roll No.

Series SHC/1 Code No. 55/1/1

Please check that this question paper contains 12 printed pages.Code number given on the right hand side of the question paper should be written onthe title page of the answer-book by the candidate.Please check that this question paper contains 27 questions.Please write down the serial number of the question before attempting it.Ñi;k tk¡p dj ysa fd bl iz'u&i=k esa eqfnzr i`"B 12 gSaAiz'u&i=k esa nkfgus gkFk dh vksj fn, x, dksM uEcj dks Nk=k mÙkj&iqfLrdk ds eq[k&i`"B ij fy[ksaA

Ñi;k tk¡p dj ysa fd bl iz'u&i=k esa 27 iz'u gSaAÑi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad vo'; fy[ks aAÑi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad vo'; fy[ks aAÑi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad vo'; fy[ks aAÑi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad vo'; fy[ks aAÑi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad vo'; fy[ks aA

Candidates must write the Code onthe title page of the answer-book.jksy ua-

dksM ua-dksM ua-dksM ua-dksM ua-dksM ua-

fo|kFkhZ mÙkj&iqfLrdk esa dksM ua- vo';fy[ksA

255/1/1

(vii) Use of calculators is not permitted. However, you may use log tables, if necessary.(viii) You may use the following values of physical constants wherever necessary:

Mass of neutronBoltzmann's constant Avogadro's number

lkekU; funsZ'k %lkekU; funsZ'k %lkekU; funsZ'k %lkekU; funsZ'k %lkekU; funsZ'k %

(i) lHkh lHkh lHkh lHkh lHkh iz'u vfuok;Z gSaA

(ii) iz'u&i=k esa lexz ij dksbZ fodYi ugha gSA fQj Hkh nks vadksa okys ,d iz'u esa] rhu vadksa okys,d iz'u esa vkSj ik¡p vadksa okys rhuksa iz'uksa esa Hkhrjh p;u fodYi miyC/k gSA ,sls iz'uksa esavkidks fn;s x;s p;u esa ls dsoy ,d iz'u gh djuk gSA

(iii) iz'u la[;k 11111 ls 55555 vfr y?kq mÙkj izdkj ds iz'u gSaA buesa izR;sd iz'u ,d,d,d,d,d vad dk gSA

(iv) iz'u la[;k 66666 ls 1212121212 y?kq mÙkj izdkj ds iz'u gSaA buesa izR;sd iz'u nksnk snk snk snk s vadksa dk gSA

(v) iz'u la[;k 1313131313 ls 2424242424 Hkh y?kq mÙkj izdkj ds iz'u gSaA buesa izR;sd iz'u rhu rhu rhu rhu rhu vadksa dk gSA

(vi) iz'u la[;k 2525252525 ls 2727272727 nh?kZ mÙkj izdkj ds iz'u gSaA buesa izR;sd iz'u ik¡pik¡pik¡pik¡pik¡p vadksa dk gSA

(vii) dSydqysVj ds mi;ksx dh vuqefr ugha gSA rFkkfi] vko';d gks rks vki y?kqx.kdh; lkjf.k;ksadk mi;ksx dj ldrs gSA

(viii) tgk¡ vko';d gks vki fuEufyf[kr HkkSfrd fu;rkadksa ds ekuksa dk mi;ksx dj ldrs gSa %

U;wVªku dk lagfr

cksYV~t+eku fu;rkad

vkoksxknzks dh la[;k

3 [P.T.O.55/1/1

1. An electron, an alpha-particle and a proton have the same kinetic energy. Whichone of these particles has the largest de-Broglie wavelength ? 1

fdlh bysDVªkWu] ,sYQk&d.k rFkk izksVkWu dh xfrt ÅtkZ leku gSA buesa ls fdl d.k dh ns&czkWXyhrjaxnS?;Z vf/kdre gS\

2. Why should the material used for making permanent magnets have highcoercivity ? 1

LFkk;h pqEcd cukus esa mi;ksx gksus okys inkFkZ dh mPp fuxzkfgrk D;ksa gksuh pkfg,\

3. The radioactive isotope D decays according to the sequence

If the mass number and atomic number of D2 are 176 and 71 respectively, whatis (i) the mass number (ii) atomic number of D ? 1

fdlh jsfM;ks,sfDVo leLFkkfud D dk {k; fuEufyf[kr Øe ds vuqlkj gksrk gS %

;fn D2 dh nzO;eku la[;k rFkk ijek.kq Øekad Øe'k% 176 rFkk 71 gSa] rks D dh (i) nzO;eku la[;k(ii) ijek.kq Øekad D;k gSa\

4. What will be the values of input A and B for the Boolean expression

? 1

cwyh; O;atd ds fy, fuos'kh A rFkk B ds eku D;k gSa\

5. Why is frequency modulation perferred over amplitude modulation for transmissionof music ? 1

laxhr ds izlkj.k ds fy, vk;ke eknqyu dh rqyuk esa vko`fÙk eknqyu dks D;ksa vf/kdilUn fd;k tkrk gS\

6. The output of an OR gate is connected to both the inputs of a NAND gate.Draw the logic circuit of this combination of getes and write its truth table. 2

fdlh OR xsV ds fuxZr dks fdlh NAND xsV ds nksuksa fuos'kh ls la;ksftr fd;k x;kgSA xsVksa ds bl la;kstu dk rdZ ifjiFk [khafp, rFkk lR;eku lkj.kh fyf[k,A

455/1/1

7. Draw a plot of potential energy of a pair of nucleons as a function of their separation.What is the significance of negative potential energy in the graph drawn ? 2

U;wfDyvkWuksa ds fdlh ;qxy dh fLFkfrt ÅtkZ dks buds i`Fkdu ds Qyu ds :i esa vkysf[kr

dhft,A [khaps x, xzkWQ esa _.kkRed fLFkfrt ÅtkZ dk D;k egÙo gS \

8. A convex lens of refractive index 1.5 has a focal length of 18 cm in air. Calculatethe change in its focal length when it is immersed in water of refractive

index . 2

1.5 viorZukad ds fdlh mÙky ysal dh ok;q esa Qksdl nwjh 18 lseh gSA bl ysal dks 4/3 viorZukad

ds ty esa Mqcksus ij bldh Qksdl nwjh esa gksus okyk ifjorZu ifjdfyr dhft,A

9. Distinguish between the terms 'average value' and 'rms value' of an alternatingcurrent. The instantaneous current from an a.c. source is I = 5 sin (314 t) ampere.What are the average and rms values of the current ? 2

fdlh izR;korhZ /kkjk ds ^vkSlr eku* rFkk ôxZek/; ewy eku* esa Hksn dhft,A fdlh a.c. lzksr lsizkIr rkR{kf.kd /kkjk I = 5 sin (314 t) ,sfEi;j gSA bl /kkjk ds ^vkSlr eku* rFkk ôxZ ek/;ewy

eku* D;k gSa\

10. Write the relation for the forece acting on a charge carrier q moving with a

velocity through a magnetic field in vector notation. Using this relation,deduce the conditions under which this force will be (i) maximum (ii) minimum. 2

pqEcdh; {ks=k esa osx ls xfreku fdlh vkos'k okgd q ij yxus okys cy ds fy, lfn'k

ladsru i)fr esa laca/k fyf[k,A bl laca/k dk mi;ksx mu 'krks± dks O;qRié djus ds fy, dhft,

ftuesa ;g cy (i) vf/kdre] (ii) U;wure gksrk gSA

11. A cylindrical metallic wire is stretched to increase its length by 5%. Calculate thepercentage change in its resistance. 2

/kkrq ds fdlh csyukdkj rkj dks [khapdj mldh yEckbZ esa 5% o`f) dh tkrh gSA blds

izfrjks/k esa izfr'kr ifjorZu ifjdfyr dhft,A

5 [P.T.O.55/1/1

12. The electric field E due to a point charge at any point near it is defined as

where q is the test charge and F is the force acting on it. What is the

physical significance of in this expression ? Draw the electric field linesof a point charge Q when (i) Q > 0 and (ii) Q < 0. 2

OR

Define electric flux. Write its S.I. units. A spherical rubber balloon carries a chargethat is uniformly distributed over its surface. As the balloon is blown up andincreases in size, how does the total electric flux coming out of the surface change ?Give reason.

fdlh fcUnq vkos'k ds dkj.k mlds fudV ds fdlh fcUnq ij fo|qr~ {ks=k E dks

}kjk ifjHkkf"kr fd;k tkrk gS] ;gka q ijh{k.k vkos'k rFkk F bl ij dk;Zjr cy gSA bl O;atd

esa dk D;k HkkSfrd egÙo gS \ fdlh fcUnq vkos'k Q dk fo|qr~ {ks=k [khafp, tcfd

(i) Q > 0 rFkk (ii) Q < 0 gSA

vFkokvFkokvFkokvFkokvFkok

fo|qr~ ¶yDl dh ifjHkk"kk fyf[k,A bldk S.I. ek=kd fyf[k,A fdlh jcM+ ds xksy xqCckjs ij dqN

vkos'k gS] tks mlds i`"B ij ,dleku :i ls forfjr gSA xqCckjs esa ok;q Hkjus ij bldh vkeki

esa o`f) gksrh gS] rc blds i`"B ls ckgj vkus okys dqy fo|qr~ ¶yDl esa D;k ifjorZu gksrk gS\

dkj.k fyf[k,A

13. Deduce an expression for the electric potential due to an electric dipole at anypoint on its axis. Mention one contrasting feature of electric potential of a dipole ata point as compared to that due to a single charge. 3

fdlh cS|qr f}/kzqo ds dkj.k blds v{k ij fLFkr fdlh fcUnq ij fo|qr~ foHko ds fy, O;atd O;qRié

dhft,A fdlh fcUnq ij oS|qr f}/kzqo ds dkj.k fo|qr~ foHko rFkk mlh fcUnq ij ,dy vkos'k ds

dkj.k fo|qr~ foHko ds chp ,d fojks/kh y{k.k dk mYys[k dhft,A

14. A parallel plate capacitor, each with plate area A and separation d, is charged to apotential difference V. The battery used to charge it is then disconnected. A dielectricslab of thickness d and dielectric constant K is now placed between the plates. Whatchange, if any, will take place in(i) charge on the plates

655/1/1

(ii) electric field intensity between the plates(iii) capacitance of the capacitor.Justify your answer in each case. 3

,d lekUrj ifV~Vdk la/kkfj=k] ftldh izR;sd ifV~Vdk dk {ks=kQy A rFkk i`Fkdu d gS] dks

foHkokUrj V rd vkosf'kr fd;k tkrk gSA rRi'pkr~ vkosf'kr djus okyh cSVjh dks gVk ysrs gSa rFkk

ifV~Vdkvksa ds chp ijkoS|qrkad K dk d eksVkbZ dk dksbZ ijkoS|qr xqVdk j[k nsrs gSaA fuEufyf[kr

esa D;k ifjorZu ¼;fn dksbZ gS½ gksxk %

(i) ifV~Vdkvksa ij vkos'k]

(ii) ifV~Vdkvksa ds chp fo|qr~ {ks=k rhozrk]

(iii) la/kkfj=k dh /kkfjrk

izR;sd izdj.k esa vius mÙkj dh iqf"V dhft,A

15. State Kirchhoff's rules of current distribution in an electrical network.

Using these rules determine the value of the current in the electric circuit givenbelow. 3

fdlh cS|qr usVodZ esa fo|qr~ /kkjk forj.k ds fdj[kksQ ds fu;e fyf[k,A

bu fu;eksa dk uhps fn, x, fo|qr~ ifjiFk ds fy, mi;ksx djds fo|qr~ /kkjk dk eku Kkr

dhft,A

7 [P.T.O.55/1/1

16. Write the mathematical relation for the resistivity of a material in terms of relaxationtime, number density and mass and charge of charge carriers in it. Explain, usingthis relation, why the resistivity of a metal increases and that of a semi-conductordecreases with rise in temperature. 3

fdlh inkFkZ dh izfrjks/kdrk ds fy, foJkafr dky] la[;k ?kuRo rFkk vkos'k okgdksa ds nzO;eku

,oa vkos'k ds inksa esa xf.krh; laca/k fyf[k,A bl laca/k dk mi;ksx djds ;g Li"V dhft, fd

rki esa o`f) gksus ij fdlh /kkrq dh izfrjks/kdrk D;ksa c<+ tkrh gS rFkk v/kZpkyd dh izfrjks/kdrk

D;ksa ?kV tkrh gS\

17. Explain with the help of a labelled diagram the underlying principle and workingof a step-up transformer. Why cannot such a device be used to step-up d.c.voltage ? 3

OR

Draw a labelled diagram of an a.c. generator. Explain briefly its principle andworking. 3

ukekafdr vkjs[k dh lgk;rk ls fdlh mPpk;h VªkalQkWeZj dk vk/kkjHkwr fl)kUr rFkk dk;Zfof/k

Li"V dhft,A bl izdkj dh ;qfä dk mi;ksx d.c. oksYVrk ds mPp;u ds fy, D;ksa ugha fd;k

tkrk \


fdlh a.c. tfu=k dk ukekafdr vkjs[k [khafp,A bldk fl)kUr rFkk dk;Zfof/k la{ksi esa Li"V

dhft,A

18. Given below are two electric circuits A and B

Calculate the ratio of power factor of the circuit B to the power factor ofcircuit A. 3

855/1/1

uhps nks fo|qr~ ifjiFk A rFkk B n'kkZ, x, gSa

ifjiFk B ds 'kfä&xq.kkad rFkk ifjiFk A ds 'kfä&xq.kkad dk vuqikr ifjdfyr dhft,A

19. Define the term 'resolving power' of an astronomical telescope. How does it getaffected on

(i) increasing the aperture of the objective lens ?

(ii) increasing the wavelength of the light used ?

Justify your answer in each case. 3

[kxksyh; nwjchu dh ^^foHksnu {kerk** dh ifjHkk"kk fyf[k,A fuEufyf[kr dh foHksnu {kerk ij D;k

izHkko iM+rk gS %

(i) vfHkn`';d ysal ds }kjd esa o`f)

(ii) mi;ksx fd, tkus okys izdk'k dh rjaxnS?;Z esa o`f)


20. Write any four characteristics of electromagnetic waves. Give two uses each of(i) Radio-waves (ii) Micro-waves. 3

fo|qr~ pqEcdh; rjaxksa ds dksbZ pkj vfHky{k.k fyf[k,A fuEufyf[kr esa izR;sd ds nks&nks mi;ksx

fyf[k, (i) jsfM;ks rjaxs] (ii) lw{ke rjaxsA

9 [P.T.O.55/1/1

21. In a plot of photoelectric current versus anode potential, how does

(i) the saturation current vary with anode potential for incident radiations ofdifferent frequencies but same intensity ?

(ii) the stopping potential vary for incident radiations of different intensitiesbut same frequency ?

(iii) photoelectric current vary for different intensities but same frequency ofincident radiations ?

Justify your answer in each case. 3

izdk'k&fo|qr~ /kkjk rFkk ,suksM foHko ds chp [khaps x, xzkWQ esa

(i) leku rhozrk ijUrq fofHké vko`fÙk ds vkifrr fofdj.kksa ds fy, ,suksM foHko ds lkFk larÌr

/kkjk esa fdl izdkj ifjorZu gksrk gS \

(ii) leku vko`fÙk ijUrq fofHké rhozrk ds vkifrr fofdj.kksa ds fy, fujks/kh foHko fdl izdkj

ifjofrZr gksrk gS\

(iii) vkifrr fofdj.kksa dh leku vko`fÙk ijUrq fofHké rhozrkvksa ds fy, izdk'k&fo|qr~ /kkjk esa

fdl izdkj ifjorZu gksrk gS\


22. Calculate the amount of energy released during the α-decay of

Given : 1. atomic mass of

2. atomic mass of

3. atomic mass of

Is this decay spontaneous ? Give reason. 3

1055/1/1

fuEufyf[kr α−{k; esa eqä gqbZ ÅtkZ dk ifjek.k ifjdfyr dhft, %

fn;k x;k gS % 1. dk ijek.kq nzO;eku = 238.05079 u

2. dk ijek.kq nzO;eku = 234.04363 u

3. dk ijek.kq nzO;eku = 4.00260 u

1 u = 931.5 MeV/c2.

D;k ;g {k; Lor% gksrk gS\ dkj.k fyf[k,A

23. What is a digital signal ? Explain the function of modem in data communication.Write two advantages of digital communication. 3

vadh; ladsr D;k gksrk gS\ vkadM+ksa ds lapkj esa ekWMse dk D;k egÙo gS\ vadh; lapkj ds nks ykHk

fyf[k,A

24. Explain, with the help of a schematic diagram, the principle and working of aLight Emitting Diode. What criterion is kept in mind while choosing the semi-conductor material for such a device ? Write any two advantages of Light EmittingDiode over conventional incandescent lamps. 3

O;oLFkk vkjs[k dh lgk;rk ls fdlh izdk'k&mRltZd Mk;ksM dk fl)kUr rFkk dk;Zfof/k Li"V

dhft,A bl izdkj dh ;qfä ds fy, v/kZpkyd inkFkZ dk p;u djrs le; fdl ekin.M dks

/;ku esa j[kk tkrk gS\ ijEijkxr rkinhIr ySEiksa dh rqyuk esa izdk'k&mRltZd Mk;ksM ds dksbZ nks

ykHk fyf[k,A

25. Draw a labelled diagram of a moving coil galvanometer. State the principle on whichit works.

Deduce an expression for the torque acting on a rectangular current carrying loopkept in a uniform magnetic field. Write two factors on which the current sensitivityof a moving coil galvanometer depend. 5

OR

State Biot-Savart law. Use it to derive an expression for the magnetic field at thecentre of a circular loop of radius R carrying a steady current I. Sketch the magnetic fieldlines for such a current carrying loop. 5

11 [P.T.O.55/1/1

py dq.Myh xSaYouksehVj dk ukekafdr vkjs[k [khafp,A blds dk;Z djus dk fl)kUr fyf[k,A

,dleku pqEcdh; {ks=k esa j[ks fdlh vk;rkdkj /kkjkokgh ywi ij dk;Z djus okys cy vk?kw.kZ ds

fy, O;atd O;qRié dhft,A fdlh py dq.Myh xSYouksehVj dh /kkjk lqxzzkfgrk dks izHkkfor djus

okys nks dkjd fyf[k,A


ck;ks&lkoVZ fu;e fyf[k,A bl fu;e dk mi;ksx djds R f=kT;k ds fdlh o`Ùkkdkj ywi] ftlls

1 LFkk;h /kkjk izokfgr gks jgh gS] ds dsUnz ij mRié pqEcdh; {ks=k dh rhozrk ds fy, O;atd O;qRié

dhft,A bl izdkj ds /kkjkokgh ywi dh pqEcdh; {ks=k js[kk,a [khafp,A

26. What are coherent sources ? Why are coherent sources required to produceinterference of light ? Give an example of interference of light in everyday life.

In Young's double slit experiment, the two slits are 0.03 cm apart and the screen is placedat a distance of 1.5 m away from the slits. The distance between the centralbright fringe and fourth bright fringe is 1 cm. Calculate the wavelength of lightused. 5

OR

State the condition under which the phenomenon of diffraction of light takes place.Derive an expression for the width of the central maximum due to diffraction of light at asingle slit.

A slit of width 'a' is illuminated by a monochromatic light of wavelength 700 nm atnormal incidence. Calculate the value of 'a' for position of

(i) first minimum at an angle of diffraction of 30°.

(ii) first maximum at an angle of diffraction of 30°. 5

dyk lEc) lzksr D;k gksrs gSa\ izdk'k ds O;frdj.k ds fy, dyk lEc) lzksr dh vko';drk D;ksa

iM+rh gS\ nSfud thou esa izdk'k ds O;frdj.k dk ,d mnkgj.k fyf[k,A

;ax ds f}f>jh iz;ksx esa nks f>fj;ksa ds chp dh nwjh 0.03 lseh gS rFkk inkZ f>fj;ksa ls 1.5 eh nwjh

ij fLFkr gSA dsUnzh; nhIr fÝat dh nwjh 1 lseh gSA mi;ksx fd, tkus okys izdk'k dh rjaxnS?;Z

ifjdfyr dhft,A


1255/1/1

izdk'k ds foorZu dh ifj?kVuk ds fy, vko';d 'krZ fyf[k,A fdlh ,dy f>jh ij izdk'k ds

foorZu ds dkj.k cus dsUnzh; mfPp"B dh pkSM+kbZ ds fy, O;atd O;qRié dhft,A

pkSM+kbZ a dh dksbZ f>jh 700 nm rjaxnS?;Z ds ,do.khZ izdk'k }kjk vfHkyEcor~ vk;ru ij iznhIr

dh x;h gSA fuEufyf[kr fLFkfr;ksa ds fy, 'a' dk eku ifjdfyr dhft, %

(i) 30° ds foorZu dks.k dk igyk fufEu"BA

(ii) 30° ds foorZu dks.k dk igyk mfPp"BA

27. State the principle of working of p-n diode as a rectifier. Explain, with the help of acircuit diagram, the use of p-n diode as a full wave rectifier. Draw a sketch of the inputand output waveforms. 5

OR

Draw the symbolic representation of a (i) p-n-p, (ii) n-p-n transistor. Why is the baseregion of transistor thin and lightly doped ? With proper circuit diagram, show thebiasing of a p-n-p transistor in common base configuration. Explain the movementof charge carriers through different parts of the transistor in such a configuration andshow that . 5

p-n Mk;ksM ds fn"Vdkjh dh Hkkafr dk;Z djus dk fl)kUr fyf[k,A fo|qr~ ifjiFk vkjs[k dh

lgk;rk ls p-n Mk;ksM dk iw.kZ rjax fn"Vdkjh ds :i esa mi;ksx Li"V dhft,A fuos'kh rFkk fuxZr

rjax :iksa dks xzkWQ [khapdj n'kkZb,A


(i) p-n-p rFkk (ii) n-p-n VªkaftLVj dk izrhdkRed fu:i.k [khafp,A VªkaftLVj dk vk/kkj {ks=k iryk

rFkk gYds rkSj ij vifefJr ¼ekfnr½ D;ksa gksrk gS\ mfpr ifjiFk vkjs[k dh lgk;rk ls mHk;fu"B

vk/kkj foU;kl esa fdlh p-n-p VªkaftLVj dk ck;lu n'kkZb,A bl izdkj ds foU;kl esa VªkaftLVj

ds fofHké Hkkxksa esa vkos'k okgdksa dh xfr Li"V dhft, rFkk ;g n'kkZb, fd .

1 P.T.O.55/2/1

PHYSICSHkkSfrd foKku ¼lS)kfUrd½HkkSfrd foKku ¼lS)kfUrd½HkkSfrd foKku ¼lS)kfUrd½HkkSfrd foKku ¼lS)kfUrd½HkkSfrd foKku ¼lS)kfUrd½

Time allowed : 3 hours Maximum Marks: 70fu/kkZfjr le; % 3 ?k.Vs vf/kdre vad % 70General Instructions :

(i) All questions are compulsory.(ii) There is no overall choice. However, an internal choice has been provided in one

question of two marks, one question of three marks and all three questions of fivemarks. You have to attempt only one of the choice in such questions.

(iii) Question numbers 1 to 5 are very short answer type questions, carrying one mark each.(iv) Question numbers 6 to 12 are short answer type questions, carrying two marks each.(v) Question numbers 13 to 24 are also short answer type questions, carrying three marks

each.(vi) Questions numbers 25 to 27 are long answer type questions, carrying five marks each.(vii) Use of calculators is not permitted. However, you may use log tables, if necessary.(viii) You may use the following values of physical constants wherever necessary:

Mass of neutronBoltzmann's constant Avogadro's number

Roll No.

Series SHC Code No. 55/2/1Please check that this question paper contains 11 printed pages.Code number given on the right hand side of the question paper should be written on thetitle page of the answer-book by the condidate.Please check that this question paper contains 27 questions.Please write down the serial number of the question before attempting it.Ñi;k tk¡p dj ysa fd bl iz'u&i=k esa eqfnzr i`"B 11 gSaAiz'u&i=k esa nkfgus gkFk dh vksj fn, x, dksM uEcj dks Nk=k mÙkj&iqfLrdk ds eq[k&i`"B ij fy[ksaAÑi;k tk¡p dj ysa fd bl iz'u&i=k esa 27 iz'u gSaAÑi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad vo'; fy[ksaA

dksM ua-dksM ua-dksM ua-dksM ua-dksM ua-

jksy ua-

255/2/1

lkekU; funsZ'k %lkekU; funsZ'k %lkekU; funsZ'k %lkekU; funsZ'k %lkekU; funsZ'k %

(i) lHkh lHkh lHkh lHkh lHkh iz'u vfuok;Z gSaA

(ii) iz'u&i=k esa lexz ij dksbZ fodYi ugha gSA fQj Hkh nks vadksa okys ,d iz'u esa] rhu vadksa okys ,diz'u esa vkSj ik¡p vadksa okys rhuksa iz'uksa esa Hkhrjh p;u fodYi miyC/k gSA ,sls iz'uksa esa vkidksfn;s x;s p;u esa ls dsoy ,d iz'u gh djuk gSA

(iii) iz'u la[;k 11111 ls 55555 vfr y?kq mÙkj izdkj ds iz'u gSaA buesa izR;sd iz'u ,d,d,d,d,d vad dk gSA

(iv) iz'u la[;k 66666 ls 1212121212 y?kq mÙkj izdkj ds iz'u gSaA buesa izR;sd iz'u nksnk snk snk snk s vadksa dk gSA

(v) iz'u la[;k 1313131313 ls 2424242424 Hkh y?kq mÙkj izdkj ds iz'u gSaA buesa izR;sd iz'u rhu rhu rhu rhu rhu vadksa dk gSA

(vi) iz'u la[;k 2525252525 ls 2727272727 nh?kZ mÙkj izdkj ds iz'u gSaA buesa izR;sd iz'u ik¡pik¡pik¡pik¡pik¡p vadksa dk gSA

(vii) dSydqysVj ds mi;ksx dh vuqefr ugha gSA rFkkfi] vko';d gks rks vki y?kqx.kdh; lkjf.k;ksa dk

mi;ksx dj ldrs gSA

(viii) tgk¡ vko';d gks vki fuEufyf[kr HkkSfrd fu;rkadksa ds ekuksa dk mi;ksx dj ldrs gSa %

U;wVªku dk lagfr

cksYV~t+eku fu;rkad

vkoksxknzks dh la[;k

1. Is the force acting between two point electric charges q1 and q2 kept at some distanceapart in air, attractive or repulsive when (i) q1q2 > 0 (ii) q1q2 > 0 ? 1

,d&nwljs ls ok;q esa dqN nwjh ij fLFkr nks fcUnq fo|qr~ vkos'kksa q1 rFkk q2 ds chp yxus okyk cyvkd"khZ gksxk vFkok izfrd"khZ] tcfd (i) q1q2 > 0 (ii) q1q2 > 0 gSa \

2. Show graphically how the stopping potential for a given photosensitive surface varieswith the frequency of incident radiations. 1

xzkQ [khapdj ;g n'kkZb, fd fdlh fn, x, izdk'k&lqxzkgh i`"B ds fy, vkifrr fofdj.kksa dh vko`fÙkesa ifjorZu gksus ij fujks/kh foHko fdl izdkj ifjofrZr gksrk gSA

3 P.T.O.55/2/1

3. A TV tower has a height of 71 m. What is the maximum distance upto which TVtransmission can be received ? Given that the radius of the earth = 6.4 × 106 m. 1

fdlh TV ehukj dh Å¡pkbZ 71 m gSA fdruh vf/kdre nwjh rd TV laizs"k.k izkIr fd;k tk ldrkgS\ fn;k x;k gS fd i`Foh dh f=kT;k = 6.4 × 106 m.

4. Which one of the two diodes D1 and D2 in the given figures is (i) forward biased, (ii) reverse biased ? 1

uhps n'kkZ, x, fp=kksa esa nksuksa Mk;ksMksa D1 rFkk D2 esa ls dkSulk Mk;ksM (i) vxzfnf'kd ck;flr](iii) i'pfnf'kd ck;flr gS\

5. Suggest a possible communication channel for the transmission of a message signalwhich has a bandwidth of 5 MHz. 15 MHz cS.M pkSM+kbZ ds lans'k flXuy ds laizs"k.k ds fy, dksbZ laHko lapkj pSuy lq>kb,A

6. A spherical Gaussian surface encloses a charge of .(i) Calculate the electric flux passing through the surface.(ii) How would the flux change if the radius of the Gaussian surface is doubled and

why ? 2

fdlh xksyh; xkmlh; i`"B esa vkos'k ifjc) gSA(i) i`"B ls xqt+jus okyk oS|qr ¶yDl ifjdfyr dhft,A(ii) ;fn xkmlh; i`"B dh f=kT;k nqxquh dj nh tk,] rks bl ¶yDl esa D;k ifjorZu gksxk vkSj

D;ksa \

455/2/1

7. In a copper voltameter, the mass of the ions deposited in 30 seconds is m grams. Thecurrent (i) vs. time (t) graph for the experiment is as shown in the given figure.

Calculate the value of E.C.E. of copper in terms of the mass, m, deposited. 2

OR

For a given thermocouple, the emf generated across its ends is given by E = at + bt2

where t in °C is the temperature of the hot junction, the cold junction being at 0 °C. Ifa = 10 μV /°C and b = -0.02 μV/°C2, calculate the value of inversion temperaturein °C.

fdlh dkWij oksYVkehVj esa 30 lsd.M esa m xzke vk;u fu{ksfir gksrs gSaA iz;ksx ds fy, fo|qr~ /kkjk(i) rFkk (ii) le; (t) ds chp xzkQ uhps fp=k esa n'kkZ;k x;k gSA

fu{ksfir nzO;eku m ds inksa esa dkWij ds fo|qr~&jklk;fud rqY;kad (E.C.E.) dk eku ifjdfyrdhft,A


fdlh fn, x, rki&oS|qr ;qXe ds fy, blds fljksa ij tfur fo-ok- cy (emf) E = at + bt2 }kjkO;ä fd;k x;k gS] tgk¡ t rIr laf/k dk °C esa rki gS rFkk 'khr laf/k dk rki 0 °C gSA ;fna = 10 μV/°C rFkk b = -0.02 μV/°C2 rks °C esa O;qRØe dk eku ifjdfyr dhft,A

5 P.T.O.55/2/1

8. In an ammeter (consisting of a galvanometer and a shunt), 0.5% of the main currentpasses through the galvanometer. Resistance of the galvanometer coil is G. Calculatethe resistance of the shunt in terms of galvanometer resistance, G. 2

,d ,sehVj esa ¼tks fdlh xSYosuksehVj rFkk 'kaV ls feydj cuk gS½ eq[; fo|qr~ /kkjk dk 0.5%xSYosuksehVj ls izokfgr gksrk gSA xSYosuksehVj dh dq.Myh dk izfrjks/k G gSA xSYosuksehVj dsizfrjks/k] G ds inksa esa 'kaV dk izfrjks/k ifjdfyr dhft,A

9. An electric bulb B and a parallel plate capacitor C are connected in series to the a.c.mains as shown in the given figure. The bulb glows with some brightness.

How will the glow of the bulb be affected on introducing a dielectric slab between the platesof the capacitor ? Give reasons in support of your answer. 2

fp=k esa n'kkZ, vuqlkj a.c. esUl ls ,d fo|qqr~ cYc B rFkk ,d lekUrj ifV~Vdk la/kkfj=k C dks

Js.khØe esa la;ksftr fd;k x;k gSA cYc leku |qfr ls nhfIr djrk gSA

la/kkfj=k dh ifV~Vdkvksa ds chp ijkoS|qr LySc j[kus ij cYc dh |qfr ij D;k izHkko iM+sxk\ vius

mÙkj dh iqf"V ds fy, dkj.k nhft,A

10. What does the statement, “natural light emitted from the sun is unpolarized” mean interms of the direction of electric vector ? Explain briefly how plane polarized light can beproduced by reflection at the interface separating the two media. 2

^^lw;Z }kjk mRlftZr izkÑfrd izdk'k v/kzqfor gksrk gSA** oS|qr lfn'k dh fn'kk ds inksa esa bl izdFku

ls D;k rkRi;Z gS\ nks ek/;eksa dks i`Fkd~ djus okys vUrjki`"B ij ijkorZu }kjk fdl izdkj lery

/kzqfor izdk'k mRié fd;k tk ldrk gS] la{ksi esa Li"V dhft,A

655/2/1

11. The output of a 2-input NOR gate is fed to a NOT gate. Draw the logic circuit of thiscombination of gates and write the truth table for the output of the combination for allinputs. (i) attractive, (ii) repulsive. 2

2&fuos'kh NOR xsV ds fuxZr dks fdlh NOT xsV dks fn;k tkrk gSA xsVksa ds bl la;kstu dk rdZ

ifjiFk [khafp, rFkk lHkh fuos'kksa ds fy, la;kstu ds fuxZr dh lR;eku lkj.kh fyf[k,A

12. What is remote sensing ? Write its two applications. 2

lqnwj laosnu D;k gS\ blds nks vuqiz;ksx fyf[k,A

13. On what principle does a metre bridge work ? Draw a circuit diagram and explain howthis device can be used for determination of an unknown resistance. 3

ehVj lsrq ds dk;Z djus dk D;k fl)kUr gS\ ,d fo|qr~ ifjiFk [khapdj ;g Li"V dhft, fd bl

;qfä dk mi;ksx fdlh izfrjks/kd ds vKkr izfrjks/k dks fu/kkZfjr djus esa fdl izdkj fd;k tk ldrk

gSA

14. Derive a mathematical expression for resistivity of a conductor in terms of numberdensity of charge carries in the conductor and relaxation time. 3

fdlh pkyd dh izfrjks/kdrk ds fy, ml pkyd ds vkos'k okgdksa ds la[;k ?kuRo rFkk foJkafr dky

ds inksa esa xf.krh; O;atd O;qRié dhft,A

15. State Ampere’s circuital law. Write the expression for the magnetic field at the centre of acircular coil of radius R carrying a current I. Draw the magnetic field lines due to thiscoil. 3

,sfEi;j dk ifjiFkh; fu;e fyf[k,A R f=kT;k dh o`Ùkkdkj dq.Myh ftlls I fo|qr~ /kkjk izokfgr gks

jgh gS] ds dsUnz ij mRié pqEcdh; {ks=k ds fy, O;atd fyf[k,A bl dq.Myh ds dkj.k pqEcdh; {ks=k

js[kk,¡ [khafp,A

16. Write the expression for the force acting on a charged particle of charge q moving with

velocity in the presence of magnetic field . Show that in the presence of this force

(i) the kinetic energy of the particle does not change.

(ii) its instantaneous power is zero. 3

pqEcdh; {ks=k dh mifLFkfr esa osx ls xfr'khy q vkos'k ds fdlh vkosf'kr d.k ij dk;Zjr cy

ds fy, O;atd fyf[k,A ;g n'kkZb, fd bl cy dh mifLFkfr esa

(i) d.k dh xfrt ÅtkZ esa ifjorZu ugha gksrk gSA

(ii) d.k dh rkR{kf.kd 'kfä 'kwU; gksrh gSA

7 P.T.O.55/2/1

17. In a series LCR circuit, define the quality factor (Q) at resonance. Illustrate itssignificance by giving one example.

Show that power dissipated at resonance in LCR circuit is maximum. 3

,d Js.khc) LCR fo|qr~ ifjiFk ds fy, vuqukn ij xq.krk dkjd (Q) dh ifjHkk"kk fyf[k,A ,d

mnkgj.k nsdj bldk egÙo Li"V dhft,A

;g n'kkZb, fd vuqukn dh fLFkfr esa LCR ifjiFk esa 'kfä {k; vf/kdre gksrk gSA

18. A circular copper disc 10 cm in radius rotates at a speed of 20π rad/s about an axisthrough its centre and perpendicular to the disc. A uniform magnetic field of 0.2 T actsperpendicular to the disc.

(i) Calculate the potential difference developed between the axis of the disc and therim.

(ii) What is the induced current if the resistance of the disc is ? 3

OR

A resistor of and a capacitor of 40 μF are connected in series to 220 V a.c.source with angular frequency . Calculate the voltages (rms) across theresistor and the capacitor. Why is the algebraic sum of these voltages more than thesource voltage ? How do you resolve this paradox ?

10 cm f=kT;k dh rkacs dh dksbZ o`Ùkkdkj fMLd] fMLd ds yEcor~ rFkk mlds dsUnz ls xqtjus okys v{k

ds ifjr% 20π rad/s dh pky ls ?kw.kZu xfr dj jgh gSA 0.2 T dk ,dleku pqEcdh; {ks=k bl fMLd

ds yEcor~ dk;Z djrk gSA

(i) fMLd ds v{k rFkk mlds fdukjksa ds chp mRié foHkokUrj ifjdfyr dhft,A

(ii) ;fn fMLd dk izfrjks/k gS] rks blesa izsfjr /kkjk dk eku D;k gS\


300 Hz dks.kh; vko`fÙk ds 220 V ds izR;korhZ /kkjk (a.c.) lzksr ls Js.khØe esa yxs dk

izfrjks/kd rFkk 40 mF dk la/kkfj=k la;ksftr fd;k x;k gSA izfrjks/kd rFkk la/kkfj=k ds fljksa ij

oxZ&e/;&ewy (rms) oksYVrk ifjdfyr dhft,A bu nksuksa oksYVrkvksa dk chtxf.krh; ;ksx lzksr dh

oksYVrk ls vf/kd D;ksa gksrk gS\ vki bl fojks/kkHkkl dk lek/kku dSls djsaxs \

19. Draw a labelled diagram of Hertz’s experiment. Explain how electromagnetic radiationsare produced using this set-up. 3

gVZ~t+ ds iz;ksx dk ukekafdr vkjs[k [khafp,A bl izk;ksfxd O;oLFkk dk mi;ksx djds fo|qr~&pqEcdh;

fofdj.k dSls mRié fd, tkrs gSa] Li"V dhft,A

855/2/1

20. How does the frequency of a beam of ultraviolet light get affected when it goes from airinto glass ?

A ray of light incident on an equilateral glass prism shows minimum deviation of 30°.Calculate the speed of light through the glass prism. 3

ok;q ls dk¡p esa izos'k djrs le; ijkcSaxuh izdk'k iqUt dh vko`fÙk fdl izdkj izHkkfor gksrh

gS\

dk¡p ds leckgq fizT+e ij vkifrr dksbZ izdk'k dh fdj.k 30° dk vYire fopyu n'kkZrh

gSA dk¡p ds fizT+e ls xqtjus okys izdk'k dh pky ifjdfyr dhft,A

21. An electron, a-particle and a proton have the same de-Broglie wavelength. Which ofthese particles has (i) minimum kinetic energy, (ii) maximum kinetic energy, and why ?In what way has the wave nature of electron been exploited in electron microscope ? 3

fdlh bysDVªkWu] ,sYQk d.k rFkk izksVkWu dh ns&czkXyh rjaxnS?;Z leku gSA buesa ls fdl d.k

dh xfrt ÅtkZ (i) fuEure] (ii) vf/kdre gS] vkSj D;ksa\ bysDVªkWu lw{en'khZ esa bysDVªkWu dh

rjax izÑfr dk fdl izdkj ykHk mBk;k x;k gS\

22. State the law of radioactive decay. Establish a mathematical relation between half-lifeperiod and disintegration constant of a radioactive nucleus. 3

jsfM;k,sfDVo {k; dk fu;e fyf[k,A fdlh jsfM;ks,sfDVo ukfHkd dh v/kZ&vk;q rFkk fo?kVu fLFkjkad

ds chp xf.krh; lEcU/k LFkkfir dhft,A

23. Distinguish between nuclear fission and fusion. In a fusion reaction

calculate the amount of energy (in MeV) released. Given

. 3

ukfHkdh; fo[kaMu rFkk ukfHkdh; lay;u esa Hksn dhft,A ukfHkdh; lay;u vfHkfØ;k

esa eqä ÅtkZ dh ek=kk ( MeV esa) ifjdfyr dhft,A fn;k x;k gS

9 P.T.O.55/2/1

24. Draw a schematic diagram of a single optical fibre structure. On what principle does such adevice work ? Explain the mechanism of propagation of light signal through anoptical fibre. 3

,dy izdkf'kd rUrq dh cukoV dk O;oLFkkRed vkjs[k [khafp,A bl izdkj dh ;qfä fdl

fl)kUr ij dk;Z djrh gS\ fdlh izdkf'kd rUrq ls izdk'k flXuy ds lapj.k dh fØ;kfof/k Li"V

dhft,A

25. Derive the expression for the energy stored in a parallel plate capacitor of capacitance Cwith air as medium between its plates having charges Q and — Q. Show that this energy

can be expressed in terms of electric field as where A is the area of eachplate and d is the separation between the plates.

How will the energy stored in a fully charged capacitor change when the separationbetween the plates is doubled and a dielectric medium of dielectric constant 4 isintroduced between the plates ? 5

OR

Define the term dipole moment of an electric dipole indicating its direction. Writeits SI unit.

An electric dipole is placed in a uniform electric field . Deduce the expression forthe torque acting on it. In a particular situation, it has its dipole moment aligned withthe electric field. Is the equilibrium stable or unstable ?

fdlh lekUrj ifV~Vdk la/kkfj=k] ftldh /kkfjrk C IysVksa ij vkos'k Q rFkk — Q vkSj IysVksa ds chp

ek/;e ds :i esa ok;q gS] dh lafpr ÅtkZ ds fy, O;atd O;qRié dhft,A ;g n'kkZb, fd fo|qr~&{ks=k

ds inksa ea bl ÅtkZ dks ds :i esa O;ä fd;k tk ldrk gS] tgk¡ A izR;sd ifV~Vdk dk

{ks=kQy rFkk d ifV~Vdkvksa ds chp i`Fkdu gSA

;fn ifV~Vdkvksa ds chp i`Fkdu nqxquk dj nsa rFkk ifV~Vdkvksa ds chp ijkoS|qrkad 4 dk dksbZ ijkoS|qr

ek/;e Hkj nsa] rks fdlh iw.kZr% vkosf'kr la/kkfj=k dh lafpr ÅtkZ esa D;k ifjorZu gksxk\


fdlh oS|qr f}/kzqo ds f}/kzqo vk?kw.kZ dh ifjHkk"kk mldh fn'kk dks n'kkZrs gq, dhft,A bldk

SI ek=kd fyf[k,A

dksbZ oS|qr f}/kzqo fdlh ,dleku fo|qr~&{ks=k esa fLFkr gSA bl ij dk;Zjr cyvk?kw.kZ ds fy, O;atd

O;qRié dhft,A fdlh fo'ks"k ifjfLFkfr esa bldk f}/kqzo vk?kw.kZ fo|qr~&{ks=k ds lkFk lajsf[kr gSA D;k

larqyu LFkk;h gS vFkok vLFkk;h \

1055/2/1

26. Define the term ‘wavefront’. Draw the wavefront and corresponding rays in the case of a(i) diverging spherical wave, (ii) plane wave.

Using Huygen’s construction of a wavefront, explain the refraction of a plane wavefrontat a plane surface and hence verify Snell’s law. 5

OR

Derive the relation between the focal length of a convex lens in terms of the radii of curvature ofthe two surfaces and refractive index of its material. Write the sign conventions andtwo assumptions used in the derivation of this relation,

A convex lens of focal length 40 cm and a concave lens of focal length — 25 cm arekept in contact with each other. What is the value of power of this combination ?

^rjaxkxz* dh ifjHkk"kk fyf[k,A (i) vilfjr xksyh; rjax] (ii) lery rjax ds rjaxkxz rFkk laxr

fdj.ksa [khafp,A

gkbxsUl ds rjaxkxz dh jpuk dk mi;ksx djds fdlh lery i`"B ij lery rjaxkxz dk viorZu Li"V

dhft, rFkk Lusy ds fu;e dk lR;kiu dhft,A


fdlh mÙky ysal dh Qksdl nwjh] ysal ds nks i`"Bksa dh oØrk f=kT;k,¡ rFkk ysal ds inkFkZ ds viorZukad

ds chp lEcU/k O;qRié dhft,A bl lEcU/k dks O;qRié djus esa mi;ksx dh xbZ fpg~u ifjikVh rFkk

nks vfHkx`ghr fyf[k,A

40 cm Qksdl nwjh ds mÙky ysal rFkk — 25 Qksdl nwjh ds vory ysal ,d nwljs ds lEidZ esa j[ks

gSaA bl la;kstu dh {kerk dk eku D;k gS\

27. Explain, with the help of a circuit diagram, the use of an n-p-n transistor as an amplifierin common-emitter configuration. Write the expression for voltage gain of the transistor.Draw frequency response curve of this amplifier.

How will the current gain of a transistor be affected if its base region is made thickeras compared to a usual transistor and why ? 5

OR

Draw energy band diagrams for (i) an intrinsic semiconductor, (ii) p-type semiconductor.

Draw symbolic representation of a zener diode. Draw its V-I characteristics andexplain, with the help of a circuit diagram, its use as a voltage regulator.

Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.inPortal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks

7 10

9 2 2

0

4 101 9 10

4

TmA

Nm C

μ π

πε

− −

−

= ×

×

Mass of electron me = 9.1 ×10-31 kg Mass of neutron mn 1.675 ×10-27 kg Boltzmann’s constant k = 1.381 ×10-23 JK-1

Avogadro’s number NA = 6.022 ×1023 / mol-1

Radius of earth = 6400 km

Q1. Name the electromagnetic radiation to which waves of wavelength in the range of 10-2 m belong. Give on use of this part of EM spectrum. [1]

Q2. What is ground wave propagation? [1]

Q3. You are given following three lenses. Which two lenses will you use as an eyepiece and as an objective to construct an astronomical telescope? [1]

Lenses Power (P) Aperture (A) L1 3D 8 cm L2 6D 1 cm L3 10D 1 cm

Q4. Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why? [1]

Q5. Unpolarized light is incident on a plane surface of glass of refractive index μ at angle i. If the reflected light gets totally polarized, write the relation between the angle i and refractive index μ .

[1]

Q6. Draw a diagram to show refraction of a plane wave front incident in a convex lens and hence draw the refracted wave front. [1]

Q7. the figure shows a plot of three curves a, b, c showing the variation of photocurrent vs collector plate potential for three different intensities I1, I2 and I3 having freq1uencies v1, v2 and v3 respectively incident on a photosensitive surface. Point out the two curves of which the incident radiations have same frequency but different intensities. [1]


Q8. Two nuclei have mass numbers in the ratio 1:3. What is the ratio of their nuclear densities? [1]

Q9 (i) can two equi – potential surfaces intersect each other? Give reasons. [2]

(ii) Tow charges –q and +q are located at points A (0, 0, -a) and B (0, 0, +a) respectively. How much work is done in moving a test charge from point P (7, 0, 0) to Q (-3, 0, 0)?

Q10. A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable resistor ‘R’. Plot a graph showing the variation of terminal potential ‘V’ with Resistance R. [2]

Q11. The output of a 2 – input AND gete is fed to a NOT gate. Give the name of the combination and its logic symbol. Write down its truth table. [2]

Q12. A charge ‘q’ moving along the X-axis with a velocity v�

is subjected to a uniform magnetic field B acting along the Z-axis as it crosses the origin O. [2]

(i) Trace its trajectory. (ii) Does the charge gain kinetic energy as it enters the magnetic field? Justify your answer.

Q13. How does a charge q oscillating at certain frequency produce electromagnetic waves? [2] Sketch a schematic diagram depicting electric and magnetic field for an electromagnetic wave propagating along the Z-direction.

Q14. Derive an expression for drift velocity of the free electrons in a conductor in terms of relaxation time. [2]


Q15. By what percentage will the transmission range of a TV tower be affected when the height of tower is increased by 21%? [2]

Q16. A radioactive nucleus ‘A’ undergoes a series of decays according to the following scheme: [2]

1 2 3 4A A A A Aα β α γ⎯⎯→ ⎯⎯→ ⎯⎯→ ⎯⎯→

The mass number and atomic number of A4 are 172 and 69 respectively. What are these numbers for A?

Q17. Why is high frequency carrier waves used for transmission? [2] OR

What is meant by term ‘modulation’? Draw a block diagram of a simple modulator for obtaining an AM signal.

Q18. State Biot-Savart law. [2] A current I flows in a conductor placed perpendicular to the plane of the paper. Indicate the direction of the magnetic field due to a small element d l

� at point P situated at a distance r

�from

the element as shown in the figure.

Q19. The equivalent capacitance of the combination between A and B in the given figure is 4 μ F. [3]

(i) Calculate capacitance of the capacitor C. (ii) Calculate charge on each capacitor if a 12 V battery is connected across terminals A and B. (iii) What will be the potential drop across each capacitor?

Q20. State Gauss’s law in electrostatics. Using this law derive an expression for the electric field due to a uniformly charged infinite plane sheet. [3]


Q21. In a single slit diffraction experiment, when a tiny circular obstacle is placed in the path of light from distant source, a bright spot is seen at the centre of the shadow of the obstacle. Explain why? [3] State two points of difference between the interference patterns obtained in Young’s double slit experiment and the diffraction pattern due to a single slit.

Q22. An electron and a proton are accelerated through the potential. Which one of the two has (i) greater value of de-Broglie wavelength associated with it and (ii) less momentum? Justify your answer. [3]

Q23. (a) The energy levels of an atom are as shown below. Which of them will result in the transition of a photon of wavelength 275 nm? [3]

(b) Which transition corresponds to emission of radiation of maximum wavelength?

Q24. Derive the expression for force per unit length between two long straight parallel current carrying conductors. Hence define one ampere. [3]

OR

Explain the principle and working of a cyclotron with the help of a schematic diagram. Write the expression for cyclotron frequency.

Q25. Three light rays red (R), green (G) and blue (B) are incident on a right angled prism ‘abc’ at face ‘ab’. The refractive indices of the material of the prism for red, green and blue wavelength are 1.39, 1.44 and 1.47 respectively. Out of the three which colour ray will emerge out of face ‘ac’? Justify your answer. Trace the path of these rays after passing through face ‘ab’. [3]


Q26. (a) Define self inductance. Write is S.I. units.

(b) Derive an expression for self inductance of a long solenoid of length l, cross-sectional area A having N number of turns.

Q27.

The figure shows experimental set up of a bridge. When the two unknown resistances X and Y are inserted, the null point D is obtained 40 cm from the end A. when a resistance of 10 is connected in series with X, the null point shifts by 10 cm. find the position of the null point when the 10 resistance is instead connected in series with resistance ‘Y’. Determine the values of the resistances X and Y. [3]

Q28. (i) Draw a circuit diagram to study the input and output characteristics of an n – p – n transistor in its common emitter configuration. Draw the typical input and output characteristics. [5]

(ii) Explain, with the help of a circuit diagram, the working of n – p – n transistor as a common emitter amplifier.

OR

How is a zener diode fabricated so as to make it a special purpose diode? Draw I – V characteristics fo zener diode and explain the significance of breakdown voltage. Explain briefly, with the help of a circuit diagram, how a p – n junction diode works as a half wave rectifier.

Q29. (a) Derive an expression for the average power consumed in a series LCR circuit connected to a.c. source, in which the phase difference between the voltage and the current in the circuit is φ .

(b) Define the quality factor in an a.c. circuit. Why should the quality factor have high value in receiving circuits? Name the factors on which it depends.


OR

(a) Derive the relationship between the peak and the rms value of current in an a.c. circuit. (b) Describe briefly, with the help of a labeled diagram, working of a step – up A step – up transformer converts a low voltage into high voltage. Does it not violate the principle of conservation of energy? Explain.

Q30. Trace the rays of light showing the formation of an image due to a point object placed on the axis of a spherical surface separating the two media of refractive indices n1 and n2. Establish the relation between the distances of the object, the image and the radius of curvature from the central point the spherical surface. Hence derive the expression of lens maker’s formula. [5]

OR

Draw the labeled ray diagram for the formation of image by a compound microscope. Derive the expression for the total magnification of a compound microscope. Explain why both the objective and the eyepieces of a compound microscope must have short focal lengths.

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Answers to 2008 CBSE Physics Paper I have answered the questions and taken care that there are no errors. In case of any errors that might have crept in please write to me at [email protected]. In case of any confusion or if you would like to discuss any answers you can leave a question in FREE homework help forum at http://www.TutorBreeze.com. I have written the answers to set 2 there are minor variations in questions in other sets. In case there are any particular questions for which you wish to know the answers please write to me or post them on the website.

Physics (Theory)−−−−2008

Code No. 55/1/2

Time Allowed: 3 hours] [Maximum Marks: 70

1. Name the part of the electromagnetic spectrum of wavelength 102 m and mention its one application.

Radio waves; radio signals like AM radio

1. An electron and alpha particle have the same kinetic energy. How are the de−Broglie wavelengths associated with them related?

� � ��

� � � �

�

� ��

� �

� ��

� ��

��

α

α

λ

λλ

λλ

= =

= =

= =

Masses are given in question paper, substitute values and calculate.

3.A converging lens of refractive index 1.5 is kept in a liquid medium having same refractive index. What would be the focal length of the lens in this medium?

Ans Infinite

� �

� � �

� � ��

� ��

��

� ��

�

−= −

=

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2. A 500 μC charge is at the centre of a square of side 10 cm. Find the work done in moving a charge of 10 μ C between two diagonally opposite points on the square.

Work done = q(V2 – V1). As potential at the two diagonally opposite points is same work done will be zero.

5. The plot of the variation of potential difference across a combination of three identical cells in series, versus current is as shown below. What is the emf of each cell?

2V.

��

�

� ��

�

εε

ε

= −

=

emf of each cell is 2V

6. How does the angular separation of interference fringes change, in Young’s experiment, if the distance between the slits is increased?

�λθ = ; so if d is increased then angular separation will decrease.

7. What is the direction of the force acting on a charged particle q, moving with a velocity in a uniform magnetic filed ?

F is perpendicular to both velocity vector and magnetic field vector.

8. State the reason, why heavy water is generally used as a moderator in a nuclear reactor.

It helps to slow down the neutrons so that the probability of their participating in a nuclear reaction increases. Since heavy water has a mass that is comparable with neutrons they are effective in slowing down the neutrons.

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9. A nucleus undergoes β−decay and becomes . Calculate the maximum kinetic energy of electrons emitted assuming that the daughter nucleus and anti−neutrino carry negligible kinetic energy.

�� !β−→ + +

22.994466u - 22.989770u = 0.004696u Energy = 0.004696u x 931.5 MeV = 4.374 MeV

10. Distinguish between an intrinsic semiconductor and P−type semiconductor. Give reason, why a P−type semiconductor crystal is electrically neutral, although nh >> ne?

An intrinsic semiconductor has a few free electrons and an equal number of holes. Its conductivity is temperature dependant and increases with an increase in temperature. A p-type semiconductor is doped with an element from the 3rd group to increase its conductivity. So the number of holes in this semiconductor is much larger than the number of electrons. It is electrically neutral, as charged particles are not added to make the semiconductor p-type. When a semiconductor is doped, atoms are added to it and then no charges are removed or added.So they cannot make the material charged.

11. Draw a ray diagram of an astronomical telescope in the normal adjustment position. State two drawback of this type of telescope. See diagram from book Drawbacks: Limit to its resolving power which means the smallest distance between objects that can be clearly seen. Spherical aberration and chromatic aberration of its lenses.

12.Calculate the distance of an object of height h from a concave mirror of focal length 10 cm, so as to obtain a real image of magnification 2.

f = -10cm, m = -v/u = -2 u = ?; v = 2u � � �

� � ��

� �� "

� #

� # #

� #�# $�

= +

= +

=

= −= −

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13. . Draw the output wave form at X, using the given inputs A, B for the logic circuit shown below. Also identify the gate.

A B X 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0

AND gate

14. A transmitting antenna at the top of a tower has a height of 36 m and the height of the receiving antenna is 49 m. What is the maximum distance between them, for satisfactory communication in the LOS mode? (Radius of earth = 6400 km)

� � � �� %��&� �"&� ��&'

( �� )� )� )�

+ = × × × + × × ×= + =

=

15. Derive an expression for the potential energy of an electric dipole of the dipole moment in an electric field

[ ]%

&

�� *� *� &

+ �

+ � � � � � θ

τ θ

θ θ θ θ

=

= = = − = −

��

��

16. Define magnetic susceptibility of a material. Name two elements, one having positive susceptibility and the other having negative susceptibility. What does negative susceptibility signify?

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, -χ= where M is the magnetization of the material and H is magnetic intensity. It is a measure of how a material behaves in an external field.

Paramagnetic and ferromagnetic substances example iron have positive susceptibility and diamagnetic substances example copper have negative susceptibility.

17. The oscillating magnetic field in a plane electromagnetic wave is given by

(i) Calculate the wavelength of the electromagnetic wave.

(ii) Write down the expression for the oscillating electric field.

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� � �

� �� "

� . � � � �� /

�.&� � *� � ��

0

)

)

�

1 � �

2 �� 3�� ( (

ππλ

πλπ

π

ω

−

=

=

= =

= × × × × +

= = − =� � or

Prove that an ideal inductor does not dissipate power in an a.c. circuit.

OR

Derive an expression for the self-inductance of a long air-cored solenoid of length l and number of turns N.

�

�*��4��4 ��4��*�4��56��

� � �

7

� ��

�� 7 ��

μμ

μ μ μ μ

Φ=

=

= = = =

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19. Prove that the current density of a metallic conductor is directly proportional to the drift speed of electrons.

OR

Define conductivity of a conductor. Explain the variation of conductivity with temperature in (a) good conductors (b) ionic conductors.

.8�

�

�� 9�

��9 ��

==

= = =

Or

�9 σ

σρ

=

=

� ��

where j is the current density and E is the electric field. With increase in temperature in good conductors the conductivity decreases. With

increase in temperature the average speed of electrons increases. This decreases the time between collisions hence resistivity increases or conductivity decreases. In ionic conductors conductivity will increase as mobility of ions will increase.

20. A potentiometer wire of length 1m is connected to a driver cell of emf 3V as

shown in the figure. When cell of 1.5 V emf is used in the secondary circuit, the

balance point is found to be 60 cm. On replacing this cell and using a cell of

unknown emf, the balance point shifts to 80 cm.

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� �

� �

�&" � .

��

1

εε

=

=

No, a balance point will not be reached and current will flow for all positions of the jockey.

No, it does not affect the balance point as at balance, as the current through the circuit with R is zero at balance.

21. An electromagnetic wave of wavelength λ is incident on a photosensitive surface of negligible work function. If the photo-electrons emitted from this surface have

the de –Broglie wavelength λ1, prove that .

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� �

�

$ $ � �

$ �

$� � ��

� �� $��

λ λ

λ

λ

λ

λ

= −

=

= =

= =

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22. . The energy level diagram of an element is given below. Identify, by doing necessary calculations, which transition corresponds to the emission of a spectral line of wavelength 102.7 nm.

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� �

�� . �� .

� � % % �%

�

�&�� &�� &' � � �&' � �&� �

� � $�

$ � : ��

ν

λ

λ

− −

− − −

= −

= −

× × × × × ×− = = = =× × × ×

Ans is D

23. . Draw a plot of the variation of amplitude versus ω for an amplitude modulated wave. Define modulation index. State its importance for effective amplitude modulation.

Amplitude of side bands is ��μ

Modulation index = ��4�� *��4�*� ��*��

#��#��

.

In practice this is kept less than 1 to avoid distortion.

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24. How is a wave front defined? Using Huygen’s construction draw a figure showing the propagation of a plane wave reflecting at the interface of the two media. Show that the angle of incidence is equal to the angle of reflection.

It is a surface of constant phase. Proof is given in book NCERT page 357 part II

25. A coil of number of turns N, area A, is rotated at a constant angular speed ωωωω, in a uniform magnetic field B, and connected to a resistor R. Deduce expressions for:

(i) Maximum emf induced in the coil

(ii) Power dissipation in the coil

��

*� *�

��

�� 56

��56 �

��

��

�2�3��

ε

θ ω

ε ω ω

ωω

Φ= −

Φ = =Φ= − =

= = =

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26i) . The figure below shows the V-I characteristic of a semiconductor diode

(i) Identify the semiconductor diode used.

(ii) Draw the circuit diagram to obtain the given characteristic of this device.

(iii) Briefly explain how this diode can be used as a voltage regulator

Zener diode

Across the zener diode voltage remains constant even though the current through it

changes. Example if the input voltage decreases, the current through the series resistor in the circuit decreases and through the zener diode also decreases. The voltage across the series resistor will decrease but the voltage across the zener diode will not change. Thus the zener diode acts as a voltage regulator.

27.An inductor 200 mH,, capacitor 500μF, resistor 10Ω are connected in series with a 100V, variable frequency a.c. source. Calculate the

(i) frequency at which the power factor of the circuit is unity;

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(ii) current amplitude at this frequency;

(iii) Q-factor

Power factor is unity at resonance as φ =�

; <�� 4 ��4 4��6��*��=��

� ��

; <�� 4 ��4 4��

7>

��7?�

ω

ω

=

=

=

28. (a) For a ray of light travelling from a denser medium of refractive index n1to rarer

medium of refractive index n2, prove that , where ic is the critical angle of incidence for the media.

(b) Explain with the help of a diagram, how the above principle is used for transmission of video signals using optical fibres.

OR

(a) What is plane polarized light? Two polaroids are placed at 900 to each other and the transmitted intensity is zero. What happens when one more Polaroid is placed between these two, bisecting the angle between them? How will the intensity of transmitted light vary on further rotating the third Polaroid?

(b) If a light beam shows no intensity variation when transmitted through a Polaroid which is rotated, does it mean that the light is unpolarized? Explain briefly.

�

�

�� %

$$

� � �

= = =

OR In plane polarized light the electric field vector is confined to a plane. This plane is

perpendicular to the direction of the light.

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Intensity is no longer zero. A certain component of light that is transmitted by first polarizer is transmitted by second polarizer.

As the light reaching the first sheet is unpolarized, the transmitted light will be one-half that of the incident light.

�

� � � �

� � � �

��

� �*� *� �"� �� *� *� �"� .

� �

� � � �

� � � �

θ

θ

=

= = =

= = =

angle is 45 degrees as the Polaroid bisects the angle between the two polaroids. The intensity will vary in proportion to �*� θ on rotating the Polaroid. Yes, in unpolarized light the electric vector is not in any particular direction so for all

orientations the intensity will appear to be half. So it is not possible to distinguish between the directions.

29. (a) Using Gauss’ law, derive an expression for the electric field intensity at any point outside a uniformly charged thin spherical shell of radius R and charge density σC /m2. Draw the field lines when the charge density of the sphere (i) positive, (ii) negative.

(b) A uniformly charged conducting sphere of 2.5 m in diameter has a surface charge density of 100 μC/m2. Calculate the

(i) charge on the sphere

(ii) total electric flux passing through the sphere

OR

(a) Derive an expression for the torque experienced by an electric dipole kept in a uniform electric field.

(b) Calculate the work done to dissociate the system of three charges placed on the vertices of a triangle as shown:

Here q = 1.6 × 10-10C.

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Take a gaussian surface inside the shell and outside it. Prove that inside field is zero and outside it is as if entire charge is placed at the center of the spherical shell.

For positive charge field lines will be outward

For negative charge field lines will be inward b) Charge on sphere = � � � �� / �� /�� > � � �σ π−= ×Calculate and find the charge. Since it is a conducting sphere all the charges will reside on the surface of the sphere and

field inside the sphere will be zero. Flux passing through the sphere is zero. Flux outside the sphere, leaving the surface of the sphere is kq/r.

OR

a) � ��<��*��

��

��$� ��$#��

@ � �

ττ θ

= ×

= = ×��

b) � � �

� � � � � � � � �� )@ @ )@ @ ) @ @+ − − −

− + + −= + +× × ×

Substitute values and calculate.

30. . (a) Using Biot-Savart’s law, derive an expression for the magnetic field at the centre of

a circular coil of radius R, number of turns N, carrying current i. See derivation in NCERT book for field along the axis. Then take special case for center

of coil.

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Field due to coil 1 is

�

� � � � �/�

�

� � � �/�

��

��

�� 1 �

��#�� 1 �

μ

μ

= =+

= =+

Draw a schematic diagram of a cyclotron. Explain its underlying principle and working, stating clearly the function of the electric and magnetic fields applied on a charged particle.

Deduce an expression for the period of revolution and show that it does not depend on the speed of the charged particle. Or

See diagram from NCERT book Principle; It is a machine that uses crossed electric and magnetic fields to accelerate

charged particles to high energies. It uses the principle that the frequency of revolution of the charged particle is independent of its velocity. This frequency depends on charge to mass ratio of the charged particle. So once it is adjusted the charged particle will experience a force due to the electric field at just the right instant to accelerate it.

Working At resonance the charged particle crosses the gap between the dees at just the right time so that the alternating voltage that is applied between the dees, accelerates it. A magnetic field acts perpendicular to the plane of the dees. An electric field is applied between the gap of the dees by an oscillator that is connected to the dees. Charged particles are released at the center of the dees and as they move the electric field accelerates them. They stay in a circular path due to the magnetic field. To exit the particles they are deflected by a magnetic field.

Function of electric and magnetic fields Electric field applies a force in the direction of velocity. The force accelerates the particle

and increases its velocity. Magnetic field applies a force on the charged particle in a direction perpendicular to its

velocity. So it does not change the velocity of the particle. It helps to keep the particle confined to the dees so that it can be accelerated to high velocities.

�

� �

A @ �� @��

�@��

�(@�

ω

ω

π πω

= ×

=

=

=

= =

This is independent of the velocity of the charged particle.

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CBSE Physics XII Board Paper – SET C

Physics (Theory) [Time allowed: 3 hours] [Maximum marks:70] General Instructions: (i) All questions are compulsory. (ii) There are 30 questions in total.

Questions 1 to 8 carry one mark each. Questions 9 to 18 carry two marks each. Question 19 to 27 carry three marks each. Question 28 to 30 carry five marks each.

(iii) There is no overall choice. However, an internal choice has been provided in one question of two

marks; one question of three marks and all three questions of five marks each. You have to attempt only one of the choices in such questions.

(iv) Use of calculators is not permitted. (v) You may use the following values of physical constants wherever necessary:

C = 3 × 108 ms–1 H = 6.626 × 10 –34 Js e = 1.602 × 10–19 C

0 = 4 × 10–7 Tm A–1 9 2 2

0

1 9 10 Nm C4

29 29 10 Nm9 2

0

9 1

Mass of electron me = 9.1 × 10–31 kg Mass of neutron mn 1.675 × 10–27 kg Boltzmann’s constant k = 1.381 × 10–23 JK–1 Avogadro’s number NA = 6.022 × 1023 mol–1 Radius of earth = 6400 km


1. A plot of magnetic flux ( ) versus current (I) is shown in the figure for two inductors A and Β. Which of

the two has larger value of self inductance? 1

Solution: Inductor A has the larger value of self-inductance. 2. Figure shows three point charges +2q, –q and + 3q. Two charges + 2q and –q are enclosed within a surface

‘S’. What is the electric flux due to this configuration through the surface ‘S’? 1

Solution:

The net electric flux through the surface ‘S’ is00

q , where 00 is the permittivity of free space.

3. In which orientation, a dipole placed in a uniform electric field is in (i) stable, (ii) unstable equilibrium?

1 Solution: A dipole placed in a uniform electric filed is in (i) Stable equilibrium when the electric field is directed along the direction of the dipole i.e., when E is

parallel to p . (ii) Unstable equilibrium when the electric filed is directed at an angle of 180 degrees with the direction of

the dipole, i.e., when E is anti-parallel to p . 4. Which part of electromagnetic spectrum is used in radar systems? 1 Solution: The microwave range of electromagnetic spectrum is used in radar systems.


5. Calculate the speed of light in a medium whose critical angle is 30°. 1 Solution:

Speed of light in the medium Speed of light in airRefractive index of the medium with respect to airR f ti

8

8

8

3 10 m/s1

sin 30

3 10 m/s2

1.5 10 m/s

810 m/s83 10 m111

sin 30i 30sin 30

810 m/s832

10 m

81.5 10 m/s8

6. A glass lens of refractive index 1.45 disappears when immersed in a liquid. What is the value of refractive

index of the liquid? 1 Solution: The refractive index of the liquid is 1.45. 7. Write the expression for Bohr’s radius in hydrogen atom. 1 Solution:

The expression for Bohr’s radius in hydrogen atom is2

00 2π

02

0hame

.

8. A wire of resistance 8R is bent in the form of a circle. What is the effective resistance between the ends of

a diameter AB? 1

Solution:

The effective resistance between the ends of diameter AB is 1 12

1 1 14 4 2

R

R R R

12

1R

1 14 2R4 2

.


9. Explain the function of a repeater in a communication system. 2 Solution: A repeater is used for extending the range of a communication system. It consists of a receiver and a transmitter. The receiver of a repeater collects the signal from the transmitter of another repeater and after amplifying, it retransmits the signal. Sometimes, it also changes the carrier frequency of the pick-up signal before transmitting it to the receiver. 10. (i) Write two characteristics of a material used for making permanent magnets.

(ii) Why is the core of an electromagnet made of ferromagnetic materials?

OR

Draw magnetic field line when a (i) diamagnetic, (ii) paramagnetic substance is placed in an external magnetic field. Which magnetic property distinguishes this behaviour of the field line due to the substances? 2

Solution: (i) The material used for making permanent magnets should have the following characteristics:

(a) High retentivity: It ensures that the magnet remains strong even after removal of the magnetising field.

(b) High coercivity: It ensures that the magnetism of the material does not get easily lost. Apart from these two criteria, the material should have high permeability.

(ii) The core of an electromagnet should have high permeability and low retentivity. The high permeability of

the core of an electromagnet ensures that the electromagnet is strong. On the other hand, low retentivity of the core ensures that the magnetism of the core material gets lost as soon as the current is switched off. Ferromagnetic materials have both high permeability and low retentivity. Hence, ferromagnetic materials are the most suitable for making the core of an electromagnet.

OR (i) The magnetic field lines, when a diamagnetic material is placed in an external magnetic field,

can be diagrammatically represented as

(ii) The magnetic field lines, when a paramagnetic material is placed in an external magnetic field, can be diagrammatically represented as


Diamagnetic and paramagnetic materials are distinguished by the magnetic property called magnetic susceptibility. For diamagnetic materials, magnetic susceptibility is negative, whereas for paramagnetic materials, magnetic susceptibility is slightly positive.

11. What is the range of frequencies used in satellite communication? What is common between these waves

and light waves? 2 Solution: The waves used for satellite communication lie in the following two frequency ranges. (i) 3.7–4.2 GHz for downlink (ii) 5.9–6.4 GHz for uplink The waves used for satellite communication and light waves are both electromagnetic waves. Both of them travel in a straight line. 12. A coil Q is connected to low voltage bulb B and placed near another coil P as shown in the figure. Give

reasons to explain the following observations: 2 (a) The bulb ‘B’ lights (b) Bulb gets dimmer if the coil Q is moved towards left.

Solution: (a) The A.C. source creates a varying magnetic field in coil P. This varying magnetic field of P is linked to

coil Q. Hence, an induced current is produced in Q, which lights bulb B. (b) As coil Q moves away from P, the rate of variation of magnetic flux changes. Therefore, the induced

e.m.f. inside coil Q decreases and bulb B gets dimmer. 13. Find the radius of curvature of the convex surface of a plano-convex lens, whose focal length is 0.3 m

and the refractive index of the material of the lens is 1.5. 2


Solution: The focal length of a combined lens can be determined by the formula

1 2

2

1

1

1 1 1( 1)

Here, and 0.3 m1 1( 1)

0.30.3( 1)0.3(1.5 1)0.3 0.50.15 m15 cm

f R RR f

RR

1 1(( 1)) 11 11

1 2R R1R RR RR and 0.3 mf and

( 11)R

0.3( 1)0 3(1 5 1)0.3(1.5 1)0.3 0.50.15 m15 cm

14. An electron is accelerated through a potential difference of 64 volts. What is the de-Broglie wavelength

associated with it? To which part of the electromagnetic spectrum does this value of wavelength correspond? 2

Solution:

de-Broglie wavelength, 22

hmeV

31

34

31 19

34

50

34

25

9

9

10

Where,Massof electron 9.1 10 kg

6.626 102 9.1 10 1.6 10 646.626 10

1863.63. 106.626 101063.86 10

6.626 1043.170.15 10 m1.5 10 m

Massof electron 9.1 10 kg31kg31

10 34

9.1 10 1.6 10 6431 191 6 10 6431 19

10 34266.6210 50

10 346.6261063 8 10 25

6.626 1043 17

9

0.15 10 m9 m9

1.5 10 m1 5 10 10 m1010

m

This value of wavelength corresponds to the X-ray region of the electromagnetic spectrum. 15. (i) Out of blue and red light which is deviated more by a prism? Give reason.

(ii) Give the formula that can be used to determine refractive index of materials of a prism in minimum deviation condition. 2


Solution: (i) Between blue and red light, blue light is deviated more by a prism. This is because the wavelength of blue

light is smaller than that of red light. Therefore, the speed of blue light is lower than that of red light in a medium.

(ii) The formula used for determining the refractive index of materials of a prism in minimum deviation

condition,

21

sin ( ) / 2

sin2

mA Dn

A) / 2msin (

A22

Where, n21 Refractive index of prism material with respect to the surrounding medium A Angle of the prism Dm Angle of minimum deviation

16. Plot a graph showing the variation of stopping potential with the frequency of incident radiation for two

different photosensitive materials having work functions W1 and W2 (W1 > W2). On what factors does the (i) slope and (ii) intercept of the lines depend? 2

Solution:

(i) The slope of the graph is content and equals to hehhee

. Therefore, the slope does not depend on any factor.

(ii) The intercept of the lines depends on the work function ‘ ’ of the metals. 17. Draw the circuit diagram of an illuminated photodiode in reverse bias. How is photodiode used to

measure light intensity? 2 Solution: The circuit diagram of an illuminated photodiode in reverse bias can be represented as


The greater the intensity of light, the greater is the number of photons falling per second per unit area. Thus, the greater the intensity of light, the greater is the number of electron–hole pairs produced at the junction. The photocurrent is, thus, directly proportional to the intensity of light. This can be used for measuring the intensity of incident light. 18. A heavy nucleus X of mass number 240 and binding energy per nucleon 7.6 MeV is split into two

fragments Y and Z of mass numbers 110 and 130. The binding energy of nucleons in Y and Z is 8.5 MeV per nucleon. Calculate the energy Q released per fission in MeV. 2

Solution: Total energy of nucleus X = 240 × 7.6 = 1824 MeV

Total energy of nucleus Y = 110 × 8.5 = 935 MeV

Total energy of nucleus Z = 130 × 8.5 = 1105 MeV Therefore, energy released from fission, Q = 935 + 1105 1824 = 216 MeV 19. (a) Depict the equipotential surfaces for a system of two identical positive point charges placed a distance

‘d’ apart. (b) Deduce the expression for the potential energy of a system of two point charges q1 and q2 brought

from infinity to the points 1rr and 2rr respectively in the presence of external electric field EE . 3 Solution: (a)


(b) The work done in bringing charge q1 from infinity to 1r1r is q1V( 1r1r ). Work done on q2 against external field = q2 V( 2r2r )

Work done on q2 against the field due to q11 2

124π o

q qr12or1

1 2

4q q1

Where, r12 is the distance between q1 and q2. By the superposition principle for fields,

Work done in bringing q2 to 2r22rr is 1 222

12

( )4π o

q qq V rr

)2q Vq V2 (((V ( 22

124π o 12π or12 )2

4πq2 (

π r4q qq q))22 ) 1q1q q1 .

Thus, Potential energy of system = The total work done in assembling the configuration

1 21 21 2

12

( ) ( )4π o

q qqV r q V rr12or1

1 2( ) ( )24

qV1 2( ) (1 21q q1 2) ( )2q q1) () (1

20. In a meter bridge, the null point is found at a distance of l1 cm from A. If now a resistance of X is

connected in parallel with S, the null point occurs at l2 cm. Obtain a formula for X in terms of l1, l2 and S. 3

Solution: Initially, when X is not connected

1

1

Condition for balance ( )100

lR iS l

1 Condition for balance ( )l1100 1l1

Condil

The equivalent resistance (Req) of the combination of X and S is


eq

eq

2

eq 2

2

2

1 1 1

100

( ) ( )(100 )

R X SSXR

X SlR

R llR X S ii

SX l

1 1X SSX

X SS2l2

100 2l2l) 2 ( )l2

(100 2 )22 )

On dividing (i) by (ii), we obtain

1 2

2 1

1 2

2 1

2 1 1 2

2 1 1 2 1 2

1 2

2 1 1 1

(100 )( ) (100 )

(100 )(100 )

(100 ) ( ) (100 )

(100 ) (100 ) (100 )

(100 )(100 ) (100 )

l lR SXR X S X l l

l lXX S l l

Xl l X S l l

Xl l Xl l Sl l

Sl lXl l l l

2 )221l1 (100SX

2 1) 100 )2 1) (100) 2 1(100

2 )221l1 (100

2 1)1S l2 (100 1l (100

1 1 2) ( ) (100 )1 1 21) ( ) (100) ( ) (1001 1 211 1

1 1 2 1 2) (100 ) (100 )1 1 2 1 21 2 1) (100 ) (100) (100 ) (1001 1 2 1 21 2 11 1 2 1

2 )22Sll (100 1 1 1) (100 )1 1 11) (100)1 1 111 1

This is the expression for X in terms of S, l1 and l2. 21. What is space wave propagation? Give two examples of communication system which use space wave

mode. A TV tower is 80 m tall. Calculate the maximum distance upto which the signal transmitted from the tower can be received. 3

Solution: Space wave propagation is the propagation of waves whose frequencies lie above 40 MHz. Examples of communication systems which use space wave mode are

(i) Television broadcast (ii) Microwave links (iii)Satellite communication

(Any two examples can be taken) The maximum distance up to which signals can be received, 2 E Td R hE TR h2 E TE T


2 6400000 8032000 m32 km

2 6400000 8032000 m32 km

Hence, the maximum distance up to which the transmitted signal can be received is 32 km. 22. (i) Define ‘activity’ of a radioactive material and write its S.I. units.

(ii) Plot a graph showing variation of activity of a given radioactive sample with time. (iii) The sequence of stepwise decay of a radioactive nucleus is

1 2D D D1 2D D1D DD

If the atomic number and mass number of D2 are 71 and 176 respectively, what are their corresponding values of D? 3

Solution: (i) The activity of a radioactive material is defined as the decay rate of a sample containing one or more radio

nuclides. The SI unit of radioactivity is becquerel (B).

(ii)

(iii)

1761 71 2

176 17672 1 71 2

180 176 17674 72 1 71 2

D D D

Therefore,

D D D

Therefore,

D D D

1 71 2D D1 71176D D17611

72 1 71 2D D72 1 711 71176 176D D176 17611

72 1 71 2D D72 1 711 71176 176D D176 17611

So, the corresponding values of atomic number and mass number for D are 74 and 180.


23. What is an unpolarized light? Explain with the help of suitable ray diagram how an unpolarized light can

be polarized by reflection from a transparent medium. Write the expression for Brewster angle in terms of the refractive index of denser medium. 3

Solution:

An unpolarised light is one in which the vibration of electric field vector is not restricted in one particular plane. When an unpolarised light falls on the surface, the reflected light is such that the vibration of its electric field vector is confined to one particular plane. The direction of this plane is parallel to the surface of reflection. A component of electric field vector is absent from the refracted light. Therefore, the refracted light is partially polarised. The expression for Brewster angle in terms of the refractive index of denser medium is Btan i Where, is the refractive index of the denser medium with respect to the rarer medium. 24. Write the principle of working of a potentiometer. Describe briefly, with the help of a circuit diagram,

how a potentiometer is used to determine the internal resistance of a given cell. 3 Solution: The working principle of a potentiometer is based on Kirchhoff’s voltage law. According to this rule, the algebraic sum of changes in voltage around any closed loop involving resistors and cells in the loop is zero.

Let be the potential drop per unit length in the potentiometer wire.


When only a cell is connected, the balance point is N1. Appling Kirchhoff’s voltage law, = l1 [l1 = Length at which the balance point is achieved]

When some current is drawn using the resistance box, the balance point is achieved at N2. V = l2 This gives,

1

2

lV l

l1l1l1

= I (r + R) [R = Resistance of the resistance box] V = IR This gives,

1

2

1

r RV R

lr Rl

r RR

r R

lR l1 11 1l12l2ll

The internal resistance of the cell can be determined by plugging-in the measured values of l1 and l2. 25. Write the expression for the magnetic moment ( )m) due to a planar square loop of side ‘l’ carrying a

steady current I in a vector form. 3

In the given figure this loop is placed in a horizontal plane near a long straight conductor carrying a steady current I1 at a distance l as shown. Give reason to explain that the loop will experience a net force but no torque. Write the expression for this force acting on the loop.

Solution: The expression for the magnetic moment ( )m) due to a planar square loop of side ‘l’ carrying a steady current I in a vector form is given as

2

Therefore,ˆ( )

m I A

m I l n

I A

2 ˆ( )I l n2 ˆ( )

m I ATherefor

m 2I l 2( )

Where, n̂ is the unit vector along the normal to the surface of the loop. The attractive force per unit length on the loop is


a 0 1

0a 1

2π

2π

F I Il l

F I I

I I0 1

l20 1I I1

1I I01

0 I I0

The repulsive force per unit length on the loop is 0r 1

0 1r

net a r

01

0net 1

2π 2

2π 2

112π 2

4π

F I Il l

I IFl

F F F

I I

F I I

I I

I I

10

l2 210 I I0 10

0 1

2 2l0 1I I1

a rF Fa ra

1012 1I I1

0 I I 11 11122

12

1I I01

0 I I0

Since the attractive force is greater than the repulsive force, a net force acts on the loop. The torque on the loop is given as

sinsin

m BmBIAB

m BsinmBsinIAB

m B

= 0 ( Area vector is parallel to the magnetic field) = IAB sin0 = 0 The torque acting on the loop is zero.

26. A long straight wire of a circular cross-section of radius ‘a’ carries a steady current ‘I’. The current is

uniformly distributed across the cross-section. Apply Ampere’s circuital law to calculate the magnetic field at a point ‘r’ in the region for (i) r < a and (ii) r > a.

OR

State the underlying principle of working of a moving coil galvanometer. Write two reasons why a galvanometer can not be used as such to measure current in a given circuit. Name any two factors on which the current sensitivity of a galvanometer depends. 3

Solution: (i) For r < a


0 enclosed

enclosed2 2

2

encolsed 2

2

0 2

2

0 2

2

0 2

02

π π

cos 1

(2π )

2π

B dl I

I Ia r

rI Ia

B dl Bdl

rBdl Ia

rB dl Ia

rB r Ia

IB ra

ed

I

ose

2

I

2

rI

dl Bdl 1

0 2

rI0

22r0

20 I r0 I

lololo

encolsed

B dl Bdl cos 1

0 encl0 enclB dl 0 enclI0 eB dl I

2

a0 2a

2rBdl 0 2

rI0

2

a0 2

2rdla0 2

rI0

(ii) For r > a

From Ampere’s circuital law,


0 enclosed

enclosed

0

0

0

0

cos0

(2π )

2π

B dl I

B dl Bdl

B dl BdlI I

Bdl I

B dl I

B r IIBr

sed

I

los

cosdl Bdl0

dl BdlI

0I0

0

20 I

clcl

B dl Bdl

B

0

dl Bdl

0 encB dl 0 encI0 eB dl IB dl

0Bdl 0I0

(2 )0dldl 0I00

OR The underlying principle for the working of a moving coil galvanometer is that when a current-carrying conductor is placed inside a magnetic field, it experiences a magnetic force. The two reasons why a galvanometer cannot be used for measuring current are The high resistance of galvanometer can disturb the original current flowing through the circuit The high current present in the circuit can destroy the coil windings present in the galvanometer

The factors on which the current sensitivity of a galvanometer depends are Number of turns in the coil Torsional spring constant Area of the coil Strength of the magnetic field

(Any two can be taken as the answer) 27. A parallel-plate capacitor is charged to a potential difference V by a dc source. The capacitor is then

disconnected from the source. If the distance between the plates is doubled, state with reason how the following change: 3 (i) electric field between the plates (ii) capacitance, and (iii) energy stored in the capacitor

Solution: (i) Q = CV

0

0

0

( )AQ Edd

Q AEQE

A0 A

A0 A )))d(0 (0 A E0 (Ad

)d

((d

0 AE0

QEA


Therefore, the electric field between the parallel plates depends only on the charge and the plate area. It does not depend on the distance between the plates. Since the charge as well as the area of the plates does not change, the electric field between the plates also does not change. (ii) Let the initial capacitance be C and the final capacitance be C'. Accordingly,

0

0

2

2

2

ACd

ACd

CC

CC

A

A

0

d0 A

A2d

0

2d0 A

22

C22C

Hence, the capacitance of the capacitor gets halved when the distance between the plates is doubled. (iii)

Energy of a capacitor, U 21

2QC

12

QC

Since Q remains the same but the capacitance decreases, 21

22

12

2

QUC

UU

U U

1 Q212

QCCCC22

122

2U2

The energy stored in the capacitor gets doubled when the distance between the plates is doubled. 28. (a) Explain the formation of depletion layer and potential barrier in a p–n junction.

(b) In the figure given below the input waveform is converted into the output waveform by a device ‘X’.

Name the device and draw its circuit diagram.

(c) Identify the logic gate represented by the circuit as shown and write its truth table.


OR (a) With the help of circuit diagram explain the working principle of a transistor amplifier as an

oscillator. (b) Distinguish between a conductor, a semiconductor and an insulator on the basis of energy band

diagrams. 3 Solution: (a) In a p–n junction, a p-type and an n-type material are joined together. The concentration of holes is higher

in p-type material as compared to that in n-type material. Therefore, there is a concentration gradient between the p-type and n-type materials. As a result of this concentration gradient, holes move from p-side to n-side (p → n) by the process of diffusion. Similarly, electrons move from n-side to p-side (n → p). As the holes diffuse from p-side, they leave ionised spaces (negatively charged) on p-side near the junction. These ionised spaces are immobile. Hence, a negative space-charge region is formed on the p-side near the junction. Similarly, a positive space-charge region is formed on the n-side. These two space-charge regions on either sides of the junction constitute what is called a depletion layer. Since the n-side loses electrons and p-side gains electrons, a potential difference is developed across the junction of the two regions. This potential difference tends to oppose further motions of electron from the n-region into the p-region. The same happens for holes too. The reverse polarity of this potential opposes further flow of carriers and is thus called the barrier potential.

(b) The device is a full-wave rectifier.

The circuit diagram of a full-wave rectifier is represented as

(c) The logic gate represented by the circuit is an AND gate. The truth table of the AND gate is represented as

A B Α.B 0 0 0 1 1 1 1 0 0 0 1 0


OR (a) The circuit diagram for a transistor amplifier as an oscillator is represented as

In an oscillator, a sustained Α.C. output is obtained without any input oscillation. For this to happen, the output of a transistor amplifier is fed back into its input. This is achieved by coupling the winding T1 to winding T2. When key S1 is closed, the collector current begins to increase, which supports the forward bias of the emitter–base circuit. Collector current increases until it reaches saturation. When the saturation is reached, the magnetic flux linked to winding T1 becomes steady. Hence, the forward bias of the emitter–base circuit is no longer supported. The transistor is now driven into cut-off. This cycle repeats itself and an oscillating output is obtained. (b) The energy-band diagram of a conductor is represented as

The energy-band diagram of a semiconductor is represented as

The energy-band diagram of an insulator is represented as


29. Describe briefly, with the help of a labelled diagram, the basic elements of an A.C. generator. State its

underlying principle. Show diagrammatically how an alternating emf is generated by a loop of wire rotating in a magnetic field. Write the expression for the instantaneous value of the emf induced in the rotating loop.

OR A series LCR circuit is connected to a source having voltage v = vm sin t. Derive the expression for the instantaneous current I and its phase relationship to the applied voltage. Obtain the condition for resonance to occur. Define ‘power factor’. State the conditions under which it is (i) maximum and (ii) minimum. 5

Solution: Basic elements of an A.C. generator

An A.C. generator consists of a rotor shaft on which a coil is mounted. A magnetic field is created around an armature coil with the help of permanent magnets. The terminals of the coil are connected to two slip rings. Carbon brushes are attached to slip rings so as to make connection with an external circuit. Underlying principle of an A.C. generator The underlying principle responsible for the working of an Α.C. generator is electromagnetic induction. According to this principle, if a conductor is placed in a varying magnetic field, then current is induced in the conductor.


Generation of an alternating e.m.f. by a loop of wire rotating in a magnetic field

Expression of the instantaneous value of the induced e.m.f. in a rotating loop = NBA sin t

Where N = number of turns in armature coil B = Magnetic field vector A =Area vector of the coil

= Angular speed OR v = vm sin t Let the current in the circuit be led the applied voltage by an angle .

m sin( )i i tm sin(im sin(( )(

The Kirchhoff’s voltage law givesC

di qL Ri vdt C

qRi vq .

It is given that v = vm sin t (applied voltage)

2

m2 sin ... 1C

d q dq qL R v tdt dt m s

Cidq qR vm sindq q

dt

On solving the equation, we obtain


m

m

22

m2

sin( )

cos( )

sin( )

q q tdq q tdtd q q tdt

m i (qm sin(( )(

mqmm cos( )tm cos(

mqm2

m i ( )t2m sin(

On substituting these values in equation (1), we obtain C L m

C C

2 2C L

C Lm

cos( ) ( )sin( ) sin1C

( )

( )cos( ) sin( ) sin ... 2

m

m

q R t X X t v t

X X L

Z R X X

X XRq Z t t v tZ Z

(R tcos(

CCC

Z

C L m) ( ) i ( ) i t) ( )sin( ) sinC L mL

1 X1 LCX C

2 2C L( )C LR2 ( C L

(R (R (R )() ( CC) ( CC ) i) i)L i ()LLL i ()LLcos(cos( ) sin( ) sin) sin( ) sin) sinC L( C sin(L )L

Z Z mZ Zcos(

Z( mm) sin( ) sinin( ) sinmZ

)

Let cos2R2R and C L sinX X

ZLX L sinsin

This gives C Ltan X X

RLX LCX C

RLX LX

On substituting this in equation (2), we obtain

mcos( ) sinmq Z t v t(Z t v tcos( m) ivm) sinm On comparing the two sides, we obtain

m m

m

m

π and ( )2

πor 2

cos( )

cos( )

m

m

m

v q Z i Zi q

dqi q tdt

i t

mq mZ i Zm

mqπ)2

π2

mdq qmdqdt

cos( )tcos(

m cos(im cos(( )(

Or

m m2 2

C L

sin( )

Where, ( )

m

m

i i tv viZ R X X

s (i (mii sin(i (m ( )( )((

m2

v vm

Z 2C L( )C L( C L

And

1 C Ltan X XR

XCXC LX Ltan 1 XC LCCXC LLXRR


The condition for resonance to occur

m 2 2C L( )

mviR X X2 2

C L( )C L( C L

For resonance to occur, the value of im has to be the maximum. The value of im will be the maximum when

C L

2

1C

1LC1LC

12πLC1

2π LC

X X

L

f

f

C2

LX L

LL

1LC1LC

1LC1

2 LC

Power factor = cos

Where,

2 2C L

cos( )

R RZ R X X2

RZ 2

C L( )C L( C L

(i) Conditions for maximum power factor (i.e., cos = 1) XC = XL

Or

R = 0 (ii) Conditions for minimum power factor

When the circuit is purely inductive When the circuit is purely capacitive


30. State Huygens’s principle. Show, with the help of a suitable diagram, how this principle is used to obtain the diffraction pattern by a single slit.

Draw a plot of intensity distribution and explain clearly why the secondary maxima becomes weaker with increasing order (n) of the secondary maxima.

OR Draw a ray diagram to show the working of a compound microscope. Deduce an expression for the total magnification when the final image is formed at the near point. In a compound microscope, an object is placed at a distance of 1.5 cm from the objective of focal length 1.25 cm. If the eye piece has a focal length of 5 cm and the final image is formed at the near point, estimate the magnifying power of the microscope. 5

Solution: Huygen’s principle states that Each point on a wave front behaves as a source of secondary wavelets The secondary wavelets travel with the speed of light in that medium The position of new wave front at a later time can be found out by drawing a common tangent to all these

secondary wavelets Intensity distribution of single slit distribution

For the first secondary maxima (n = 1), only one-third of the slit contributes to its intensity. Secondly, for n = 2, only one-fifth of the slit contributes to the intensity. Therefore, with increasing n, the intensity decreases. OR Ray diagram for a compound microscope


Total angular magnification, m

Angle subtended by the image Angle subtended by the object

Since and are small, tan and tan

tantan

ABtan

m

D

and tantant

ABD

And A Btan

tan A B A Btan AB AB

DDm

DA

BADB

A BBtant AB AB

A A BB

On multiplying the numerator and the denominator with A B , we obtain

A B A BA B AB

m B A BAA

B ABB ABA

Now, magnification produced by objective, 0A'B'AB

m A BAB

Magnification produced by eyepiece, eA BAB

m BAAB

B

Therefore, Total magnification, (m) = m0 me

00

0

ee

(Image distance for image produced by objective lens )(Object distance for the objective lens)

1

vmu

Dmf

0 (Image dv

DD11 D

efeff

fe Focal length of eyepiece 0 e

0

0 e

1

m m m

v Du f

0 em m0

D0v0 D11 D

efeff

0 Lv L (Separation between the lenses)


0 0

0 e

L 1

u f

Dmf f

0f0

L DmfL D111 D

efeff

0

0

0 0 0

0

0

1.5 cm1.5cm

1 1 1

1 1 11.25 1.51 1 1

1.25 1.5100 10125 151500 1250

1875

uf

f v u

v

v

1.5 cm1.5cm1 1

1 11 5

1 11 25 1 5

100 10125 15

125015001875

1

0

0

e

0

0 e

1 25018757.5 cm5 cm

1

7.5 2511.5 57.5 61.530

vvf

v Dmu f

m

25018757.5 cm5 cm

D0v D11 D

efeff

257.5 251 2511.51 5

1555

1

7.5 61 530

1.What is the highest frequency for which antennas can be made (approximately)

1012 to 1013 Hz.

2. What is the condition of the electrons in the transmitting antenna when maximum

magnetic field is being transmitted?

A maximum current is flowing, so the electrons have maximum speed up and

down the antenna. The electric current produces the magnetic field.

3. How can the electric portion of the electro-magnetic wave be detected?

It can be detected by an antenna similar to the transmitting antenna except that a

detector of electric current replaces the voltage source.

4. How can the magnetic field portion of an electro-magnetic wave be detected?

The magnetic wave is best detected by placing a loop of wire (with its ends hooked

to a current detector) in the path of the wave. The changing magnetic field causes a

current in the loop.

5.The small ozone layer on the top of the atmosphere is crucial for human survival.

Why?

The ozone in the atmosphere is confined to the ozone layer, some 50-80 km above

the ground. The ozone layer blocks the passage of the ultra-violet radiations; x-rays and

y-rays from the solar and other extra-terrestrial sources and effectively protects us from

the dangerous and harmful portions of solar radiations as they cause genetic damages

to living cells. Practically all radiations of wave length less than 3 x 10-7m are absorbed

by the ozone layer. This explains why ozone layer on the top of the atmosphere is

crucial for human survival.

6.How does "Green House Effect" affect the temperature of the earth's surface ?

Green house effect serves to keep the earth's surface warm at night.

7.How do we make television broadcasts for larger coverage and for long distance?

By using (i) tall antennas which is familiar landmark in many cities and (ii) using

artificial satellites —called geostationary satellites. Since television signals are of high

frequency and are not reflected by ionosphere so we use satellites to get them reflected

& transmission of TV signals can be used for larger coverage as well as for long

distance.

8. Scientists put x-ray astronomical telescope on the artificial satellite orbiting above the

earth's atmosphere whereas they build optical and radio-telescopes on the surface of the

earth. Why ?

X-rays have very high frequency and much smaller wavelength. These rays get

absorbed by the earth's atmosphere. On the other hand, optical (visible) radiations and

radio-waves can pass through the atmosphere. That is why optical and radio telescopes

can be installed on the earth's surface.

9. F o r a n e le ctrom ag ne tic w a ve , w rite the re la tio nsh ip b e tw ee n a m p litud e o f

e lec tric and m ag ne tic fie lds in fre e sp ace .

[H in ts If E o is th e a m p litu d e o f a n e le c tr ic f ie ld a n d B o is th e a m p litu d e o f th e

a sso c ia te d m a g n e tic f ie ld in fre e sp a ce th e n 0

0

BEc = w h e re c is th e sp e e d o f lig h t

in fre e sp a ce i.e . 3 x1 0 8 m /s .

10. The charging current for a capacitor is 0.25 A. What is the displacement current

across its plates?

Hints: Displacement current = Charging current = 0.25 A]

11. What is a ground wave? How does it differ from a sky wave?

Ans. A signal emitted by an antenna from a certain point can be received at another point of

the surface of the earth in two ways. The wave which travels directly following the surface of the

earth is called ground nave. The wave that can reach the same point after being reflected

from the ionosphere is called sky wave.

12. Why short wave communication over long distances is not possible via ground waves?

|Hints: Because the wave gets attenuated.]

13 . A re conduction and d isp lacem ent cu rren ts the sam e?

[H in t: N o ; they a re d iffe ren t bu t they a re equa l .

14 . It is necessary to use sa te llites fo r long d istance T V transm iss ion . W hy?

It is so because te levis ion s igna ls a re no t p rope rly re flected by the

ionosphe re . T here fo re , fo r re flec tion o f s igna ls sa te llites a re needed as re flec tion is

e ffec ted by sa te llites .

15 . O p tica l and rad io te lescopes a re bu ilt on g round bu t X-ray astronom y is

poss ib le on ly from sa te llites o rb iting the earth . W hy?

A tm osphe re absorbs X-rays, wh ile vis ib le and rad iowaves can pene tra te it.

T ha t is why op tica l and rad io te lescopes can work on earth 's su rface bu t X -ray

as tronom ica l te lescopes m ust be used on sa te llites o rb iting the ea rth .

16 . If the earth d id no t have an a tm osphere , wou ld its ave rage surface tem pera tu re

be h igher o r lowe r than wha t it is now?

A ns. T he tem pera tu re o f the earth wou ld be lowe r because the g reen house e ffec t

o f the a tm osphere wou ld be absen t.

.

17 . W ha t is the equa tion fo r the speed o f e lec trom agnetic w aves in free space?

C =00

1εμ

18 . T he wave leng th o f e lec tro m agnetic rad ia tion is doub led . W hat w ill happen to

the ene rgy o f the pho ton?

T he energy w ill be ha lved because frequency w ill be ha lved .

19 . N am e the pa rt o f e lec trom agnetic spectrum to wh ich waves o f wave leng th (i)

1A° and (ii) 10 -2 m be long . U s ing the re la tion λT = (0 .29 cm ) K , ob ta in the

characte ris tic ke lv in tem pera tu re correspond ing to these two wave leng ths.

(i) X -rays, (ii) M icrowaves

A ga in , (i) Kcm

cmT 810 1029

10129.0 −

− ×=×

= (ii) Kcm

cmT 29.0129.0

==

20 . G ive a s im p le a rgum ent to suggest tha t an acce le ra ted charge m ust em it

e lec trom agne tic rad ia tion

A ns. W hen charge m oves w ith constan t ve loc ity, the m agnetic fie ld does no t

change w ith tim e. S o , it canno t p roduce an e lectric fie ld . W hen cha rge is

acce le ra ted , bo th e lec tric and m agnetic fie lds change w ith tim e and space , one

becom ing a source o f ano ther. T h is g ives rises to e lectrom agne tic wave .

21 . S how tha t the average energy density o f the E fie ld equa ls the average energy

dens ity o f the B fie ld .

A ns. E ne rgy dens ity in E fie ld , 2

021 EuE ε=

E nergy density in B fie ld ,--------------

2

021 BuB μ

=

U sing E = cB and c =00

1εμ

, uE = uB .

22 . O n what fac to rs does its ve loc ity in vacuum depend?

A ns. E lectrom agnetic waves consist o f s inuso ida l va ria tion o f e lec tric and

m agnetic fie ld vecto rs . T he fie ld vecto rs v ib ra te w ith the sam e frequency and a re

in the sam e phase . T he fie ld vecto rs and the d irection o f p ropaga tion a re a ll

m utua lly pe rpend icu la r. T he ve loc ity o f e lec trom agnetic w aves in vacuum

depends upon abso lu te perm eab ility μo and abso lu te perm ittiv ity ε0.N o te tha t c

=00

1εμ

23 . W ha t is the nam e assoc ia ted w ith the fo llow ing equa tions?

0.)(.)(0

== ∫∫ SdBiiqSdEi��

ε

∫∫∫∫ +=−= ISdEdtdSdBiiSdB

dtdldEiii 000 ..)(..)( μεμ

��

(i) G auss 's law (ii) N o pa rticu la r nam e

(iii) Faraday's law (iv) A m pere 's law .

24 . E lec trom agnetic waves w ith w ave leng th

(i) λ1a re used to trea t m uscu la r stra in

(ii) λ2 a re used by a FM rad io sta tion fo r b roadcasting

(iii) λ3 a re used to de tec t frac tu re in bones

(iv) λ4 a re absorbed by the ozone layer o f the a tm osphe re .

Iden tify and nam e the part o f the e lec trom agnetic spectrum to wh ich these

rad ia tions be long . A rrange these wave leng ths in decreasing o rder o f m agn itude .

A ns. (i) λ1 -» in fra red (ii) λ2 -» rad iowaves

(iii) λ3 — > X-rays (in ) λ4 — > u ltra -v io le t rays λ2 > λ1 > λ4 > λ3.

25 . If you find c losed loops o f B in a reg ion in space , does it necessarily m ean tha t

ac tua l charges a re flow ing across the a rea bounded by the loops?

A ns. N o t necessa rily. A d isp lacem ent cu rren t such as tha t be tween the p la tes o f a

capac ito r tha t is be ing cha rged can a lso p roduce loops o f B •

26 . A c losed loop o f B is p roduced by a chang ing e lec tric f ie ld . D oes it necessa rily

m ean tha t E and dtdE

are non -zero a t a ll po in ts on the loop and in the a rea

enclosed by the loop?

A ns. N o t necessarily. A ll tha t is needed is tha t the to ta l e lec tric flux th rough the

a rea enclosed by the loop shou ld vary in tim e. T he flux change m ay a rise from

any po rtion o f the a rea . E lsewhere E o r dtdE

m ay be ze ro . In particu la r, the re need

be no e lec tric fie ld a t the po in ts wh ich m ake the loop .

27 . W hy is it tha t induced e lec tric fie lds due to chang ing m agnetic flux a re m ore

read ily observab le than the induced m agnetic f ie lds due to chang ing e lectric

fie lds?

A ns. T he m agn itude o f the m agnetic f ie ld due to d isp lacem ent cu rren t is too sm a ll

to be eas ily observab le . T h is e ffec t can o f course be increased by increasing the

d isp lacem ent cu rren t. [In an A C c ircu it, th is can be done by increasingω.]

O n the o ther hand , the e ffect o f induced e lec tric f ie ld due to chang ing m agnetic

flux can be increased s im p ly by tak ing m ore and m ore num ber o f tu rns in the co il.

T he induced em fs in d iffe ren t tu rns o f the sam e co il add up in se ries.

28 . A variab le -frequency A C sou rce is connected to a capac ito r. W ill the

d isp lacem ent cu rren t increase o r decrease w ith increase in frequency?

A ns. Increase in frequency causes decrease in im pedance o f the capac ito r and

consequent increase in the cu rren t wh ich equa ls d isp lacem en t cu rren t be tween

the p la tes .

29 . S om e sc ien tis ts have p red ic ted tha t a g loba l nuc lear wa r on the earth wou ld

be fo llowed by a severe 'nuc lear w in te r' w ith a devasta ting e ffec t on life on earth .

W hat m igh t be the bas is o f th is p red iction?

A ns. T he c louds p roduced by a g loba l nuc lear war wou ld perhaps cove r

substan tia l pa rts o f the sky p reven ting so la r ligh t from reach ing m any parts o f the

g lobe . T h is wou ld cause a 'w in te r'.

30. What is the contribution of the Greenhouse effect towards the surface temperature of

the earth?

Ans. The infrared radiation emitted by the earth's surface keeps the earth warm. In the

absence of this effect, the surface temperature of earth would be lower.

31. Why the small ozone layer on top of the stratosphere is crucial for human survival?

Ans. The small ozone layer on the top of the stratosphere absorbs ultraviolet radiations, y-

rays etc. from the sun. It also absorbs cosmic radiations. So, these radiations, which can

cause genetic damage to the living cells, are prevented from reaching the earth. Thus, the

small ozone layer on top of the stratosphere is crucial for human survival.

32. A plane electromagnetic wave travels in vacuum along z-direction. What can you say

about the directions of its electric and magnetic field vectors? If the frequency of the wave

is 30 MHz, what is the wavelength?

Ans. E and B lie in the x-y plane and are mutually perpendicular. Wavelength,

mm 101030

3xlO6

8

=×

=λ

33. Given below are some famous numbers associated with electromagnetic radiation in

different contexts in physics. State the part of the e m spectrum to which each belongs.

(i) 21 cm (wavelength emitted by atomic hydrogen in interstellar space).

(ii) 1057 MHz [frequency of radiation arising from two close energy levels in hydrogen;

known as Lamb shift].

(Hi) 2.7 K temperature associated with the isotropic radiation filling all space-thought to be

a relic of the 'big-bang’ origin of the universe.

(iv) 5890 A - 5896 A [double lines of sodium].

(v) 14.4 keV [energy of a particular transition in 57Fe nucleus associated with a famous

high resolution spectroscopic method (Mossbauer spectroscopy).

Ans. (i) Radio (short wavelength end) (ii) Radio (short wavelength end) (Hi) Microwave (iv)

Visible (Yellow) (v) X-rays (or soft y-ray) region.

34. Electromagnetic waves in a cavity with conducting walls can exist only in certain

modes i.e., they cannot exist, for example, with any arbitrary wavelength. Suggest a

simple reason why this should be so.

Ans. The waves must satisfy a boundary condition. The electric field should be zero on the

walls of the conductor. This restricts the possible modes. [It is something like the restricted

modes of a string fixed at two ends.]

7. Write the order of frequency range and one use of the following e. m radiations. i)Microwaves ii) Ultra-violet rays iii) gamma rays

a. i) Microwaves :- 109 to 1012 Hz approx used in radars/microwave ovens ii) Ultra violet rays:-1015 to 10 18 Hz approx. sterilizing the medical instruments iii) gamma rays:- 10 18 to 10 22 Hz in radio therapy ,treating cancer and tumours.

8. How are the following e.m radiations produced, Mention one used of them. i) radio waves ii ) infra red rays iii) x rays

a. i) radio waves :produced by oscillating circuits having inductor and capacitor. Used in radio and TV communication. ii)infra red rays: produced by all hot bodies treating muscular strains/ solar appliances etc., iii) gamma rays: produced when high energy electrons bombards metals. . to detect fracture in bones/ study crystal structure

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SAMPLE PAPER IXII - PHYSICS

Time : Three Hours Max. Marks : 70

General Instructions(a) All questions are compulsory.(b) There are 30 questions in total. Questions 1 to 8 carry one mark each, questions 9 to 18 carry two marks each,

questions 19 to 27 carry three marks each and questions 28 to 30 carry five marks each.(c) There is no overall choice. However, an internal choice has been provided in one question of two marks, one

question of three marks and all three questions of five marks each. You have to attempt only one of the givenchoices in such questions.

(d) Use of calculators is not permitted.(e) You may use the following physical constants wherever necessary :

c = 3 x 108ms-1

h = 6.6 x 10-34Jse = 1.6 x 10-19 C

oμ = 17 AmT10x4 −− π

Boltzmann constant k = 1.38 x 1023 JK-1

Avogadro’s number NA = 6.023 x 1023/moleMass of neutron mn = 1.6 x 10-27 kg

1. Two identical charged particles moving with same speed enter a region of uniform magnetic field. If one of theseenters normal to the field direction and the other enters along a direction at 300with the field, what would be theratio of their angular frequencies?

2. Why does a metallic piece become very hot when it is surrounded by a coil carrying high frequency alternatingcurrent?

3. How is a sample of an n-type semiconductor electrically neutral though it has an excess of negative charge carriers?

4. Name the characteristics of electromagnetic waves that(i) increases(ii) remains constant

in the electromagnetic spectrum as one moves from radiowave region towards ultravoilet region.

5. How would the angular separation of interference fringes in young’s double slit experiment change when thedistance of separation between the slits and the screen is doubled?

6. Calculate the ratio of energies of photons produced due to transition of electron of hydrogen atom from its,

(i) Second permitted energy level to the first level, and(ii) Highest permitted energy level to the second permitted level

7. Give expression for the average value of the a c voltageV = V0 Sin tω

(4)

over the time interval t = 0 and t =

8. How is the band gap, Eg, of a photo diode related to the maximum wavelength, m , that can be detected by it?

9. Keeping the voltage of the the charging source constant, what would be the percentage change in the energy storedin a parallel plate capacitor if the separation between its plates were to be decreased by 10%?

10. Explain how the average velocity of free electrons in a metal at constant temperature, in an electric field, remainconstant even though the electrons are being constantly accelarated by this electric field?

11. How is the resolving power of a microscope affected when,(i) the wavelength of illuminating radiations is decreased?(ii) the diameter of the objective lens is decreased?Justify your answer.

12. What is the basic difference between the atom or molecule of a diamagnetic and a paramagnetic material? Why areelements with even atomic number more likely to be diamagnetic?

13. Why are infrared radiations referred to as heat waves also? Name the radiations which are next to these radiationsin electromagnetic specturm having(i) Shorter wavelength.(ii) Longer wavelength.

14. The following data was recorded for values of object distance and the corresponding values of image distance inthe experiment on study of real image formation by a convex lens of power +5D. One of these observations isincorrect. Indentify this observation and give reason for your choice:

15. Two students X and Y perform an experiment on potentiometer separately using the circuit diagram shown here.

S.No. 1 2 3 4 5 6

Object distance 25 30 35 45 50 55(cm)

Image distance 97 61 37 35 32 30(cm)

(5)

Keeping other things unchanged(i) X increases the value of distance R(ii) Y decreases the value of resistance S in the set up.How would these changes affect the position of null point in each case and why?

16. The following table gives the values of work function for a few photo sensitive metals

S.No. Metal Work Function(eV)

1. Na 1.92

2. K 2.15

3. Mo 4.17

If each of these metals is exposed to radiations of wavelength 300 nm, which of them will not emit photo electronsand why?

ORBy how much would the stopping potential for a given photosensitive surface go up if the frequency of the incidentradiations were to be increased from 4 x 1015 Hz to 8 x 1015 Hz?Given h = 6.4 x 10-34 J-s, e = 1.6 x 10-19 C and c = 3 x 108 ms-1

17. Prove that the instantaneous rate of change of the activity of a radioactive substance is inversely proportional to thesquare of its half life.

18. What does the term LOS communication mean? Name the types of waves that are used for this communication.Which of the two-height of transmitting antenna and height of receiving antenna - can affect the range over whichthis mode of communication remains effective?

19. The following data was obtained for the dependence of the magnitude of electric field, with distance, from areference point O, within the charge distribution in the shaded region.

(i) Identify the charge distrubution and justify your answer.(ii) If the potential due to this charge distribution, has a value V at the point A, what is its value at the point

A′

? 3

(6)

20. A charge Q located at a point is in equilibrium under the combined electric field of three charges q1,q2, q3. If the

charges q1, q2 are located at points and respectively, find the direction of the force on Q, due to q3 in terms

of q1,q2, . 3

21. 12 cells, each of emf 1.5V and internal resistance , are arranged in m rows each containing n cells connectedin series, as shown. Calculate the values of n and m for which this combination would send maximum currentthrough an external resistance of .

OR

For the circuit shown here, calculate the potential difference between points B and D

3

22. A beam of light of wavelength 400 nm is incident normally on a right angled prism as shown. It is observed that thelight just grazes along the surface AC after falling on it. Given that the refractive index of the material of the prismvaries with the wavelength as per the relation

calculate the value of b and the refractive index of the prism material for a wavelength .

[(Given = Sin-1 (0.625)]

(7)

3

23. Three students X, Y, and Z performed an experiment for studying the variation of alternating currents with angularfrequency in a series LCR circuit and obtained the graphs shown below. They all used a.c. sources of the same r.m. s. value and inductances of the same value.What can we (qualitatively) conclude about the(i) capacitance value(ii) resistance valuesused by them? In which case will the quality factor be maximum?What can we conclude about nature of the impendance of the set up at frequency wo?

3

24. An equiconvex lens with radii of curvature of magnitude r each, is put over a liquid layer poured on top of a planemirror. A small needle, with its tip on the principal axis of the lens, is moved along the axis until its inverted realimage conicides with the needle itself. The distance of the needle from the lens is measured to be ‘a’. On removingthe liquid layer and repeating the expriment the distance is found to be ‘b’.Given that two values of distances measured represent the focal length values in the two cases, obtain a formula forthe refractive index of the liquid.

3

(8)

25. A circular coil having 20 turns, each of radius 8 cm, is rotating about its vertical diameter with an angularspeed of 50 radian s-1 in a uniform horizontal magnetic field of magnitude 30 mT. Obtain the maximumaverage and r. m. s. values of the emf indued in the coil.If the coil forms a closed loop of resistance , how much power is dissipased as heat in it? 3

26. The nucles of an atom of , initially at rest, decays by emitting an -particle as per the equation

It is given that the binding energies per nucleon of the parent and the daughter nuclei are 7.8 MeV and 7.835 MeVrespectively and that of -particle ia 7.07MeV/nucleon. Assuming the daughter nucleus to be formed in theunexcited state and neglecting its share in the energy of the reaction, calculate the speed of the emitted -particle.Take mass of -particle to be 6.68 x 10-27 kg. 3

27. Define the term ‘modulation index’ for an AM wave. What would be the modulation index for an AM wave forwhich the maximum amplitude is ‘a’ while the minimum amplitude is ‘b’ ? 3

28. Two circular coils X and Y having radii R and respectively are placed in horizontal plane with their centrescoinciding with each other. Coil X has a current I flowing through it in the clockwise sense. What must be thecurrent in coil Y to make the total magnetic field at the common centre of the two coils, zero?

With the same currents flowing in the two coils, if the coil Y is now lifted vertically upwards through a distance R,what would be the net magnetic field at the centre of coil Y?

ORA straight thick long wire of uniform cross section of radius ‘a’ is carrying a steady current I. Use Ampere’scircuital law to obtain a relation showing the variation of the magnetic field (Br) inside and outside the wire withdistance r, ( ) and ( ) of the field point from the centre of its cross section. Plot a graph showing thenature of this variation.

Calculate the ratio of magnetic field at a point above the surface of the wire to that at a point below its

sruface. What is the maximum value of the field of this wire? 5

29. State the principle which helps us to determine the shape of the wavefront at a later time from its given shape at anytime. Apply this principle to

(i) Show that a spherical/ plane wavefront contiunes to propagate forward as a spherical/plane wave front.(ii) Derive Snell’s law of refraction by drawing the refracted wavefront corresponding to a planewavefront incident on the boundary separating a rarer medium from a denser medium. 5

ORWhat do we understand by ‘polarization’ of a wave? How does this phenomenon help us to decide whether a

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given wave is transverse or longitudinal in nature?

Light from an ordinary source (say a sodium lamp) is passed through a polaroid sheet P1.The transmitted light isthen made to pass through a second polaroid sheet P2 which can be rotated so that the angle ( ) between the twopolaroid sheets varies from O0 to 90o. Show graphically the variation of the intensity of light, transmitted by P1andP2, as a fuction of the angle . Take the incident beam intensity as I0. Why does the light from a clear blue portionof the sky, show a rise and fall of intensity when viewed through a polaroid which is rotated? 5

30. A student has to study the input and output characteristics of a n-p-n silicon transister in the Common Emitterconfiguration. What kind of a circuit arrangement should she use for this purpose?

Draw the typical shape of input characteristics likely to be obtained by her. What do we understand by the cut off,active and saturation states of the transistor? In which of these states does the transistor not remain when beingused as a switch?

ORInput signals A and B are applied to the input terminals of the ‘dotted box’ set-up shown here. Let Y be the finaloutput signal from the box.

Draw the wave forms of the signals labelled as C1and C2within the box, giving (in brief) the reasons for gettingthese wave forms. Hence draw the wave form of the final output signal Y. Give reasons for your choice.

What can we state (in words) as the relation between the final output signal Y and the input signals A and B ?

(10) (24)

SAMPLE QUESTION PAPER -IIXII - PHYSICS

Time : 3 Hours Max.Marks : 70

General Instructions(a) All questions are compulsory.(b) There are 30 questions in total. Questions 1 to 8 carry one mark each, questions 9 to 18 carry two marks each,

questions 19 to 27 carry three marks each and questions 28 to 30 carry five marks each.(c) There is no overall choice. However, an internal choice has been provided in one question of two marks, one



c = 3 x 108ms-1

h = 6.6 x 10-34Jse = 1.6 x 10-19 C

oμ = 17 AmT10x4 −− π


Avogadro’s number NA = 6.023 x 1023/moleMass of neutron mn = 1.6 x 10-27 kgMass of electron me = 9 x 10-31 kg

1. What is the angle between the directions of electric field at any (i) axial point and (ii) equitorial point due to anelectric dipole? 1

2. A (hypothetical) bar magnet (AB) is cut into two equal parts. One part is now kept over the other, so that pole C2is above C1. If M is the magnetic moment of the original magnet, what would be the magnetic moment of thecombination so formed? 1

A C1 C2 B

3. A rectangular wire frame, shown below, is placed in a uniform magnetic field directed upward and normal to theplane of the paper. The part AB is connected to a spring. The spring is stretched and released when the wire ABhas come to the position (t=0). How would the induced emf vary with time? Neglect damping 1

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4. From the following, identify the electromagnetic waves having the (i) Maximum (ii) Minimum frequency. 1(i) Radio waves (ii) Gamma-rays (iii) Visible light(iv) Microwaves (v) Ultraviolet rays, and (vi) Infrared rays.

5. A partially plane polarised beam of light is passed through a polaroid. Show graphically the variation of thetransmitted light intensity with angle of rotation of the polaroid.

6. The given graphs show the variation of photo electric current (I) with the applied voltage (V) for two differentmaterials and for two different intensities of the incident radiations. Identify the pairs of curves that correspond todifferent materials but same intensity of incident radiations.

7. Four nuclei of an element fuse together to form a heavier nucleus. If the process is accompanied by release ofenergy, which of the two - the parent or the daughter nucleus would have a higher binding energy/nucleon?

8. Zener diodes have higher dopant densities as compared to ordinary p-n junction diodes. How does it affect the

(i) Width of the depletion layer? (ii) Junction field?

9. Four point charges are placed at the four corners of a square in the two ways (i) and (ii) as shown below. Will the(i) electric field(ii) Electric potential, at the centre of the square, be the same or different in the two configrations and why?

(i) (ii)(26)

10. The I-V characteristics of a resistor are observed to deviate from a straight line for higher values of current asshown below. Why?

11. A charged particle moving with a uniform velocity enters a region where uniform electric and magnetic fields

and are present. It passes through the region without any change in its velocity. What can we conclude

about the

(i) Relative directions of , , and ?

(ii) Magnitudes of and ?

12. Figure shows two long cooxial solenoids, each of length ‘L’. The outer soleniod has an area of cross-section A andnumber of turns/ length n1 . The corresponding values for the inner solenoid are A2 and n2. Write the expression for

self inductance L1, L2 of the two coils and their mutual inductance M. Hence show that M< .

13. Two indentical plane metallic surfaces A and B are kept parallel to each other in air separated by a distance of 1.0cm as shown in the figure.

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Surface A is given a positive potential of 10V and the outer surface of B is earthed. (i) What is the magnitude anddirection of the uniform electric field between points Y and Z? (ii) What is the work done in moving a charge of 20

C from point X and point Y?

14. In the circuit shown below, R represents an electric bulb. If the frequency of the supply is doubled, how shouldthe values of C and L be changed so that the glow in the bulb remains unchanged?

ORAn air cored coil L and a bulb B are connected in series to the ac mains as shows in the given figure :

The bulb glows with some brightness. How would the glow of the bulb change if an iron rod were inserted in thecoil? Give reasons in support of your answer. 2

15. Experimental observations have shown that X-rays(i) travel in vaccum with a speed of 3 x 108 ms-1,(ii) exhibit the phenomenon of diffraction and can the polarized.What conclusion can be drawn about the nature of X-rays from each of these observations? 2

16. Write the relation between the angle of incidence (i), the angle of emergence (e), the angle of prism (A) and theangle of deviation ( ) for rays undergoing refraction through a prism. What is the relation between and for rays undergoing minimum deviation? Using this relation, write the expression for the refractive index ( ) of thematerial of a prism in terms of and the angle of minimum deviation ( ) 2

17. A radioactive material is reduced to of its original amount in 4 days. How much material should one begin with

so that 4 x 10-3 kg of the material is left after 6 days. 2

18. Distinguish between ‘point to point’ and ‘broadcast’ communication modes. Give one example of each. 2

19. In a double slit interference experiment, the two coherent beams have slightly different intensitiesI and . Show that the resultant intensity at the maxima is nearly 4I while that at the minima is nearly

. 3

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20. An electric dipole of dipole moment is placed in a uniform electric field . Write the expression for the

torque experienced by the dipole. Identify two pairs of perpendicular vectors in the expression. Show

diagramatically the orientation of the dipole in the field for which the torque is (i) Maximum (ii) Half the maximumvalue (iii) Zero.

ORTwo capacitors with capacity C1 and C2 are charged to potential V1 and V2 respectively and then connected inparallel. Calculate the common potential across the combination, the charge on each capacitor, the electrostaticenergy stored in the system and the change in the electrostatic energy from its initial value. 3

21. Using a suitable combination from a NOR, an OR and a NOT gate, draw circuits to obtain the truth table givenbelow: 3

(i) (ii)

22. Which two main considerations are kept in mind while designing the ‘objective’ of an astronomical telescope?Obtain an expression for the angular magnifying power and the length of the tube of an astronomical telescope in its‘normal adjustment’ position. 3

23. Calculate the de-Broglie wavelength of (i) an electron (in the hydrogen atom) moving with a speed of of

the speed of light in vacuum and (ii) a ball of radius 5mm and mass 3 x 10-2 kg. moving with a speed of 100ms-1.Hence show that the wave nature of matter is important at the atomic level but is not really relevant at themacroscopic level. 3

24. Show that during the charging of a parallel plate capacitor, the rate of change of charge on each plate equals

times the rate of change of electric flux linked with it. What is the name given to the term ? 3

25. The spectrum of a star in the visible and the ultraviolet region was observed and the wavelength of some of thelines that could be identified were found to be :

.

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Which of these lines cannot belong to hydrogen atom spectrum? (Given Rydberg constant R = 1.03 X 107m-1 and

. Support your answer with suitable calculations. 3

26. What is space wave propagation? Which two communication methods make use of this mode of propagation? Ifthe sum of the heights of transmitting and receiving antennae in line of sight of communication is fixed at h, show that

the range is maximum when the two antennae have a height each.

27. Draw the transfer characteristics of a base biased transistor in its common emitter configuration. Explain brieflythe meaning of the term ‘active region’ in these characteristics. For what practical use, do we use the transistor inthis ‘active region’?

28. A cell of unkonown emf E and internal resistance r, two unknown resistances R1 and R2 (R2>R1) and a perfectammeter are given. The current in the circuit is measured in five different situations : (i) Without any externalresistance in the curcuit, (ii) With resistance R1 only, (iii) With resistance R2 only, (iv) With both R1 and R2 used inseries combination and (v) With R1 and R2 used in parallel combination. The current obtained in the five cases are0.42A, 0.6A, 1.05A, 1.4A, and 4.2A, but not necessarily in that order. Identify the currents in the five cases listedabove and calculate E, r,, R1 and R2.

ORDescribe the formula for the equivalent EMF and internal resistance for the parallel combination of two cells withEMF E1and E2 and internal resistances r1 and r2 respectively. What is the corresponding formula for the seriescombination? Two cells of EMF 1V, 2V and internal resistances 2 and 1 respectively are connected in (i)series, (ii) parallel. What should be the external resistance in the circuit so that the current through the resistance bethe same in the two cases? In which case more heat is generated in the cells ? 5

29. (i) Describe an expression for the magnetic field at a point on the axis of a current carrying circular loop.(ii) Two coaxial circular loops L1 and L2 of radii 3cm and 4cm are placed as shown. What should be themagnitude and direction of the current in the loop L2 so that the net magnetic field at the point O be zero?

OR(i) What is the relationship between the current and the magnetic moment of a current carrying circular loop? Usethe expression to derive the relation between the magnetic moment of an electron moving in a circle and its relatedangular momentum?(ii) A muon is a particle that has the same charge as an electron but is 200 times heavier than it. If we had an atomin which the muon revolves around a proton instead of an electron, what would be the magnetic moment of the

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muon in the ground state of such an atom?

30. (i) Derive the mirror formula which gives the relation between f, v and u. What is the corresponding formula for athin lens?(ii) Calculate the distance d, so that a real image of an object at O, 15cm in front of a convex lens of focal length10cm be formed at the same point O. The radius of curvature of the mirror is 20cm. Will the image be inverted oreract?

OR(i) Using the relation for refraction at a single spherical refracting surface, derive the lens maker’s formula.

(ii) In the accompanying diagram, the direct image formed by the lens (f = 10cm) of an object placed of O and thatformed after reflection from the spherical mirror are formed at the same point . What is the radius of curvatureof the mirror?

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SAMPLE PAPER IIIXII - PHYSICS

Time : Three Hours Max. Marks : 70

General Instructions :(a) All questions are compulsory.(b) There are 30 questions in total. Questions 1 to 8 carry one mark each, questions 9 to 18 carry two marks each,

questions 19 to 27 carry three marks each and questions 28 to 30 carry five marks each.(c) There is no over all choice. However, an internal choice has been provided in one question of two marks, one



c = 3 x 108ms-1

h = 6.6 x 10-34Jse = 1.6 x 10-19 C

=


Avogadro’s number NA = 6.023 x 1023/moleMass of neutron mn = 1.6 x 10-27 kgMass of electron me = 9 x 10 31 kg

1. The graph shown here, shows the variation of the total energy (E) stored in a capacitor against the value of thecapacitance(C) itself. Which of the two - the charge on the capacitor or the potential used to charge it is keptconstant for this graph?

1

2. An - particle and a proton are moving in the plane of the paper in a region where there is a unifom magentic field

( ) directed normal to the plane of the paper. If the two particles have equal linear momenta, what will be the ratioof the radii of their trajectories in the field? 1

3. State the condition under which a microwave oven heats up a food item containing water molecules mostefficiently. 1

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4. An electrical element X, when connected to an alternating voltage source, has the current through it leading the

voltage by radii. Identify X and write an expression for its reactance. 1

5. A double convex lens, made from a material of refractive index , is immersed is a liquid of refractive index

where . What change, if any, would occur in the nature of the lens? 1

6. The de Broglie wavelengths, associated with a proton and a neutron, are found to be equal. Which of the two hasa higher value for kinetic energy? 1

7. Carbon and silicon are known to have similar lattice structures. However, the four bonding electrons of carbon arepresent in second orbit while those of silicon are present in its third orbit. How does this difference result in adifference in their electrical conductivities? 1

8. An unknown input (A) and the input (B) shown here, are used as the two inputs in a NAND gate. The output Y, hasthe form shown below. Identify the intervals over which the input ‘A’ must be ‘low’.

1

9. The two graphs drawn below, show the variation of electrostatic potential (V) with (r being distance of the field

point from the point charge) for two point charges q1 and q2.

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(i) What are the signs of the two charges?

(ii) Which of the two charges has a larger magnitude and why? 2

10. Calculate the temperature at which the resistance of a conductor becomes 20% more than its resistance at 270C.

The value of the temperature coefficient of resistance of the conductor is . 2

11. A student records the following data for the magnitudes (B) of the magnetic field at axial points at differentdistances x from the centre of a circular coil of radius a carrying a current I. Verify (for any two) that theseobservations are in good agreement with the expected theoratical variation of B with x.

x = 0 x = a x = 2a x = 3a

2

12. An armature coil consists of 20 turns of wire, each of area A = 0.09m2 and total resistance 15.0 . It rotates in a

megnetic field of 0.5T at a constant frequency of . Calculate the value of (i) maximum (ii) average

induced emf produced in the coil 2

13. Two cells of emf E1 and E2 have internal resistance r1 and r2. Deduce an expression for equivalent emf of theirparallel combination.

ORA cell of emf (E) and internal resistance (r) is connected across a variable external resistance (R).Plot graphs to show variation of

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(i) E with R ,(ii) Terminal p.d. of the cell (V) with R 2

14. Fig. shows a light bulb (B) and iron cored inductor connected to a DC battery through a switch (S). 2

(i) What will one observe when switch (S) is closed?

(ii) How will the glow of the bulb change when the battery is replaced by an ac source of rms voltage equal to thevoltage of DC battery? Justify your answer in each case.

15. Electromagnetic radiations with wavelength 2(i) are used to kill germs in water purifiers.

(ii) are used in TV communication systems

(iii) play an important role in maintaining the earth’s warmth.Name the part of electromagnetic spectrum to which these radiations belong. Arrange these wavelengths indecreasing order of their magnitude.

16. What do the terms ‘depletion region’ and ‘barrier potential’ mean for a p-n junction? 2

17. We do not choose to transmit an audio signal by just directly converting it to an e.m. wave of the same frequency.Give two reasons for the same. 2

18. Light of wavelength 550 nm. is incident as parallel beam on a slit of width 0.1mm. Find the angular width and the linearwidth of the principal maxima in the resulting diffraction pattern on a screen kept at a distance of 1.1m from the slit. Whichof these widths would not change if the screen were moved to a distance of 2.2m from the slit? 2

19. The given figure shows the experimental set up of a metre bridge. The null point is found to be 60cm away from theend A with X and Y in position as shown.

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When a resistance of 15 is connected in series with ‘Y’, the null point is found to shift by 10cm towards the endA of the wire. Find the position of null point if a resistance of 3 O were connected in parallel with ‘Y’. 3

ORWhy is a potentiometer preferred over a voltmeter for determining the emf of a cell?Two cells of Emf E1 and E2are connected together in two ways shown here.

The ‘balance points’ in a given potentiometer experiment for these two combinations of cells are found to be at351.0cm and 70.2cm respectively. Calculate the ratio of the Emfs of the two cells.

20. When a circuit element ‘X’ is connected across an a.c. source, a current of A flows through it and this currentis in phase with the applied voltage. When another element ‘Y’ is connected across the same a.c. source, the same

current flows in the cricuit but it leads the voltage by radians.

(i) Name the circuit elements X and Y.(ii) Find the current that flows in the circuit when the series combination of X and Y is connected across the samea.c. voltage.(iii) Plot a graph showing variation of the net impedance of this series combination of X and Y as a function of theangular frequency of the applied voltage. 3

21. Give reasons for the following : 3(a) Astronomers prefer to use telescopes with large objective diameters to observe astronomical objects.(b) Two identical but independent monochromatic sources of light cannot be coherent.(c) The value of the Brewster angle for a transparent medium is different for lights of different colours.

22. The given graphs show the variation of the stopping potential Vs with the frequency ( ) of the incident radiationsfor two different photosensitive materials M1 and M2.

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(i) What are the values of work functions for M1 and M2?

(ii) The values of the stopping potential for M1 and M2 for a frequency of the incident radiations areV1 and V2

respectively. Show that the slope of the lines equals 3

23. What is a wavefront? Distinguish between a plane wavefront and a spherical wavefront. Explain with the help of adiagram, the refraction of a plane wavefront at a plane surface using Huygen’s construction. 3

24. Define the term ‘Activity’ of a radioactive substance. State its SI unit.

Two different radioactive elements with half lives T1 and T2 have N1 and N2 (undecayed) atoms respectivelypresent at a given instant. Determine the ratio of their activities at this instant. 3

25. (a) Draw the block diagram of a communication system.

(b) What is meant by ‘detection’ of a modulated carrier wave? Describe briefly the essential steps for detection.3

26. The given circuit diagram shows a transistor configuration along with its output characteristics. Identify(i) the type of transistor used and(ii) the transistor configuration employed.

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Use these graphs to obtain the approximate value of current amplication factor for the transistor at. 3

27. State Bohr’s postulate for the ‘permitted orbits’ for the electron in a hydrogen atom.

Use this postulate to prove that the circumference of the nth permitted orbit for the electron can ‘contain’ exactlyn wave lengths of the deBroglie wavelength associated with the electron in that orbit. 3

28. Obtain an expression for the capacitance of a parallel plate (air)capacitor.The given figure shows a network of five capacitors connected to a 100V supply. Calculate the total charge andenergy stored in the network.

ORUse Gauss’s law to obtain an expression for the electric field due to an infinitely long straight uniformly chargedwire.

Electric field in the above figure is directed along + X direction and given by Ex = 5Ax + 2B, where E is in NC-1 andx is in metre, A and B are constants with dimensions Talking and B = 5NC-1 calculate.(i) the electric flux through the cube.(ii) net charge enclosed within the cube. 5

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29. (a) Draw the labelled diagram of moving coil galvanometer. Prove that in a radial magnetic field, the deflection ofthe coil is directly proportional to the current flowing in the coil.

(b) A galvanometer can be converted into a voltmeter to measure up to

(i) ‘V’ volts by connecting a resistance R1 in series with coil.

(ii) volts by connecting a resistance R2 in series with its coil

Find the resistance (R), in terms of R1 and R2 required to convert it into a voltmeter that can read up to ‘2V’ volts.

OR(a) Draw diagrams to depict the behaviour of magnetic field lines near a ‘ bar’ of:(i) copper(ii) Aluminium(iii) Mercury, cooled to a very low temperature (4.2K)

(b) The vertical component of the earth’s agnetic field at a given place in times its horizontal component. Iftotal intensity of earth’s magnetic field at the place is 0.4 G find the value of :(i) angle of dip(ii) the horizontal component of earth’s magnetic field.

30. (a) Draw a ray diagram to show the refraction of light through a glass prism. Hence obtain the relation for the angleof deviation in terms of the angle of incidence, angle of emergence and the angle of the prism.

(b) A right angled isosceles glass prism is made from glass of refractive index 1.5. Show that a ray of light incidentnormally on(i) one of the equal sides of this prism is deviated through 900

(ii) the hypotenuse of this prism is deviated through 1800

OR

(a) With the help of a labelled ray diagram, show the image formation by a compound microscope. Derive anexpression for its magnifying power.(b) How does the resolving power of a compound microscope get affected on

(i) decreasing the diameter of its objective?(ii) increasing the focal length of its objective?

Electrostatics

1. Three identical charges each +q are placed at the corners of an equilateral triangle of side d cm. Calculate the force on a +ve charge +2q at the centroid of the triangle. 2. Force acting on a charged particle kept between the pair of plates, having equal and opposite charge, is F. If one of the plates is removed, find the force acting on the same particle. 3. The plates of a parallel plate system are charged upto 100V. A 4mm thickness dielectric slab is inserted between the plates. Then to maintain the same potential difference, the distance between the systems plates is increased by 2mm. find the dielectric constant. 4. A point charge placed at any point on the axis of an electric dipole at some large distance experiences a force F. Find the force acting on the point charge when its distance from the dipole is quadrupled. 5. In the electric field of a point charge ‘q’, the four points A,B,C and D are equidistant from q, however AB>AC>AD. Calculate the work done in taking a unit charge along AB, AC and AD. 6. N identical spherical drops charged to the same potential ‘V’ is combined to form a big drop. Find the potential of the new big drop formed. 7. An electron is projected with an initial speed of 25×105 m/s directly towards a proton which is at rest. Initially the electron is supposed to be at a fairly large distance from the proton. Find the distance of the electron from the proton when its instantaneous speed becomes twice the initial speed. 8. Two conducting spheres one of radius 6cm and the other of radius 12cm each carrying 3×10-8C are placed very par apart. If these spheres are connected by a conducting wire, find the direction of motion and the magnitude of charge transferred. 9. A solid metal disc of radius ‘R’ rotates with constant angular velocity about its axis. Calculate the electric field ‘E’ at a distance ‘x’ from the axis and the potential difference ‘V’ between the centre and the edge of the disc. 10. Three charges of +0.1C each is placed at the corners of an equilateral triangle, 1m side. If energy is supplied at the rate of 1kW, how many days would be required to move one of the charges to the mid point of the line joining the other two? 11. A parallel plate capacitor is made by stacking ‘n’ equally spaced plates connected alternatively. If the capacitance between any two plates is ‘C’, determine the resultant capacitance of the combination. 12. A 10µF capacitor is connected in the circuit as shown in figure. Calculate the charge on the capacitor plate.

13. A parallel plate capacitor is filled with two dielectrics as shown in figure. Calculate the capacitance of the system.

14. A parallel plate capacitor with air as medium has a capacitance of 24µF. The capacitor is filled with three media K1==6 and K3=10 as shown in figure. What will be the capacitance of the system?

15. Can a metal sphere of radius 1cm hold a charge of 1coulomb? Justify your answer.

d/2

d/2

d=plate separation

Plate area=A

A

dK1

K2

K3

A B

10μF

3ohm (i-i1)

i1

6V2ohm

3ohm

16. What is the p.d across the capacitor and what is the energy stored in the capacitor shown below.

17. If one of the electrons of H2 molecule is removed we get a hydrogen molecules ion H2

+.In the ground state of a H2+ the two protons are separated by

roughly 1.5Å and the electron is roughly 1 Å from each proton. Determine the potential energy of the system. 18. When two capacitors are connected in series, the effective capacitance is 2.4µF and when connected in parallel, the effective capacitance is 10µF. Calculate the individual capacitances. 19. Two fixed charges -2Q and Q are located at the points with co-ordinates (-3a,0) and (+3a,0) respectively in the x-y plane. Show that all the points in the x-y plane where the electric potential due to the two charges is 0, lie on a circle. Find its radius and location of its centre. 20. Two square metallic plates of side 1.5m are kept 0.015m apart like a parallel plate capacitor, in air in such a way that one of their edges is perpendicular to an oiled surface in a tank filled with insulating oil. The plates are connected to a battery of EMF 600V. The plates are then lowered vertically into the oil at a speed of 0.002m/s. Calculate the current drawn from the battery during the process(dielectric constant of oil=12, ��× 10-12SI Units) 21. A charged particle is free to move in an electric field. Will it always move along the electric lines of force? 22. Two point charges ‘+q’ and ‘-q’ are placed at a distance‘d’ apart. What are the points at which the resultant field is parallel to the line joining the two charges? 23. Two copper spheres of same radii, one hollow and the other solid are charged to the same potential. Which of the two will have same charge? 24. You are given three capacitors of value 2µF, 3µF, 6µF. How will you connect them to a resultant capacity of 4µF? 25. Can you create an electric field in which all the lines of force are parallel but their density increases continuously in a direction perpendicular to the lines of force? Give reason. 26. Can you suggest an arrangement of three point charges separated by some finite distance that has zero electric potential energy? 27. Calculate the work done by the electric field of the nucleus in a complete circular orbit of an electron. Is their any change in this work if the orbit is elliptical? 28.The given graph shows the variation of charge ‘q’ verses potential difference for two capacitors C1 and C2 .The capacitors have same plate separation, but the

4μF

2V4V+5VA B

plate area of C2 is double that of C1.Identify the line in the graph corresponding to C1 & C2 and why?

29.Two identical charged spheres are suspended in air by strings of equal lengths and make an angle of 600 with each other. When suspended in a liquid of density 0.4g/cc,the angle remains the same. What is the dielectric constant of the liquid? Density of the material of the sphere=0.8g/cc. 30.Two deutrons are separated by a distance ‘r’ metre and have coulomb force=F. If two alpha particles are separated by a distance of 2r metre, find the force between the alpha particles. 31.Eight dipoles of charges of equal magnitude are placed inside a cube. Calculate the total electric flux coming out of the cube. 32.An inflated balloon is charged by rubbing with fur. Will it stick readily to a conducting wall or to an insulating wall? Give reason. 33.An electron moves a distance of 6cm when accelerated from rest by an electric field of strength 2x10-4 N/C. Calculate the time of travel. Given me=9x10-31kg, e=1.6x10-19C.34.Is the capacitance of a capacitor proportional to the charge Q ? Sketch a graph to show how the capacitance C of a capacitor varies with the charge Q given to it.

Current Electricity

1. In a hydrogen atom, an electron moves in an orbit of radius 4.8 x 10-11mwith a speed of 2.5 x 10 6 m/s. Find the equivalent current.

2. Plot of current I versus time interval is given below. Find the charge that flows through the wire during this time period

3. Amount of charge passing through the cross section of a wire is q(t)=at2+bt+c.Write the dimensional formula for a, b and c. If the values of a, b and c in SI unit are 6, 4, 2 respectively. Find the value of current at t=6 seconds.

4. Current through a wire depends on time as I=I0�� 0 =15A and

��

5. One metre long metallic wire is broken into two equal parts P and Q. The part ‘P’ is uniformly extended into another wire R. Length of R is twice the length of P and the resistance of R is equal to that of Q. Find the ratio of the resistances of P and R and also the ratio of lengths of P and Q.

6. The area of cross section , length and density of a piece of a metal of atomic weight 60 are 10-6 m2, 1.0 m and 5 x 103 kg/m3 respectively . Find the number of free electrons per unit volume of every atom that contributes one free electron. Also find the drift velocity of electron in the metal when a current of 16A passes through it. Avogadro no.=6x1023 per gram per mole.

7. An n-type Silicon sample of width 4x 10-3 m thickness 25x10-4m and length 6 X 10-2 m carries a current of 4.8mA.When the voltage is applied across the length of the sample what is the current density? If the free electron density is 1022 /m3 then find how much time does it take for the electrons to travel the full length of the sample?

8. The temperature coefficient of a resistance wire is 0.00125 C-1. At 300K its resistance is 1�� 2��

6

7.5

I(A

15 t(s)

9. The length and radii of 3 wires of same metal are in the ratios 2:3:4 and 3:4:5 respectively. They are joined in parallel and included in a circuit having 5A current. Find the current in each case.

10. In the circuit diagram the voltmeter reads 30V when connected across 400� �� connected across 300� ��

11. A galvanometer together with an unknown resistance in series is connected across 2 identical cells each of emf 1.5V. When the cells are connected in series the galvanometer records a current of 1A and when the cells are connected in parallel the current is 0.6 A .What is the internal resistance of each cell?

12. An electric bulb rated for 500 Watt at 100 V is used in circuit having a 200 V supply. Calculate the resistance R that must be put in series with the bulb s that the bulb delivers 500 watt.

13. A heater is designed to operate with a power of 1000 watt in a 100 V line. It is connected in combination with a resistance of 10 and a resistance R, to a 100 V mains in series. What should be the value of ‘R’ so that the heater operates with a power of 62.5 watt

14. An electric kettle has 2 heating coils. When one of the coils is switched on , the kettle begins to boil in’6’ min and when the other coil is switched on , the boiling begins in 8 min. In what time will the boiling begin if both the coils are switched on simultaneously : a)in series b)in parallel

15. One kilowatt electric heater is to be used with 220 V d.c supply. a)What is the current in the heater? b) What is its resistance? c) What is the power dissipated in the heater d) how much heat in calories is produced per second? e) How many grams of water at 1000C will be converted per minute into steam at 1000C with the heater? Radiation losses are negligible. Latent heat of steam = 540 cal /g.

16. The walls of a closed cubical box of edge 50 cm are made of a material of thickness 1mm and thermal conductivity 4x10-4 cal per sec per cm. per oC.The interior of the box maintained at 100 0C above the outside

60V

V

300� 400�

30V

temperature by a heater placed inside the box and connected across a 40V d.c source .Calculate the resistance of the heater.

17. A part of the circuit in a steady state along with the currents following in the branches, the values of the resistance etc is shown in the fig. Calculate the energy stored in the capacitor.

19.A potentiometer wire of length 100 cm has a resistance of 100��

connected in series with a resistance and a battery of emf 2V and of negligible internal resistance. A source of emf 10mV is balanced against a length of 40cm of the potentiometer. What is the value of the external resistance?

20.A battery of internal resistance r=4� ��

as shown in figure. What must be the value of R , so that maximum power is delivered to the network? What is the maximum power?

21. A battery of emf 2V and internal resistance 0.1 � �� charged by a current of 5A. What will be the direction of current inside the battery? What is the potential difference between the terminals of the battery?

22. Two wires A and B of the same material and having same length have their cross sectional area in the ratio1:4. What would be the ratio of heat produced in these wires when same voltage is applied across each?

23. Two wires of the same material having lengths in the ratio 1:2 and diameters in the ratio 2:3 are connected in series with an accumulator. Compute the ratio of p.d across the two wires.

24. If the current supplied to a variable resistor is constant, draw a graph between voltage and resistance.

25. Observations on a given device yielded the following current – voltage data.

Current (A) Voltage

1 19.7 2 39.4 3 59.1 4 78.8 5 98.5

Draw V-I graph using this data. What conclusion can you draw from the graph with regard to ohmic or non-ohmic nature of device?

26. Current voltage graphs for a given metallic wire at different temperatures T1

and T2 are shown in figure. Which of the temperatures T1 and T2 is greater?

27. V-I graphs for two resistors and their series combination are as shown in figure. Which one of these graphs represents the series combination of the other two? Give reasons for your answer.

28. Two metallic wires of the same material and same length but of different cross sectional areas are joined together.

1) in series

2) in parallel to a source of emf.

In which of the two wires will the drift velocity of electron be more in each of the two cases and why?

V

I 2

1

3

V

I

T1

T2

29. The resistivity of a material of a conductor of uniform cross section varies �� sion for the resistance of the conductor, if its length is “L” and area of cross section is “A”.

30. A uniform wire of resistance “R” is shaped into a regular “n” sided polygon, where “n” is even. Find the equivalent resistance between

1) opposite corners of the polygon

2) adjacent corners of the polygon.

31. Under what condition is the heat produced in an electric circuit

1) directly proportional

2) inversely proportional to the resistance of the circuit?

32. A 4� ��

twisted together. What will be its new resistance?

33. What is the safest voltage you can safely put across a 98 ��

resistor?

34. A student has two wires of iron and copper of equal length and diameter. He first joins the two wires in series and passes electric current through the combination which increases gradually. After that he joins the two wires in parallel and repeats the process of passing current. Which wire will glow first in each case and why?

35. A series combination of a 2K � ��

across a battery of emf 6V and negligible internal resistance. The potential drop across the 2 � ��

1. a 30K � � ��

2. a 1K � � ��

3. both these voltmeters connected across it.

If the voltmeter readings in the three cases are V1, V2 and V3 respectively,arrange these readings in descending order.

How will the three readings be compared with one another if the potential drop were measured across the series combination of the 2 K � �� 1K � ��

i.e. across A and B?

V

+ -

6V

30K �

2K �1K �

A B

V

1K �

V

+ -

6V

1K �

2K �

1K �A B

V

+ -

6V

30K �

2K �

1K �A B

1

MAGNETIC EFFECT OF ELECTRIC EFFECT

AND MAGNETISM

1) A closed loop PQRS is lying in a magnetic field B as shown in the following figure.

P I Q

B

600

S R

The loop carries a current I and total length L . Find the magnitude of magnetic force acting on each side of the loop.

(FPS = FQR = BIL ; FPQ = FSR)

2) A magnet was found to vibrate at a place with a time period of T.A piece of brass of same length ,breadth and mass was placed over the magnet.What will be the new time period?

� �� )

3) A hypothetical bar magnet AB is cut into t wo equal parts.One part is now kept over the other as shown. If M is the magnetic moment of the original magnet, what would be the magnetic moment of the following combinations so formed?

2

(i) (ii)

4) Identify the magnetic material which follows the graphical representation given below.Also locate any two inferences about the behavior of the material from the graph.

4.2K

Temp.

5) Identify the magnetic materials from the following curves.

Res

ista

nce

N S

N S

S N

N S

N S

3

I I

M

M

6) A hypothetical bar magnet AB is cut into t wo equal parts.One part is now kept near/over the other as shown. If M is the magnetic moment of the original magnet, what would be the magnetic moment of the following combinations so formed?

(i) (ii)

(iii)

7) A circular loop and a long wire are carrying currents I1 and I2respectivelly as shown.

N S

N SN S

N S

S S

N S N S

4

The distance between the centre of the loop and long wire is 2r, where r is radius of the

loop.If I2 = 1A, find out the value of I1 when the net magnetic field at the centre of the

loop is zero.

I1 O

I2

(I1 � ��

8) Nirmala records the following data for the magnitude B of the magnetic field at axial points at different distances ‘x’ from the centre of a circular coil of radius ‘r’ carrying a current ‘I’ . Verify for ,any two, that these observations are in good agreement with the expected theoretical variation of B with ‘x’.

X *P

I

9) Identify the magnetic material corresponding to the following curves

X X = 0 X = r X = 2r X = 3r

B B0 B0

O

r

5

(1) (2)

� �

T T

10) Two co-axial circular loops C1 and C2 of radii 5 cm and 7 cm are placed as shown . What should be the magnitude and direction of the current in the loop C2 so that the net magnetic field at the point O be zero?

7cm 5cm

O

C1 C2

11) A conductor when thermally heated possess large number of freely moving electron,even then no magnetic field is experienced near such a conductor.What do you conclude?

( Electrons move randomly on account of thermal energy. Magnetic field due to random moving electrons cancel out each other.So no magnetic field is experienced near a conductor in which no net current flows)

12) Net charge within a current carrying conductor is zero .State whether it experiences a force or not when placed in a magnetic field?

( In a current carrying conductor ,free electrons move with drift velocity while positive ions remains at rest. Free electrons

R=7

6

experiences a magnetic force while positively charged ions at rest does not experience magnetic force.)

13)

Suppose a helical metallic spring is suspended from the roof and a very small weight is attached to its lower end. What will happen to the spring when the current is passed through it? Justify your answer.

( As the currents flow in the same direction through parallel turns, each trurn attract each other ,as a result the coil contracts)

14) Current flows through a long and thick conductor. The magnetic field produced by the current carrying conductor is plotted against the distance from the centre of the conductor. What do you infer from the graph?

7

y

B

x

r

15) Identify the following curves and name it. The following curves are drawn for three different magnetic materials. Describe the nature of the magnetic materials.

Out of the three ,(i)name the curve which reperesents the material usually used for making Permanent Magnets.(ii) name the curve which reperesents the material usually used for making Temporary Magnets(electromagnets.)

16) A particle of mass m and charge q moves at right angles to a uniform magnetic field. Plot a graph showing the variation of the radius of the circular path described by it with the increase in its

8

(a) charge,(b) kinetic energy,where ,in each case other factors remain constant .Justify your answer.

17) A charged paricle having a charge q ,is moving with a speed v along the x-axis. It enters a region of space where an electric field E along y-axis and a magnetic field B are both present.

The particle, on emerging from this region, is observed to be moving along the x-axis only. Obtain an expression for the magnitude of B in terms of v and E. Also give the direction of B.

18) A long wire is first bent into a circular coil of one turn and then into a circular coil of smaller radius having n turns. If the same current passes in both the cases find the ratio of the magnetic field produced at the centers in the two cases.

19) Why is diamagnetism independent of temperature?

20) What is the magnetic field at the centre of the circular loop shown in figure?

21) A toroidal coil has N = 1200 turns average length of core l = 80 cm; cross sectional area A = 60 cm2 ;current I = 15 A. Compute B , H, total flux and energy density E.Assume an empty core.

�� m = -2 X 10-6)is used.

{ Hint: B = µ0 nI =2.8274334 mT; H = B/ µ0 = 2250 A/m; � � �� 2BH=3.180626 J/m3 } { When bismuth core is used the above values decreases slightly due to the diamagnetic material}

O

1

UNIT : 3 ELECTROMAGNETIC INDUCTION & AC CIRCUITS

1.A magnet is allowed to fall through a metallic ring.During fall what will be its acceleration? (Less than g)Can a choke coil can be used as a step-up and step-down transformer.Justify

2.A magnetic flux linked with a coil,in webers, is given the equation � �

4t2+2t+15.The magnitude of induced emf at t = 2 Sec. is how much?

3.A radio frequency choke is air cored whereas an audio frequency choke is iron-cored Give reason for this difference.

4.Define self-inductance in terms of work done against the induced emf.

(L = ; Self-inductance is defined as double the work done against the

induced emf in producing unit current in the coil itself)

5.A circuit with a vertical copper wire bends as shown supports a small wodden piece W which floats in mercury. What do you expect when key is closed and current flows through the circuit?

W

Hg

2

( The wodden block sinks when current flows through the circuit, as parallel wires

carrying currents in the opposite directions repel)

The given wave form shows the input current of a transformer.

I

t

6. Draw the wave form of out put current. Substantiate your answer

( 1800 phase diff.due to Lenz’s law)

7.An electron beam is deflected in a given field. Identify whether it is an electric field or a magnetic field in the following cases?

The trajectory of the beam is a parabola and its K.E changes.

8.The trajectory of the beam is circular and its K.E. remains the same.Justify your answer.

9.A resting electron near a stationery bar magnet does not set into motion. But a moving magnet near an electron set it into motion. Why?

10.An irreqularly shaped flexible current carrying loop when placed In an external magnetic field will assume a circular shape. Give reason

11.Three identical inductors L1 ,L2 and L3 are connected as shown is a part of a circuit.The magnetic field at the centre of inductor L1 is 0.2 Tesla. What is the magnetic field inside the inductor L2 ?

3

12.Alpha particles ( m = 6.68 X 10-27 Kg. , q = +2e ) accelerated through a potential difference V to 2 KeV, enter a magnetic field B = 0.2 T perpendicular to their direction of motion. Calculate the radius of their path.

(r = = 32 m.)

13. The above figure shows a horizontal solenoid connected to a battery and a switch.A copper ring is placed on a frictionless track near the solenoid, the axis of the ring being along the axis of the solenoid. What will happen to the ring as the switch is closed? Justify your answer.

14.A particle with charge ‘q’ and mass ‘ m’ is shot with kinetic energy K into the region between two plates as shown in the figure. If the magnetic field between the plates is B and as shown, how large must B be if the particle isj to miss collision with the opposite plate?

+ + +

q + + +*

+ + +

d

4

( Just to miss the opposite plate, the particle must move in a circular path with radius d so that Bqv = mv2/d, B = (2mK)1/2/(qd) )

15.In the following diagram, a proton of charge q and mass m is shot �� -directed field B. Show that the proton will spiral along the x-��

��

��

v

B �

+q X

16.For the circuit shown below, find the magnitude and direction the force on wire AC, wire BC and wire AB. Also show that net force is zero.

A

400

B I L

C B

17.A bar PQ of mass M is suspended by two wires as shown below. Assume that a uniform magnetic field B is directed into the page. Find the tension in each supporting wire when the current through the bar is I.

5

I

P I Q

L

{According to the RHR, the magnetic force ILB is directed upward. Equilibrium in the vertical direction yields 2T + ILB = Mg, so that T = (Mg – ILB)/2 }

18.A bar of mass M is suspended by two springs as shown below . Assume that a magnetic field B is directed out of the page. Each spring has a spring constant K . Describe the bar’s displacement when a current I is sent through it in the direction shown.

I

6

{Due to RHR the magnetic force ILB is directed downward. This constant force shifts

the equilibrium position downward by a displacement = (ILB)/2K }

19.Five very long , straight , insulated wires are closely bound together to form a small cable. Currents carried by the wires are I1 = 20A, I2 = -6A, I3 = 12A, I4 = -7A, I5 = 18A.Show that the magnetic field at a distance of 10 cm from the cable B = 74 µT.

20.An equilateral triangle is formed from a piece of uniform resistance wire. Current is fed into one corner and led out of the other as detailed in the figure below. Show that the current flowing through the sides of the triangle produces no magnetic field at its centre ‘O’ (the intersection of the medians).

A B

IA O IB

C

I IC

(Wires A and B are in series. IA = IB = I/3, IC = 2I/3.Wire C makes a contribution to the field at O whose magnitude is twice that of A or B. By RHR, directions of field due to

Wire A and B are directed down into the page. That due to wire C is upward. Net field at O is zero)

The axes of two magnets are collinear. One has poles of strength 80 Am separated by 125 mm, and the second has a magnetic moment of 12 A-m2 with poles of strength 160 Am. Find the attractive force between the magnets if the north pole of one is 45 mm from the south pole of the second.

7

0.045

S N S N N

80 0.125 80 160 0.075 160

{Resultant force F = 2 attractive forces + 2 repulsive forces = 520 mN (attractive ) }

21.In the following figure, the rectangular loop of wire is being pulled to the right, away from the long straight wire through which a steady current i flows upward as shown. Does the current induced in the loop flow in the clockwise sense or in the counter clockwise sense ? Justify

i

V

{Due to Lenz’s law , the magnetic field produced by the induced current must counteract the decrease in flux and hence it must be directed ino the plane of the figure(within the loop).So the induced current must be clock –wise.}

22.Determine the separate effects on the induced emf of a generator if (a) the flux per pole is doubled, and (b) the speed of the armature is doubled.

(In both the cases the induced emf doubles)

23.An electromagnet has stored 648 J of magnetic energy when a current of 9A exists in its coils.What average emf is induced if the current is reduced to zero in 0.45 s ?

8

(E = , L = 16 H and e = 320 V)

24.A 40 Ohm resistor is connected across a 15 V variable frequency electronic oscillator. Find the current through the resistor when the frequency is (a) 100 Hz and (b) 100KHz. What is the current if the 40 Ohm resistor is replaced by a 2 mH inductor?

{ With resistor ,current is same both for 100 Hz and 100kHz. With inductor , the current is 11.9 A and 11.9 mA respectively}

25.The current in a long solenoid of radius R and having n turns per unit length is given by I = i0 ��

near the centre. Find (a) the induced emf in the coil and (b) the mutual inductance between the solenoid and the coil.

� �� 0 i0��2�� 0 nNR2 }

Give the condition for a current carrying loop not to rotate in a magnetic field

26.A coil A is connected to voltmeter V and the other coil B to an alternating current source D. If a large copper sheet CC is placed between the two coils, how does the induced e.m.f in the coil A change due to current in coil B?

9

Coil A with Voltmeter

C C

Coil B with AC source

(The induced e.m.f in coil A decreases due to large copper plate introduced between the two coils as Cu is diamagnetic material)

27.A magnet is moved in the direction indicated by an arrow between two coils A and B as shown below.Suggest the direction of induced current in each coil

V

10

Coil A

Coil B

( Due to Lenz’s law, end A will behave as south pole and end B will behave as north pole.The end face A will have clock wise direction of current and end face B will have anti clock wise direction of current when seen from the magnet side.)

28.An LC circuit contains a 20 mH inductor and a 50 µF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0

What is the total energy stored initially? Is it conserved during LC oscillations?

N

S

A

A

11

What is the natural frequency of the circuit?

At what time is the energy stored

(a)Completely electrical (stored in capacitor)

(b)Completely magnetic (stored in inductor)

29.At what time is the total energy share equally between the inductor and the capacitor?

If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat?

{Hint:

Total energy = 1/2Q02/C = 1J; Yes;

159 Hz

(c) Q = Q0��

I = dq/dt = I0��t): (i) At T = 0,T/2,T,3T/2,…… (ii) At T = T/4,3T/4,5T/4,…….

For this , the energy stored in the capacitor should become just half of its initial value .hence ,the time t =T/8,3T/8,5T/8,…..

If a resistor is inserted in the circuit, the energy stored will eventually be lost in the form of Joule’s heating}.

30.Determine the separate effects on the induced emf of a generator if (a) the flux per pole is doubled, and (b) the speed of the armature is doubled.

31.An electromagnet has stored 648 J of magnetic energy when a current of 9 A exists in its coils. What average emf is induced if the current is reduced to zero in 0.45 sec.

(Calculate = 16 H. e = L di/dt = 320 V)

E.M.WAVES

1.“Taller the antenna longer is the coverage of television broadcast”. Justify this statement with the help of a figure. 2.If vg, vx & vm represents the speed of gamma rays, X-rays & microwaves respectively then how will you how arrange these radiations according to there speeds in vacuum? 3.An amplitude modulating wave is produced by super imposing a signal of 300Hz on a carrier frequency of 3MHz. the amplitude of the resultant wave will vary with time with frequency equal to____________. 4. Give the value of impedance of a perfect conductor to EM waves. 5. At a particular instant electric field intensity in e.m.waves in vacuum is 2x10-3 N/C. Find the magnitude of magnetic induction of the wave. 6. A plane e.m.wave of frequency 20 MHz travels in free space along the

x direction. At a particular point in space & time B= 2.3x10-6 telsa. Find the value of electric field at this point. 7. The electric field in a plane electromagnetic wave is given by Ez = 60 sin (0.5X 103x+1.5X1011t) V/m. a) Determine the wavelength & frequency of the wave. b) Write an expression for the magnetic field. 8. How can you establish an instantaneous displacement current of 1.5A in the space between the two parallel plates of 3 μF capacitor? 9. A capacitor is made of two circular plates each of radius 10cm & is separated by 6mm. The capacitor is being charged by an external source. The charging current is constant & is equal to 0.1 A. using ampere’s law, calculate magnetic field between the plates at a point. a) on the axis b) 8.5cm from the axis c) 16cm from the axis. 10. Which of the following if any can act as a source of e.m.waves. Give reason. a) A charge at rest. b) A charge moving in circular orbit. c) A charge moving with constant velocity. 11. An electromagnetic radiation has energy 11KeV. To which region of e .m. spectrum does it belong to? Give any two uses of this radiation.

12. What is the condition of the electrons in the transmitting antenna when maximum magnetic field is being transmitted? A maximum current is flowing, so the electrons have maximum speed up and down the antenna. The electric current produces the magnetic field. 13. How can the electric portion of the electro-magnetic wave be detected?

It can be detected by an antenna similar to the transmitting antenna except that a detector of electric current replaces the voltage source. 14.The small ozone layer on the top of the atmosphere is crucial for human survival. Why? The ozone in the atmosphere is confined to the ozone layer, some 50-80 km above the ground. The ozone layer blocks the passage of the ultra-violet radiations; x-rays and y-rays from the solar and other extra-terrestrial sources and effectively protects us from the dangerous and harmful portions of solar radiations as they cause genetic damages to living cells. Practically all radiations of wave length less than 3 x 10-7m are absorbed by the ozone layer. This explains why ozone layer on the top of the atmosphere is crucial for human survival. 15.How does "Green House Effect" affect the temperature of the earth's surface ? Green house effect serves to keep the earth's surface warm at night. 16.How do we make television broadcasts for larger coverage and for long distance? By using (i) tall antennas which is familiar landmark in many cities and (ii) using artificial satellites —called geostationary satellites. Since television signals are of high frequency and are not reflected by ionosphere so we use satellites to get them reflected & transmission of TV signals can be used for larger coverage as well as for long distance. 17. Scientists put x-ray astronomical telescope on the artificial satellite orbiting above the earth's atmosphere whereas they build optical and radio-telescopes on the surface of the earth. Why ? X-rays have very high frequency and much smaller wavelength. These rays get absorbed by the earth's atmosphere. On the other hand, optical (visible) radiations and radio-waves can pass through the atmosphere. That is why optical and radio telescopes can be installed on the earth's surface. 18. For an electrom agnetic w ave, w rite the relationship betw een am plitude of electric and m agnetic fields in free space.[H ints If E o is the am plitude of an e lectric field and B o is the

am plitude of the associated m agnetic fie ld in free space then 0

0

BEc =

w here c is the speed of light in free space i.e . 3x108 m /s.19. The charging current for a capacitor is 0.25 A. What is the displacement current across its plates? Hints: Displacement current = Charging current = 0.25 A] 20. Why short wave communication over long distances is not possible via ground waves? |Hints: Because the wave gets attenuated.] 21. Are conduction and displacem ent currents the sam e? [Hint: No; they are different but they are equal .

22. It is necessary to use satellites for long distance TV transm ission. W hy? It is so because television signals are not properly reflected by the ionosphere. Therefore, for reflection of signals satellites are needed as reflection is effected by satellites. 23. Optical and radio telescopes are built on ground but X-ray astronom y is possible only from satellites orbiting the earth. W hy? Atm osphere absorbs X-rays, w hile visible and radiow aves can penetrate it. That is w hy optical and radio telescopes can w ork on earth's surface but X-ray astronom ical telescopes m ust be used on satellites orbiting the earth. 24. If the earth did not have an atm osphere, w ould its average surface tem perature be higher or low er than w hat it is now ? Ans. The tem perature of the earth w ould be low er because the green house effect of the atm osphere w ould be absent. .25. W hat is the equation for the speed of electrom agnetic w aves in free space?

C=00

1εμ

26. The w avelength of electro m agnetic radiation is doubled. W hat w ill happen to the energy of the photon? The energy w ill be halved because frequency w ill be halved. 27. Nam e the part of electrom agnetic spectrum to w hich w aves of w avelength (i) 1A° and (ii) 10-2 m belong. Using the relation λT = (0.29 cm ) K, obtain the characteristic kelvin tem perature corresponding to these tw o w avelengths. (i) X-rays, (ii) M icrow aves

Again, (i) Kcm

cmT 810 1029

10129.0 −

− ×=×

= (ii) Kcm

cmT 29.0129.0 ==

28. Show that the average energy density of the E field equals the average energy density of the B field .

Ans. Energy density in E field, 2

021 EuE ε=

Energy density in B field,-------------- 2

021 BuB μ

=

Using E = cB and c =00

1εμ

, uE = uB.

29. On w hat factors does its velocity in vacuum depend? Ans. Electrom agnetic w aves consist of sinusoidal variation of electric and m agnetic field vectors. The field vectors vibrate w ith the sam e frequency and are in the sam e phase. The field vectors and the direction of propagation are all m utually perpendicular. The velocity

of electrom agnetic w aves in vacuum depends upon absolute

perm eability μo and absolute perm ittivity ε0.Note that c =00

1εμ

30. W hat is the nam e associated w ith the follow ing equations?

0.)(.)(0


ε



��

(i) Gauss's law (ii) No particular nam e (iii) Faraday's law (iv) Am pere's law . 31. E lectrom agnetic w aves w ith w avelength (i) λ1are used to treat m uscular strain (ii) λ2 are used by a FM radio station for broadcasting (iii) λ3 are used to detect fracture in bones (iv) λ4 are absorbed by the ozone layer of the atm osphere. Identify and nam e the part of the electrom agnetic spectrum to w hich these radiations belong. Arrange these w avelengths in decreasing order of m agnitude. Ans. (i) λ1 -»infrared (ii) λ2 -» radiow aves (iii) λ3 — > X-rays (in) λ4 — > ultra-violet rays λ2 > λ1 > λ4 > λ3.32. If you find closed loops of B in a region in space, does it necessarily m ean that actual charges are flow ing across the area bounded by the loops? Ans. Not necessarily. A displacem ent current such as that betw een the plates of a capacitor that is being charged can also produce loops of B • 33. A closed loop of B is produced by a changing electric field. Does

it necessarily m ean that E and dtdE are non-zero at all points on the

loop and in the area enclosed by the loop? Ans. Not necessarily. All that is needed is that the total electric flux through the area enclosed by the loop should vary in tim e. The flux

change m ay arise from any portion of the area. Elsew here E or dtdE

m ay be zero. In particular, there need be no electric field at the points w hich m ake the loop. 34. W hy is it that induced electric fields due to changing m agnetic flux are m ore readily observable than the induced m agnetic fields due to changing electric fields? Ans. The m agnitude of the m agnetic field due to displacem ent current is too sm all to be easily observable. This effect can of course be increased by increasing the displacem ent current. [In an AC circuit, this can be done by increasingω.]

On the other hand, the effect of induced electric field due to changing m agnetic flux can be increased sim ply by taking m ore and m ore num ber of turns in the coil. The induced em fs in different turns of the sam e coil add up in series. 35. A variable-frequency AC source is connected to a capacitor. W ill the displacem ent current increase or decrease w ith increase in frequency? Ans. Increase in frequency causes decrease in im pedance of the capacitor and consequent increase in the current w hich equals displacem ent current betw een the plates. 36. Som e scientists have predicted that a global nuclear w ar on the earth w ould be fo llow ed by a severe 'nuclear w inter' w ith a devastating effect on life on earth. W hat m ight be the basis of th is prediction? Ans. The clouds produced by a global nuclear w ar w ould perhaps cover substantial parts of the sky preventing solar light from reaching m any parts of the globe. This w ould cause a 'w inter'.

37. What is the contribution of the Greenhouse effect towards the surface temperature of the earth? Ans. The infrared radiation emitted by the earth's surface keeps the earth warm. In the absence of this effect, the surface temperature of earth would be lower. 38. Why the small ozone layer on top of the stratosphere is crucial for human survival? Ans. The small ozone layer on the top of the stratosphere absorbs ultraviolet radiations, y-rays etc. from the sun. It also absorbs cosmic radiations. So, these radiations, which can cause genetic damage to the living cells, are prevented from reaching the earth. Thus, the small ozone layer on top of the stratosphere is crucial for human survival. 39. Given below are some famous numbers associated with electromagnetic radiation in different contexts in physics. State the part of the e m spectrum to which each belongs. (i) 21 cm (wavelength emitted by atomic hydrogen in interstellar space). (ii) 1057 MHz [frequency of radiation arising from two close energy levels in hydrogen; known as Lamb shift]. (Hi) 2.7 K temperature associated with the isotropic radiation filling all space-thought to be a relic of the 'big-bang’ origin of the universe. (iv) 5890 A - 5896 A [double lines of sodium]. (v) 14.4 keV [energy of a particular transition in 57Fe nucleus associated with a famous high resolution spectroscopic method (Mossbauer spectroscopy). Ans. (i) Radio (short wavelength end) (ii) Radio (short wavelength end) (Hi) Microwave (iv) Visible (Yellow) (v) X-rays (or soft y-ray) region. 40. Electromagnetic waves in a cavity with conducting walls can exist only in certain modes i.e., they cannot exist, for example, with any arbitrary wavelength. Suggest a simple reason why this should be so.

Ans. The waves must satisfy a boundary condition. The electric field should be zero on the walls of the conductor. This restricts the possible modes. [It is something like the restricted modes of a string fixed at two ends.]

57

OPTICS

1. Light from sodium lamp passes through a tank of glycerin (μ = 1.47 ) 20 m long in a time t1. If it takes a time t2 to traverse the same tank when filled with carbon disulfide (μ = 1.63 ) determine t2 - t1

1) t1= 20/(c/n) = 20 X (1.47) /c t2= 20 X (1.63) / c

t2-t1=20(1.63-1.47) / C

=1.07 X 10 -8

2.Light passes from air into liquid and is deviated 19 0 when the angle of incidence is 52 0 . What is the refractive index of liquid. 2)

θ2 =52-19 =33 μ=SIN 52/SIN 33 =1.45

3.What angle of incidence should a beam of light strike the surface of a still, pond if the angle between the reflected ray and refracted ray is to be 900.

3) θ +Φ =90 Φ =90 - θθ=TAN-1 (μ)=53

58

4. In what direction does the fish see the setting sun. The refractive index of water is 4/3 and air is 1.

4)

θ2=Sin-1 (3/4)=48.6

hence the fish perceives the sun at 90 – 48.6 = 41.4 above the horizontal

5.A layer of benzene (μ = 1.5 ) floats on water . If the angle of incidence of the light entering the benzene from air is 600.What is angle of light makes with the vertical in the benzene and in the water.

5)

59

nb =1.5 =sin60 /sin θ2 ; θ2=35 nw / nb =sin θ2/sin θ3 =1.33/1.5

6.A man is shaving with his chin 0.4m from a concave magnifying mirror. If the linear magnification is 2.5. What is the radius of curvature of the mirror. 6) 1/0.4 + 1/-1 =1/f

f=1/1.5 R=2f=1.33m

7A doctor looks through a small hole at the vertex of a cancave mirror to examine a sore throat. If the R of the mirror is 462mm and the light source is 1m from the mirror, how far from the throat should the mirror be if the light source is to be imagined on the inflamed area. 7) f=462/2=231mm

u=1mm v=300.4mm

8.A object is placed infront of a concave mirror having a radius of curvature 0.3 m. If you want to produce first real and then virtual image 3 times as high as the object find the object distance in each case.

60

8) Real image =0.200m, Virtual image =0.100 m

9.Where must an object be placed in the case of the converging lens of focal length “f” if the image is to be virtual and 3 times as large as the object.

3= hi /ho = -v/u u= 2f/3

10.A man who wears glasses of power 3D must hold a news paper at least 25cm away to see the print clearly. How far away would the news paper have to be if he took off the glasses and still wanted clear vision.

3= hi /ho = -v/u u= 2f/3

11.If a beam of polarized has one tenth of its initial intensity after passing through an analyzer. What is the angle between the axis of the analyzer and initial amplitude of the beam. I = 0.1 I0 = I0 cos2 θ

cosθ= 0.316 θ=71.6

12.Two wavelengths 1 and 2 are used in the double slit experiment . If one is 430nm what value must the other have for the fourth order bright fringe of one to fall on the sixth order bright fringe of the other.

4λ1/d=x/D 4λ1=6λ26λ2/d=x/D if λ2=430, λ1=645nm

if λ 1=430, λ2 =287nm

13.The amplitude of a beam of polarized light makes an angle of 650 with axis of a Polaroid sheet. What fraction of the beam is transm itted through the sheet. I1/I=cos2θ , cos265=0.179

61

14 .What is the effect on the interference fringes in a Y. D .S experiment due to

a) the screen is moved away from the plane of the slits. b) Source is replaced by another source of shorter

wavelength. c) If the separation between is increased d) The source slit is moved closer to the double slit

plane e) The width of the source slit is increased f) The width of the slits increased g) When monochromatic source is replaced by white

light a. Angular separation of the fringes remains constant b. separation of the fringes decreases c. separation of the fringes decreases d. S/D< λ/d otherwise no pattern is observed. e. if above condition is not satisfied interference pattern disappears. f. increases the brightness of the fringes. g. clear fringes are not observed.

15..When a low flying air craft passes over the head we some times notice slight shaking of the picture on our TV screen. Explain. . interference of the direct signal received by the antenna with the signal reflected by the aircraft.

16...An object is placed between two plane parallel mirror. How many images do you expect to see) N=(360/θ)-1

17 .A ray is incident on a plane mirror at an angle X with normal. Find the angle of deviation of the ray

the ray deviated by an angle 180-2x.18.An equi convex lens of focal length 15cm is cut into two halves. What is the focal length of each half. 1/15=1/x-1/x , x=30cm

62

19.What is effect of temperature variation on the refractive index of a medium 19. as the temperature increases μ decreases.

20The surface of a goggle lens are curved, even though it does not have any power why? . R1=R2=R , P=1/f=(μ-1)(1/r-1/r)

p=021. A lens is made of two different transparent materials. How many images of a point object will be formed when the object is placed on the principal axis.

.22 How does an air bubble behaves inside water. behaves like concave lens.

23. What distance from the lens the image is formed when the object is placed at the focus of a concave lens. .v=-F/2

24 What do you understand by the ‘coma’.

63

optical defect in which point object of the optic axis focuses not in to a point image butto a comet like surface.

25Why are images in toy telescope usually coloured. lens are not achromatic lenses hence they possess chromatic aberration.

26.Parallel beam of light is incident on the system of two convex lenses of focal length 20 cm , 10cm . What should be the distance between the two lenses so that the rays after refraction from both the lenses pass undeviated. 27.A pipe 4m high driven into the bottom of a lake is 1m above the water. Determine the length of the shadow of the pipe on the bottom of the lake if the sun rays make an angle of 450 with water surface the refractive index of water is 4/3.

2.88m 28.A fish is rising up vertically inside a pond with a velocity 4 cm/s and notices a bird, which is diving downward and its velocity appears to be 16cm/s. What is the real velocity of diving bird if refractive of water is 4/3. 9 cm/s

29.Two thin converging lenses are placed on a common axis so that centre of one of them coincides with the focus of the other. An object is placed at a distance twice the focal length from the left hand lens. Where will its image be? What is the lateral magnification if the focal length of each lens is f. Image is at distance of f/2 from the right hand lens and m=-0.5.30.In an equilateral prism a ABC of μ = 1.5 the condition for minimum deviation is fulfilled . If face AC is polished find a) Net deviation. b) if the system is placed in water what is net deviation. The refractive index of water is 4/3 a) 157.2 b) 128.4

31.Maximum intensity in YDS experiment is I0. Find the intensity at a point on the screen a) the phase difference between the two �� length.

31. a) ¾ xI0 b) I0/232.A thin glass lens of refractive index μ 2 = 1.5 behaves as a interface between two media of refractive indices μ1 = 1.4 and

64

μ3 =1.6 respectively. Determine the focal length of the lens if the radius of curvature of the both the surfaces is 20cm.

f=infinity

33.In YDSS experiment ,what should be the thickness of the glass slab μ= 1.5 which should be placed before the upper slit s1so that the central maxima now lies at a point where 5th bright fringe was lying earlier?( wave length of light is used is 5000A) ( 50000 A)

34.At what angle above the horizon is the sun when a person receiving its rays from calm water ( μ = 1.327 ) finds them linearly polarized ( Tan53 0 = 1.327 ) (37) 35.In a single slit diffraction experiment the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band. (Size reduce by half and intensity increases by 4 folds) 36.When a tiny circular obstacle is placed in the path of light form a distant source, a bright spot is seen at the centre of the shadow of the obstacle explain why.

65

(Waves diffracted from the edge of the circular obstacle interfere constructively at the centre of the shadow producing bright spot.)

37. The sun subtends an angle of 0.50 on earth. What should be the radius of curvature of the mirror which produces an image of the sun 2 cm in diameter.

458 cm

38. What should be the angle between two mirrors sothat a ray parallel to one mirror may come out parallel to other mirror after one reflection from each mirror? How many images will be formed by the mirrors?

60.5 39.One face of a prism of μ= 1.5 and angle 750 is covered with a liquid of μ = 3 �� light on the clearface of prism for which the light is just totally reflected at the liquid covered face. sin-1 (3/4)

40.An astronaut photographs a bridge at a height of 1 km with a camera having a lens of focal length 50 cm. Size of the bridge on the photograph is 5 cm. Find the actual length of the bridge.

41.Two coherent monochrometic light beams of intensities I and 4I are superimposed. What is the maximum and minimum possible intensities in the resulting beam

9I,I ; Imax/ Imin= ((I1)1/2 + (I2 )1/2)2 / ((I1)1/2 - (I2 )1/2)2

42.In a double slit experiment two coherent sources have slightly different intensities I and I+dI such that dI < I. Show that resultant intensity at maxima is nearly 4I while that at the minima is nearly (dI)2 / 4I

43.Following data was recorded for values of object distance and the corresponding values of image distance in lthe

66

experiment on study of real image formation by a convex lens of power +5D. One of these observations is incorrect Identify and give reason.

I II III IV V VI Object distance

25 30 35 45 50 55

Image distance

97 6 37 35 32 30

f=1/p=0.20m=20cm Sr no. 3 is incorrect

43.PQR is right angled prism with other angles as 60 and 30 refractive index of prism is 1.5. PQ has a thin layer of liquid . Light falls normally on the face PR . Calculate the max refractive index of the medium TIR.

i should be greater than C

=> C<60° i.e, C max=60°

44.Consider coaxial system of two thin convexlenses of focal length f each separated by a distance d. Draw a ray diagram for image formation corresponding to an object at infinity placed on the principal axis in the following cases. (i) d< f (ii) d=f (ii) f<d<2f (iv) d=2f (v) d>2f.

67

2)d=f

3)f<d<2f

68

4)d=2f

69

5)d>2f

45. When a ray of light enters a glass slab from air. How its wavelength is affected ? �� decreases.

46.A partially plane polarized beam of light is passed through a Polaroid. Show graphically the variation of transmitted light with angle of rotation of Polaroid. 47. Give conditions in which a thin lens has a lateral magnification of -1? If the object is lying at a distance of double the focal length (2f) of a lens from the

lens. 48.Why scratches on the lens of a photographic camera do not appear on the photograph. .A camera has to photograph only those objects whose image is focused on the photographic film by the lens .The scratches on the lens do not satisfy this condition so they do not appear on the film. 49.How can you produce dispersion without deviation.Violet light is incident on the thin convex lens. If this light is replaced

70

by the red light. Explain with reason how the power of the lens would change? 50.A convex lens and concave lens, each having focal length 50cm are placed in contact. What is the focal length and power of combination. 51We have right angled isosceles prism, μ= 1.5. If we make incident ray of light normally on the two perpendicular surfaces. Name the phenomenon which occurs?

52.A parallel beam is incident on a convex lens of focal length f. It is then put in contact with a concave lens of focal length f/2. What will happen to its image. 53.The satellite takes 12h to rotate once about its axis . How much time does the sun take to shift by 10 when viewed from the satellite.

3600 = 12 h , 10 =360/ 12 , 8 minutes

54.How does the resolving power of microscope affects when (a)wave length of illuminating radiation decreased. (b)the diameter of the objective lens is decreased. 55.A Cassegrain telescope two mirrors such telescope is built with the mirror 20mm apart. If the radius of curvature of larger mirror is 220 mm and smaller mirror is 140 mm. Where will be final image of an object at infinity be? 1.5 m

54.A concave mirror and concave lens are held in water. What happens, in their respective focal length as compared to their values in air. 55. Two plane mirrors are arranged at right angled to each other. �� !�� reflection from the vertical mirror.

71

makes same angle

56.The refractive index of the prism is 2. Find maximum refracting angle of the prism. � ��

-1��

0

�� 0

57.One of the refracting surfaces of a prism of angle 30 is silvered. A ray of light incident at an angle of 60 retraces its path. Find the refractive index of the prism.

r2 = 0, r1 =A=300� ��

58,angle of minimum deviation is equal to the angel of prism A of an equilateral glass prism Find the angle of incidence at which minimum deviation occurs.��M�� m)/2 – 60

59.A plane mirror is made of glass slab u= 1.5 , 2.5 cm thickness and silvered on back. A point object is placed 5 cm infront of the unsilvered face of the mirror. What will be the position of the final image. .

72

i1,i2,i3 be image formed by 1)refraction from ABC . 2)refraction from DEF. 3)again refraction from AB.

BI1=5µg=7.5, EI1=2.5+7.5=10 EI2=10cm behind the mirror BI2=10+2.5=12.5 BI3=12.5/1.5=8.3

60.A 2 cm diameter coin rest flat on the bottom of a bowl in which water is 20cm deep, μ = 4/3 If the coin is viewed directly above . What is the apparent diameter. 61.Parallel beam of light is incident on the system of two convexlenses of f1 = 20 cm. f2 = 10 cm . What should be the distance between the two lenses so that the rays after refraction from both the lenses pass undeviated.

73

62 A point object is placed at a distance of 25 cm from a convex lens of f = 20 cm. If the glass slab of thickness t , μ = 1.5 is inserted between the object and lens, the image is formed at infinity, what is thickness? shift, 25-20=(1-1/µ)t t=15cm

63. A plano convexlens fits exactly in to a plano concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials of refractive indices μ1 and μ2 , R is radius of curvature then what is the focal length of the combination.

74

1/f=1/f1+1/f2��1-1)(1/��2-1)((1/-r)-1/��1-�2)

64 A plano convexlens μ = 3/2 and R = 10 cm is placed at a distance of b from a concave lens of focal length 20 cm . What should be the distance of a point object O from the plano convexlens sothat the position of final image is independent of b.

1/f=(3/2-1)*(1/10-1/∞) =20cm

65.A convexlens of focal length 10 cm is painted black at the middle portion for 2 cm. An object is placed at a distance of 20 cm from the lens then how many images are formed.

75

only one image will be formed because optic axis &both parts coincide. If optic axis are different two images would have formed

66.Two sources S1 and S2 are 24 cm apart where should a convex lens of focal length 9 cm be placed in between them sothat the images of both sources are formed at the same place? if image of s1 is real and s2 is virtual for s1=1/y+1/x=1/9 for s2=-1/y+1/(24-x)=1/9 x=6cm

67.The angle of incidence for equilateral prism is 60. What should be the μ of prism sothat the ray is parallel to the base inside the prism at minimum deviation r1=r2=a/2=30

��

68.What is the minimum value of the refractive index for a 90 – 45 – 45 prism which is used to deviate a beam through 90 by TIR. at AC µ=1/sin45 =��

69. A point object is placed on the optic axis of a convex lens of focal length f at a distance of 2f to the left of it. The diameter of the lens is d. An eye is placed at a distance of 3f to the right of the lens and distance h below the optic axis . What is the maximum value of h to see the image.

76

h/(d/2)=f/2f h=d/4

UNIT – VII DUAL NATURE OF MATTER AND RADIATIONS (4marks)

VERY SHORT ANSWER TYPE QUESTIONS:-

1. An electron and photon have same wavelength. Which one of the two has more energy? Relativistic energy of a particle, E= (m0c4+p2c2)½Hence the electron has more energy than photon.

2. If wavelength of electromagnetic waves are doubled what will happen to energy of photon? E = hν�

�� ∝ ��

3.Alkali metals are most suitable for photoelectric emission. Why? Alkali metals have too low work functions. Even visible light can eject electrons from them.

4. Out of microwaves, UV, IR which radiation will be most effecting for emission of electrons from a metallic surface? UV are most effective since they have highest frequency hence more energetic.

5. If the intensity of incident radiation on a metal is doubled what happens to the K.E of electrons emitted? K.E of photons remains unaffected since they do not depend

6. What is the value of stopping potential between the cathode and anode of photocell? If the max K.E of electrons emitted is 5eV? Stopping potential V0 = Kmax/e = 5ev/e =5 V

7. It is easier to remove an electron from sodium than from copper, which has a higher value of threshold wavelength? w0 = hν0 = hc/λ0 ∴λ0 ∝ 1/ w0 Since sodium has lower work functions than copper it is easier for electron ejection. As it is lower work function, higher wavelength.

8. An electron and proton possessing same K.E. Which one will have greater wavelength? 1/2 mv2 = (m2 v2)/2m = p2/2m

λe > λp

electrons have greater De broglie wavelength than proton .

9. In Davisson – Germer experiment if the angle of diffraction is 520 find Glancing angle? θ = 90 - φ/2 = 90 – 52/2 =64°

10. What is the effect on the velocity photo electrons, if the wavelength of incident light is decreased? KE of photoelectrons is given by Einstein’s photoelectric equation. Ek =1/2 mv2 = h�- w0

� � �� As wavelength decreases velocity increases.

11. The stopping potential for some material is 1.2 V. What is the energy range of the emitted photoelectrons? The range of energies of the emitted photoelectrons will be from 0 to 1.2 eV.

12.The intensity of incident radiations in a photoelectric experiment is doubled. How the stopping is potential affected? The stopping potential will remain unaffected because it does not depend on the intensity of the incident light.

13. If the intensity of the incident radiation on a metal is doubled, what happens to the kinetic energy of the emitted photoelectrons? There is no change in the kinetic energy of the emitted electrons. This K.E. is independent of the intensity of the incident radiation as long as its frequency remains the same.

14. The frequency (υ) of incident radiation is greater than threshold frequency (υq) in a photocell. How will the stopping potential vary if frequency (υ) is increased, keeping other factors constant? When, (υ >υo) stopping potential will be increased.

15.What is the energy and wavelength of a thermal neutron ? Kinetic energy of a thermal neutron = f/2 kBT. Since degree of freedom of a thermal neutron is three. K.E = 3/2 kBT = 6.06 x 10-21 J Wave length � �e = h/(2mK.E)1/2 � � �e = h/(3m kBT)1/2=0.147nm.

16. An X –ray tube produces a continuous spectrum of radiation with its shots wavelength end 0.45 °A. What is the maximum energy of a photon in the radiation in electron volt?(ii) From your answer to (i) what order of accelerating voltage (fo0r electron) is required in such a tube?.

� � �� 3 eV (ii)In this case energy of X-rays photon is 27.6 KeV, the striking electron must be of energy higher than 27.6 KeV. Therefore an accelerating voltage of the order of 30 KV is required.

17. It is difficult to remove free electrons from metal X as compare to metal Y . What you infer? Work function of metal X is higher than metal Y.

18. A particle behaves like a wave. What determine the wavelength of the wave? Momentum of the moving particle.

19. Draw a graph giving variation of maximum kinetic energy of photoelectrons with frequency of incident radiations. What is the slope of this graph? The equation of this straight line is K.E. = 1/2mv2

max= h (υ - υo)

20. The wavelength of radiations incident on a material is decreased. Does the maximum velocity of photoelectrons increase or decrease? A decrease in wavelength implies an increase in frequency. Since an increase in frequency increases the maximum K.E. of the emitted photoelectrons, the maximum velocity would increase.

21. For photoelectric effect in sodium, the figure shows the plot of cut off voltage versus frequency of incident radiation. Calculate the threshold frequency (υ0) the work function for sodium (ii)The work function (W) is related to the threshold frequency (υ0) by the relation. Wo = hυo = 6.6 x 10-34 x 4.5 x 1014 J = 29.7 xl0-20J = 2.97 xl0-i9J

eV1.856V

101.610 x 2.97

19-

-19

≈×

= e

22. Suppose the photoelectric effect occurs in a gaseous target rather than a solid. Will photoelectrons be produced at all frequencies of the incident photons? No; we are likely to get photoemission only for those frequencies whose photons have an energy equal to or more than the (minimum) ionization energy for the gas concerned.

23. Yellow light does not eject photoelectrons from a given photosensitive surface, whereas green light does. What shall be situation in case of red and violet light?

We will not get any photoemission with red light since its frequency is less than that of yellow light. We will, however, get photoemission with violet light since its frequency is more than that of green light.

24. By what factor does the maximum velocity of the emitted photoelectrons change when the wavelength "the incident radiation is increased four times? (Given that the initial frequency used is five times the threshold frequency) When the wavelength is increased four times, the frequency goes down

by a factor of four.

( ) ( )

02

0122

21

022201

21 2

121

νννν

νννν

−−

=

−=−=

vv

hmvandhmv

Now,

164

14

455

0

0

00

0022

21 ==

−−

=ν

ννν

ννvv

4

2

1 =vv

Thus, the maximum velocity goes down by a factor of 4. 25. A cesium photocell, with a steady potential difference of 90 volt across it, is illuminated by a small bright light placed one metre away. The number of electrons that cross the photocell is n. What will be the number of electrons crossing the photocell when the same light is placed half metre away? When the light is brought to a distance of 0.5 m, the intensity of the light falling on the photocell goes up four times. Since the number of photoelectrons emitted is directly proportional to the intensity of incident light, the new number of photoelectrons emitted would become 4n. 26. The sun rays are focused on a metal surface , and it produces a current. The lens forming the image is then replaced by another lens of the same diameter but only half in focal length. What will be the effect on the photoelectric current? Hence, the intensity of light falling on the metal surface gets reduced in case (b) and, we, therefore, get a reduced photoelectric current.

27. To work functions 2ev and 5ev for two metals x and y respectively. Which metal will emit electrons, when it is irradiated with light and wave length 400nm and why?

�= 400 x 10-9m=4 x 10-7m E= h c/� = (6.6 x 10-34 x 3 x 108)/ (4 x 10-7) = 4.98 x 10-19 j E= (4.98 x 10-19)/ (1.6 x 10-19) =3ev Hence, metal x will emit electrons.

28. A photon and an electron have same de-broglie wavelength. Which has greater total energy. Explain ?

For a photon E1=hc/� For an electron �=h/mv or m=h/�v E2=mc2

= (h/�v) x c2

E2/E1=c/v>1 Therefore,E2>E1.thus, electron has total energy greater then that of photon.

29. The de-broglie wave length of a photon is same as the wave length of electron. Show that K.E. of a photon is 2m��/h times K.E. of electron. Where ‘m’ is mass of electron, c is velocity of light.

�ph=�e=�=h/mv K.E. of photon Eph=hν=hc/� K.E. of electrons E=1/2mv2=1/2 m [h/m�]2

=h2/2m�2

Eph/Ee= (hc/�) x 2m�2/h2

=2mc�/h ∴ Eph=Ee(2mc�/h)

30. How may photons are required for emission of one photo electron if frequency of incident radiation is less than threshold frequency. More than threshold frequency. (i)No photo – electron will be emitted and photons are absorbed by electrons. ii)One photon will emit one photo electron.

31. State the dependence of work function on the kinetic energy of electrons emitted in a photocell. If the intensity of incident radiation is

doubled, what changes occur in the stopping potential and the photoelectric current? According to Einstein theory of photoelectric effect, kinetic energy of emitted electron is

02

max21 WhmVEk −== ν

Greater the work function of the metal, lesser the kinetic energy of the photoelectron. on doubling the intensity of the incident radiation stopping potential remains the same, whereas photoelectric current is doubled.

32. Using Davisson and Germer Experiment to establish the existence of de Broglie waves. The experimental set up consists of an electron gun connected to a low tension battery. The electrons emitted by the gun are accelerated to a desired velocity by applying a suitable potential difference V using a high tension battery. Value of V can be varied. Using Bragg's law of diffraction of light through crystal lattices, the wavelength of the wave showing diffraction peak at 50° was calculated as 1.65 A. The predicted de Broglie wavelength of electrons accelerated through 54 V is

��

�

�

�

AAAVmeV

hmEh

ph 66.1

5427.1227.12

22======λ

The excellent agreement between theoretical and experimental values of de Broglie wavelength confirms the wave nature of electrons and hence the existence of the de Broglie waves.

33. Through what potential difference an electron be accelerated so that it may have de – broglie wavelength 0.5��

Let v = potential through which electron is accelerated. Therefore, Energy = ½ mv2 = eV

�� 1/2 = h/(2mev)1/2

=> v = h2� ��2

here, h = 6.625 × 10-34Js m = 9.1 × 10-31kg e = 1.6 × 10-19 C

� � � � × 10-10 m hence v = 6.03 × 104 V

34. An e- and photon have the same energy of 100eV. Which has greater associated wavelength? �� e = h/(2mEe)1/2

=> Ee = h2��e

2 …………………………………………..(1) Now, Ep � ��p => Ep

2 = h2c2 ………………………………..(2) �p

2

as Ee = Ep = E = 100eV ………………………………………..(3) Dividing equation (1) by (2) and using equation (3) we get E = h2c2

��p2

h2�� e

2

=> E = 2mc2�e

2

�p2

�e� �p = (E/2mc2)1/2

as E = 100eV => 2mc2 � �� therefore E << 2mc2

�� e � �p Therefore the wavelength associated with a photon is greater than an electron for the same energy.

35. the frequency of the light falling on the metal is doubled, what will be the effect on photocurrent & the maximum Kinetic Energy? The photo current does not depend on the frequency of incident radiation as: Ek = h� – W If the frequency is doubled Ek

/ = 2h� - W => Ek

//Ek = (2h� – W)/(h� – W) = (2h� – 2W + W)/(h� – W) = 2 + W/(h� – W) > 2 i.e. maximum KE will increase slightly more than double.

36.e work function of ‘Li’ and ‘Cu’ are 2.3eV & 4eV. Which of these metals will be useful for the photoelectric cells working with the visible light? The threshold wavelength of a metal is:

�o = hc/W = 12475/(W in eV) � => Li�o = 12375/2.3 � � �� and Cu�0 = 12375/4 � � �� The wavelength 5380� �� useful for the photoelectric cell.

37. An e- has a speed of 5 × 106 m/s in a magnetic field of 10-4 T. What is the acceleration of e- if e/m = 1.76 × 1011 C/kg. BeV = mv2 as the force due to magnetic field provides the necessary centripetal force. => v2/r = Bev/m as acceleration = v2/r => a = B(e/m) => a = v2/r = 10-4 × 1.76 × 1011 × 5 × 106

=> a = 8.8 × 1013 ms-2.

38. Assume that the potential difference between cathode and anode is the same as that between two deflecting plates. If this potential difference is doubled, calculate by what factor the magnetic field should changed to keep the electron beam undeflected? e/m = E2/2vB2 But E = v/d e/m = v2/2vB2d2 = v/2B2d2

or, B2 = v . 2(e/m)d2

or B2� v => B � ��

if v is doubled, then B//B = (2)1/2 or B/ = (2)1/2B Thus, the magnetic field should be increased by a factor of (2)1/2

39. Work function of the metals: Na : 1.92 eV ; k : 2.15 ev ; Mo :4.17 ; Ni : 5.0; Which of these willnot give photo electric emission for a radiation of wavelength 3300Å from a He-Cd laser placed 1m away ? What happens if laser is brought nearer and placed 50 cm away ? Sol: Wavelength of the incident radiation , �� Å

�� 8/3300*10-10 = 9.1*1014 Hz Threshold frequencies for different metals ;

� 0 (Na)= 1.92*1.6*10-19/6.3*10-34= 4.6*1014 Hz � 0 (K)= 5.2 *1014 Hz

� 0 (Mo) =1.0 * 1015 Hz� 0 (Ni)= 1.2 *1015 Hz

�� 0 �� 0 (K) but less �� 0 �� 0 (Ni) , therefore Mo and Ni will not give photo electric emission. If the laser is brought closer , intensity decreases. This does not effect the result regarding Mo and Ni but photoelectric current will increase for Na and K.

40. a) show that a free e- at rest can not absorb a photon and thereby acquire K.E. equal to the energy of the photon. Would the conclusion change if the e- has a constant velocity. b) If the absorption of a photon by a free e- as proved in (a) , how does photo electric takes place? Ans: a) the total energy of an e- , E = (m0

2c4+p2c2)1/2

= m0c2��

Squaring both the sides p2c2+2m0c2pc= p2c2 Or 2m0c2pc=0 This is impossible b) we have shown in (a) that e-

�� -. however, for an e- a lattice the momentum of the incident photon can be shared by both the e- and the lattice while the lattice due to large mass does not share the energy of the photon. Thus, e- � � � �� - +lattice is not forbidden.

41. A monochromatic point source, S radiating wavelength 6000 Å with power 2W, an aperture A of diameter .1m are placed , area A = .5 cm2,efficiency = .9 , h = 6.63*10-34js, c= 3*108 , e= 1.6*10-9C . calculate the photon flux at the center of the screen and photo current in the detector if a concave lens L of focal length .6m is inserted in the aperture find the new values of photon flux and photocurrent , uniform average transmission is 80% .If the work function of the photo emissive surface is 1eV , calculate the values of the stopping potential.

Sol : Energy of each ph�� -34*3*108/6*10-7 J =3.315*10-19J Therefore number of photon emitted= power / energy of each photon = 6.03*1018s -1 Number of photons passing through the aperture of diameter .1m NA = 6.03*1018s-1

�� 2 *

��2=1.047*1016s-1

Now the screen is at a distance of 6m from the source let the area of �� 2 �� m2

The number ns = 1.33 *1016 photons Number of photoelectrons = .6*1012 electrons Photocurrent = .096 microA

b) 1/v = 1/f+ 1/u and thus, v= -.3m photons transmitted through the lens n’ = .838* 1016 s-1

�� 2

photon flux = n’/a’= 2.95*1015 photons therefore photocurrent = .012 microA

42: Standing distance of the waves = 2 Å , d increased to 2.5 Å . energy of the electrons = ? . least value of d for which wave is defined ? �� Therefore n = 2d1� � �� 2� � Therefore n+1-n = 2d2� � -2d1� � For least value of d, n is 1 !�� min Energy of the electron E = p2/2me

"�� #! �� Therefore E= 150.95 eV

SEMICONDUCTOR DEVICES 1.What is the order of energy gap in a conductor, semi conductor, and insulator?. Conductor - no energy gap Semi Conductor - It is of the order of 1 ev. Insulator - 6 ev (or) more than 6 ev. 2. Zener effect and avalanche effect are the two possible break down mechanisms that helps the external current . Why Zener effect : The electric field in the depletion layer reach a point that it can break the covalent bonds and generate electron–hole pairs. Avalanche breakdown : The minority carriers that across the depletion layer under the influence of the electric field gain sufficient kinetic energy to be able to break covalent bond in atoms which they collide.

3. Light emission in semiconductor is the process of creation of a photon by means of the annihilation of an electron-hole pair. How can we create them. Give the necessary condition for the light emission? hω = Eeh greater than or equal to Eg. Condition for light emission is excess carriers.

4.Why does the conductivity of a semi conductor change with the rise in temperature ? When a semi conductor is heated more & more electrons get enough energy to jump across the forbidden energy gap from valence band to the conduction band, where they are free to conduct electricity. Thereby increasing the conductivity of a semi conductor.

5. On the basis of energy level diagram, identify the P-type semi conductor & N-type semi conductor

C.B _ _ _ _ _ _ _ _ _ _ _

V.B

.

C.B _ _ _ _ _ _ _ _ _ _ _ _ V.B

Donor energy level

Acceptor energy level

6. A student has to study the characteristics of a P-N Junction diode. What kind of a circuit arrangement should she use for this purpose?

7. Draw the typical shape of input characteristics likely to be obtainedby a student . What do we understand by the forward bias and reverse bias of the diode? In which of these states does the diode being used as a rectifier.?

8. To achieve light amplification, We should provide positive feed back in LASER .Why? Laser is not an amplifier but an oscillator! However, any oscillator is an amplifier with a positive feedback. To obtain lasing , it is necessary to achieve light amplification and provide positive optical feedback.

9. Self supporting stimulated emission is the principle of a Laser .why? Probability of stimulated emission is proportional to the density of excess electrons and holes , and to the density of photons. Under the normal circumstances it is negligible. Therefore if we provide a positive feedback , the stimulated emission can become self supporting.

11. If the active layer in a P-N photo diode is the thick depletion layer then P-N Photodiode act very effective . Why? In p-I-n photodiode ,due to thick i – layer the sensitivity improves dramatically.. Large reverse biases (< 100V for Si ) may be required.

12. Modern technology use poly silicon instead of metal to form the gate. Why? Poly silicon has high conductivity compare to metal.

15. Digiatal signal is preferred for communication Why not analog signal?Give its waveform. A continuous time varying wave form of a current (or) voltage is called analogue signal.

A digital signal in a two level voltage signal (ie) “0” and “1” . Digital signals are in the form of pulse of equal level.

16. In a given diagram ,is the diode reverse (or) forward biased?.

Reverse biased.

17.Identify the logic gate, Give its truth table and output wave form?.

NAND GATE.

18.The ratio of number of free electrons to holes ne/nh for two different materials A and B are 1 and <1 respectively. Name the type of semi conductor to which A and B belongs. If ne/nh =1 . Hence A is intrinsic semi conductor. If ne/nh <1 , ne<nh hence B is P-type.

19.Can you identify waveform. How will you convert A.C To D.C?

20. Under what conditions an amplifier can be converted in to an oscillator.Draw a suitable diagram . 1. When feed back is positive. 2. When feed factor k is equal to l/AV

21.Using basic logic gates (NOT, OR, AND ) construct the circuit for the given logic gate & give its truth table and wave form.?

22. Convert a Fraction from Decimal (0.625)10 to Binary? Hint:(0.625)10 = (0.101)223. Convert an octal number (4536) into decimal number? (4536)8 = 4x83 + 5x82 + 3x81 + 6x80 = (1362)1024. Convert Hexa decimal (3A9F) and (2D3.5) into decimal number? (3A9F)16 = 3x163 + 10x162 + 9x161 + 15x160 = 1499910(2D3.5)16 = 2x162 + 13x161 + 3x160 + 5x16-1 = 723.312510

25. In the circuit diagram given , a volt meter is connected across a lamp , what changes would occur at lamp”L” and voltmeter “V:” , if the resistor R is reduce in value? Give reason for your answer?

In the given circuit emitter –base junction of N-P-N transistor is forward biased , with battery “B”. When “r” decreases IE increases . Because IC = IE – IB . Therefore IC will also increase. Hence bulb will glow with more brightness and voltmeter reading will increase.

26.Determine the current through resistance “R” in each circuit. Diodes D1 and D2 are identical and ideal.

In circuit (i) Both D1 and D2 are forward baiased hence both will conduct current and resistance of each diode is “0”. .Therefore I = 3/15 = 0.2 A (ii) Diode D1 is forward bias and D2 is reverse bias, therefore resistance D1 is “0” and resistance D2 is infinite. Hence D1 will conduct and D2 do not conduct . No current flows in the circuit.

27.Write the output wave form of the OR gate for the inputs given? Time Interval

1 2 3 4 5 6 7 8

Input A 0 1 1 0 0 1 1 0

Input B 0 0 1 1 0 0 0 1 Output, Y=A+B

0 1 1 1 0 1 1 1

28.In the figure given below is (i) emitter and (ii) collector forward or ereverse biased. With the help of a circuit diagram explain the action of a N-P-N transistor?

Emitter –base is reverse biased and (ii) collector – base is forward biased . This will not acts as transistor. 29. In only one of the circuits given below the lamp“L” light glow . Identify which circuit is it? Give reason for your answer?

In fir (i) emitter –base junction has no source of emf . Therefore Ic =0, bulb will not glow. In figure (ii) emitter – base junction is forward biased, therefore lamp “L” will glow.

30. the emitter and base of n-p-n transistor have same doping concentrations, explain how will the collector and base currents be affected? All charge carriers entering the base will be neutralise in the base due to electron –hole combination. Therefore collector current in this situation is almost zero.( IE =IB ) . 31 From the given graph identify the KNEE voltage and breakdown voltage. Explain?

32.Differentiate the electrical conductivity of both types of extrinsic semiconductors in terms of the energy band picture.

33. semiconductors obey OHM’S law for only low fields .Give reason? The drift velocity of a charge carrier is proportional to electric E. Therefore V = eET/m ie. V α EBut V cannot be increased indefinitely by increasing E . At high speed relaxation time (T) begins to decrease due to increase in collision frequency. S: so drift velocity saturates at thermal velocity (lOms-1). An electric field of 106 V/m causes saturation of drift velocity. Hence semi- conduction obey ohm’s law for low electrical field and above this field ( E < 106 V/m ) current becomes independent of potential.

34. Relate input frequency and the output frequencies of a half wave rectifier and a full wave rectifier? In half-wave rectification, we get pulsating output for half cycle only. Therefore output ripple frequency is same as the input frequency. But in full wave rectification we get output for both half cycle. Hence the output at ripple frequency is full-wave rectification is double the input frequency.

35. Emitter is heavily doped while collector is moderately doped . Why? There are two main differences between emitter and collector of a transistor construction wise. First emitter is heavily doped while collector is moderately doped. Second the area of the collector is larger than the emitter.So output will be maximum.

36. Key point for its proper functioning of base region in a transistor depends upon the thickness of the base Why ? Base region in a transistor controls the current. The majority charge carriers supplied by the emitter do not combine in the same region due to its thin size and light doping and most of them pass on to the collector. This is the key point for its proper functioning.

37. For faster action which transistor is used and why? For faster action NPN Transistor is used .In an NPN transistor, current conduction is mainly by free electron ,whereas in PNP type transistor .it is mainly holes Since electron are more mobile than holes we prefer NPN for faster action as well as high conduction current.

38.A student has to study the input and output characteristics of a n-p-n silicon transistor in the common emitter configuration. What kind of a circuit arrangement should she use for this purpose?

39. Draw the typical shape of input characteristics likely to be obtained by a student. What do we understand by the cut off, active and saturation of the

transistor? In which of these states does the transistor not remain when being used as a switch?

When both emitter and collector are reverse biased, no current flows through the transistor. This condition is known as cut-off state.

When both Emitter and collector are reverse biased, no current flows through the transistor. This condition is known as saturation state. 40.A germanium diode is preferred to a silicon one for rectifying small voltages. Explain why? Because the energy gap for Ge ( Eg = 0.7 ev) is smaller than the energy gap for Si (Eg = 1.1ev ) . Moreover, the germanium diode is much more open to the danger of high temperature affect than silicon at high voltage.

41. Draw the logic circuit and the output wave form for given output Y=0,0,1,1. A

B

Y

The output of the AND gate is Y = A.B consequently the input of the OR gate are A and A.B . Then the final Y = A + A.B

Input for AND gate Output of AND gate

Input of OR gate

output of OR gate

A B Y= A.B A Y Y = A + Y 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1

42. Construct the truch table for the Boolean equation Y=(A+B).C and represent by logic circuit .

Y

AB

C

The output of OR gate is A+B. Consequently, the inputs of AND gate are A+B & C Hence the Boolean equation for the given circuit is Y=(A+B).C

43.Write the output wave form of the OR gate for the inputs given? Time Interval

1 2 3 4 5 6 7 8

Input A 0 1 1 0 0 1 1 0 Input B 0 0 1 1 0 0 0 1 Output, Y=A+B

0 1 1 1 0 1 1 1

44. Is it Logic gate used to prove Commutativity and Associativity ? Draw the truth table ? The Commutative Property: a + b = b + a a · b = b · a The Associative Property: a + (b + c) = (a + b) + c a · (b · c) = (a · b) · c

45. Diode acts as rectifier Why? Differentiate between Half wave and full wave rectification?

Rectification — It is the process in which alternating current is converted to direct current.P-N junction Diode as Half wave rectifier

As shown in the figure above the a.c input is applied across the primary of transformer. The secondary is connected to junction diode and load resistance (Rc) in series. WORKING PRINCIPLE:- when positive half cycle or a.c takes place the diode is forward biased and output is obtained across the load resistance Rc. But when it negative half cycle diode is reverse biased and no current flows, hence there is no output across load resistance Rc. So only half is obtained as output. Full wave rectification:

46.Construct AND gate using NAND GATE and give its truth table?. AND Gate using NAND GATE:-

A B Y= A.B 0 0 0 0 1 0 1 0 0 1 1 1

4.Construct NOT gate using NAND gate and give its truth table.

NOT gate using NAND gate:- Truth Table:-

A Y=A 0 1 1 0

47.. Using suitable block diagram for explain the function of feed back amplifier.?Explain.. Transistor as an oscillator- It consists of three main parts 2. Feedback circuit 3. Transistor acts as an amplifier. Feed back circuit : It is used to give the part of the output of the transistor as an input .

Transistor acts as an amplifier : in this circuit the NPN transistor acts as an amplifier. It amplifies the input signal. This amplified output goes to the Rl .

48.Compliment(1’s) the following binary numbers (a) 110010 (b) 111101 (c) 101010 (d)111111 (a) 1’s compliment=001101 (b) 1’s compliment=000010 (c) 1’s compliment=010101 (d) 1’s compliment=000000

49. In the circuit, Vs=0.2V, V0 = -10 V. Find Vi & gain Av = V0 / Vi & Av ‘ = V0 / Vs ?Sol: Vs=0.2 V, V0 = -10 V

NAND acts as NOT gate

Vf = 1/99+1 V0 =(/100) x (-10) = -0.1V Vi = Vs – Vf = 0.2-(-0.1)= 0.3V Vi = Vs + Vf = 0.2+(-0.1)=0.1V Therefore, gain Av = V0 / Vi = -10/0.1 = -100 Av = V0 / Vs = -10/0.2= -50

50 . Why should we use Zener diode in the output stage of the electronic circuit? Zener effect : The electric field in the depletion layer reach a point that it can break the covalent bonds and generate electron–hole pairs. If the output voltage of a DC power supply does not change with load it is called regulated power supply Explain the working of a Zener diode as a voltage regulator. Zener diode as a voltage regulator.

Using basic building block construct AND,OR,NOT and give its truth table and output waveform.

��

��

��

51.For the given Boolean expression F = x(y+z’) and its output Y=0,0,0,0,1,0,1,1 . Draw the logic circuit for the Boolean expression and input / output wave form.

53. The output of the transistor amplifier is 180º out of phase Why ? CE Transistor acts as an amplifier:-

Using Kirchhoffs first law, IE = IB + ICThis voltage drop ICRL is clearly in opposition to the applied voltage Vcc. Net collector voltage, VCE = Vcc - ICRL .. (1)

54.Draw a circuit diagram for PNP common emitter transistor characteristics. Explain the input and output characteristics. Common Emitter Transistor characteristics.

Output Characteristics of PNP represent the variation of collector current 1 with collector voltage Vce , keeping base constant current Ib.

55.Identify which basic gate OR, AND and NOT is represented by the circuits in the dotted lines boxes 1,2 and 3. Give the truth table for the entire circuit for all possible values of A and B?

The dotted line box 1 represents a NOT gate. The dotted line box 2 represents an OR gate.Here we use de Morgan’s theorem. The dotted line 3 represents AND gate. 56.Two input waveforms A and B shown in figure (a) and (b) are applied to an AND gate . Write the output

Time interval

1 2 3 4 5 6

Input A 0 1 1 0 0 1 Input B 0 0 1 1 0 0 Output Y = A.B

0 0 1 0 0 0

waveform.

57. In NPN transistor circuit, the collector current is 5mA. If 95% of the electrons emitted reach the collector region, what is the base current? Here Ic=95% of Ie = (95 / 100 ) Ie Ie = (100 / 95) × 5 mA = 5.26mA Ie= Ic+ Ib Ib = 0.25 mA

58. A circuit symbol of a logic gate and two input wave forms A and B are shown.

A Y B A

B

a) Name the logic gate b) Give the output wave form

This is AND logic gate Output wave form

A

B

Y

59. For a transistor working as a common base amplifier, current gain is 0.96. If the emitter current is 7.2mA, then calculate the base current.

Here α = 0.96 , Ie = 7.2mA α = Ic / Ie ∴Ic = α Ie = 6.91 mA Ib = Ie – Ic Ib = 0.29 mA.

60. The base current of a transistor is 105 μA and collector current is 2.05 mA. Deterine the value of β , Ie , and α A change of 27 μA in the base current produces a change of 0.65 mA in the collector current . Find βa.c.

Ib = 105 × 10-6 A Ic = 2.05 × 10-3A β = Ic / Ib = 19.5 Also, Ie = Ib + Ic = 2.155 × 10-3 A α = Ic / Ie = 0.95 �Ib = 27μA = 27 × 10-6 A β = �Ic / �Ib = 24.1

61.In a silicon transistor, a change of 7.89mA in the emitter current produces a change of 7.8 mA in the collector current. What change in the base current is necessary to produce an equivalent change in the collector current?

Here �Ie = 7.89 × 10-3 A �Ic = 7.8 × 10 –3 A Now αa.c. = �Ic / �Ie = 0.9886

We have,

βac = αac / (1-αac) = 86.72

Also, βac = �Ic / �Ib ∴�Ib = �Ic / βac �Ib = (7.8 × 10-3 ) / (86.72) �Ib = 89.94 × 10-6A

1.What is the highest frequency for which antennas can be made (approximately)

1012 to 1013 Hz.

2. What is the condition of the electrons in the transmitting antenna when maximum

magnetic field is being transmitted?

A maximum current is flowing, so the electrons have maximum speed up and

down the antenna. The electric current produces the magnetic field.

3. How can the electric portion of the electro-magnetic wave be detected?

It can be detected by an antenna similar to the transmitting antenna except that a

detector of electric current replaces the voltage source.

4. How can the magnetic field portion of an electro-magnetic wave be detected?

The magnetic wave is best detected by placing a loop of wire (with its ends hooked

to a current detector) in the path of the wave. The changing magnetic field causes a

current in the loop.

5.The small ozone layer on the top of the atmosphere is crucial for human survival.

Why?

The ozone in the atmosphere is confined to the ozone layer, some 50-80 km above

the ground. The ozone layer blocks the passage of the ultra-violet radiations; x-rays and

y-rays from the solar and other extra-terrestrial sources and effectively protects us from

the dangerous and harmful portions of solar radiations as they cause genetic damages

to living cells. Practically all radiations of wave length less than 3 x 10-7m are absorbed

by the ozone layer. This explains why ozone layer on the top of the atmosphere is

crucial for human survival.

6.How does "Green House Effect" affect the temperature of the earth's surface ?

Green house effect serves to keep the earth's surface warm at night.

7.How do we make television broadcasts for larger coverage and for long distance?

By using (i) tall antennas which is familiar landmark in many cities and (ii) using

artificial satellites —called geostationary satellites. Since television signals are of high

frequency and are not reflected by ionosphere so we use satellites to get them reflected

& transmission of TV signals can be used for larger coverage as well as for long

distance.

8. Scientists put x-ray astronomical telescope on the artificial satellite orbiting above the

earth's atmosphere whereas they build optical and radio-telescopes on the surface of the

earth. Why ?

X-rays have very high frequency and much smaller wavelength. These rays get

absorbed by the earth's atmosphere. On the other hand, optical (visible) radiations and

radio-waves can pass through the atmosphere. That is why optical and radio telescopes

can be installed on the earth's surface.

9. Fo r a n e le ctrom ag ne tic w a ve , w rite the re la tio nsh ip b e tw ee n a m p litud e o f

e lec tric and m ag ne tic fie lds in fre e sp ace .

[H in ts If E o is th e a m p litu d e o f a n e le c tr ic f ie ld a n d B o is th e a m p litu d e o f th e

a sso c ia te d m a g n e tic f ie ld in fre e sp a ce th e n 0

0

BEc = w h e re c is th e sp e e d o f lig h t

in fre e sp a ce i.e . 3 x1 0 8 m /s .

10. The charging current for a capacitor is 0.25 A. What is the displacement current

across its plates?

Hints: Displacement current = Charging current = 0.25 A]

11. What is a ground wave? How does it differ from a sky wave?

Ans. A signal emitted by an antenna from a certain point can be received at another point of

the surface of the earth in two ways. The wave which travels directly following the surface of the

earth is called ground nave. The wave that can reach the same point after being reflected

from the ionosphere is called sky wave.

12. Why short wave communication over long distances is not possible via ground waves?

|Hints: Because the wave gets attenuated.]

13 . A re conduction and d isp lacem ent cu rren ts the sam e?

[H in t: N o ; they a re d iffe ren t bu t they a re equa l .

14 . It is necessary to use sa te llites fo r long d istance T V transm iss ion . W hy?

It is so because te levis ion s igna ls a re no t p rope rly re flected by the

ionosphe re . T here fo re , fo r re flec tion o f s igna ls sa te llites a re needed as re flec tion is

e ffec ted by sa te llites .

15 . O p tica l and rad io te lescopes a re bu ilt on g round bu t X-ray astronom y is

poss ib le on ly from sa te llites o rb iting the earth . W hy?

A tm osphe re absorbs X-rays, wh ile vis ib le and rad iowaves can pene tra te it.

T ha t is why op tica l and rad io te lescopes can work on earth 's su rface bu t X -ray

as tronom ica l te lescopes m ust be used on sa te llites o rb iting the ea rth .

16 . If the earth d id no t have an a tm osphere , wou ld its ave rage surface tem pera tu re

be h igher o r lowe r than wha t it is now?

A ns. T he tem pera tu re o f the earth wou ld be lowe r because the g reen house e ffec t

o f the a tm osphere wou ld be absen t.

.

17 . W ha t is the equa tion fo r the speed o f e lec trom agnetic w aves in free space?

C =00

1εμ

18 . T he wave leng th o f e lec tro m agnetic rad ia tion is doub led . W hat w ill happen to

the ene rgy o f the pho ton?

T he energy w ill be ha lved because frequency w ill be ha lved .

19 . N am e the pa rt o f e lec trom agnetic spectrum to wh ich waves o f wave leng th (i)

1A° and (ii) 10 -2 m be long . U s ing the re la tion λT = (0 .29 cm ) K , ob ta in the

characte ris tic ke lv in tem pera tu re correspond ing to these two wave leng ths.

(i) X -rays, (ii) M icrowaves

A ga in , (i) Kcm

cmT 810 1029

10129.0 −

− ×=×

= (ii) Kcm

cmT 29.0129.0

==

20 . G ive a s im p le a rgum ent to suggest tha t an acce le ra ted charge m ust em it

e lec trom agne tic rad ia tion

A ns. W hen charge m oves w ith constan t ve loc ity, the m agnetic fie ld does no t

change w ith tim e. S o , it canno t p roduce an e lectric fie ld . W hen cha rge is

acce le ra ted , bo th e lec tric and m agnetic fie lds change w ith tim e and space , one

becom ing a source o f ano ther. T h is g ives rises to e lectrom agne tic wave .

21 . S how tha t the average energy density o f the E fie ld equa ls the average energy

dens ity o f the B fie ld .

A ns. E ne rgy dens ity in E fie ld , 2

021 EuE ε=

E nergy density in B fie ld ,--------------

2

021 BuB μ

=

U sing E = cB and c =00

1εμ

, uE = uB .

22 . O n what fac to rs does its ve loc ity in vacuum depend?

A ns. E lectrom agnetic waves consist o f s inuso ida l va ria tion o f e lec tric and

m agnetic fie ld vecto rs . T he fie ld vecto rs v ib ra te w ith the sam e frequency and a re

in the sam e phase . T he fie ld vecto rs and the d irection o f p ropaga tion a re a ll

m utua lly pe rpend icu la r. T he ve loc ity o f e lec trom agnetic w aves in vacuum

depends upon abso lu te perm eab ility μo and abso lu te perm ittiv ity ε0.N o te tha t c

=00

1εμ

23 . W ha t is the nam e assoc ia ted w ith the fo llow ing equa tions?

0.)(.)(0


ε



��

(i) G auss 's law (ii) N o pa rticu la r nam e

(iii) Faraday's law (iv) A m pere 's law .

24 . E lec trom agnetic waves w ith w ave leng th

(i) λ1a re used to trea t m uscu la r stra in

(ii) λ2 a re used by a FM rad io sta tion fo r b roadcasting

(iii) λ3 a re used to de tec t frac tu re in bones

(iv) λ4 a re absorbed by the ozone layer o f the a tm osphe re .

Iden tify and nam e the part o f the e lec trom agnetic spectrum to wh ich these

rad ia tions be long . A rrange these wave leng ths in decreasing o rder o f m agn itude .

A ns. (i) λ1 -» in fra red (ii) λ2 -» rad iowaves

(iii) λ3 — > X-rays (in ) λ4 — > u ltra -v io le t rays λ2 > λ1 > λ4 > λ3.

25 . If you find c losed loops o f B in a reg ion in space , does it necessarily m ean tha t

ac tua l charges a re flow ing across the a rea bounded by the loops?

A ns. N o t necessa rily. A d isp lacem ent cu rren t such as tha t be tween the p la tes o f a

capac ito r tha t is be ing cha rged can a lso p roduce loops o f B •

26 . A c losed loop o f B is p roduced by a chang ing e lec tric f ie ld . D oes it necessa rily

m ean tha t E and dtdE

are non -zero a t a ll po in ts on the loop and in the a rea

enclosed by the loop?

A ns. N o t necessarily. A ll tha t is needed is tha t the to ta l e lec tric flux th rough the

a rea enclosed by the loop shou ld vary in tim e. T he flux change m ay a rise from

any po rtion o f the a rea . E lsewhere E o r dtdE

m ay be ze ro . In particu la r, the re need

be no e lec tric fie ld a t the po in ts wh ich m ake the loop .

27 . W hy is it tha t induced e lec tric fie lds due to chang ing m agnetic flux a re m ore

read ily observab le than the induced m agnetic f ie lds due to chang ing e lectric

fie lds?

A ns. T he m agn itude o f the m agnetic f ie ld due to d isp lacem ent cu rren t is too sm a ll

to be eas ily observab le . T h is e ffec t can o f course be increased by increasing the

d isp lacem ent cu rren t. [In an A C c ircu it, th is can be done by increasingω.]

O n the o ther hand , the e ffect o f induced e lec tric f ie ld due to chang ing m agnetic

flux can be increased s im p ly by tak ing m ore and m ore num ber o f tu rns in the co il.

T he induced em fs in d iffe ren t tu rns o f the sam e co il add up in se ries.

28 . A variab le -frequency A C sou rce is connected to a capac ito r. W ill the

d isp lacem ent cu rren t increase o r decrease w ith increase in frequency?

A ns. Increase in frequency causes decrease in im pedance o f the capac ito r and

consequent increase in the cu rren t wh ich equa ls d isp lacem en t cu rren t be tween

the p la tes .

29 . S om e sc ien tis ts have p red ic ted tha t a g loba l nuc lear wa r on the earth wou ld

be fo llowed by a severe 'nuc lear w in te r' w ith a devasta ting e ffec t on life on earth .

W hat m igh t be the bas is o f th is p red iction?

A ns. T he c louds p roduced by a g loba l nuc lear war wou ld perhaps cove r

substan tia l pa rts o f the sky p reven ting so la r ligh t from reach ing m any parts o f the

g lobe . T h is wou ld cause a 'w in te r'.

30. What is the contribution of the Greenhouse effect towards the surface temperature of

the earth?

Ans. The infrared radiation emitted by the earth's surface keeps the earth warm. In the

absence of this effect, the surface temperature of earth would be lower.

31. Why the small ozone layer on top of the stratosphere is crucial for human survival?

Ans. The small ozone layer on the top of the stratosphere absorbs ultraviolet radiations, y-

rays etc. from the sun. It also absorbs cosmic radiations. So, these radiations, which can

cause genetic damage to the living cells, are prevented from reaching the earth. Thus, the

small ozone layer on top of the stratosphere is crucial for human survival.

32. A plane electromagnetic wave travels in vacuum along z-direction. What can you say

about the directions of its electric and magnetic field vectors? If the frequency of the wave

is 30 MHz, what is the wavelength?

Ans. E and B lie in the x-y plane and are mutually perpendicular. Wavelength,

mm 101030

3xlO6

8

=×

=λ

33. Given below are some famous numbers associated with electromagnetic radiation in

different contexts in physics. State the part of the e m spectrum to which each belongs.

(i) 21 cm (wavelength emitted by atomic hydrogen in interstellar space).

(ii) 1057 MHz [frequency of radiation arising from two close energy levels in hydrogen;

known as Lamb shift].

(Hi) 2.7 K temperature associated with the isotropic radiation filling all space-thought to be

a relic of the 'big-bang’ origin of the universe.

(iv) 5890 A - 5896 A [double lines of sodium].

(v) 14.4 keV [energy of a particular transition in 57Fe nucleus associated with a famous

high resolution spectroscopic method (Mossbauer spectroscopy).

Ans. (i) Radio (short wavelength end) (ii) Radio (short wavelength end) (Hi) Microwave (iv)

Visible (Yellow) (v) X-rays (or soft y-ray) region.

34. Electromagnetic waves in a cavity with conducting walls can exist only in certain

modes i.e., they cannot exist, for example, with any arbitrary wavelength. Suggest a

simple reason why this should be so.

Ans. The waves must satisfy a boundary condition. The electric field should be zero on the

walls of the conductor. This restricts the possible modes. [It is something like the restricted

modes of a string fixed at two ends.]

7. Write the order of frequency range and one use of the following e. m radiations. i)Microwaves ii) Ultra-violet rays iii) gamma rays

a. i) Microwaves :- 109 to 1012 Hz approx used in radars/microwave ovens ii) Ultra violet rays:-1015 to 10 18 Hz approx. sterilizing the medical instruments iii) gamma rays:- 10 18 to 10 22 Hz in radio therapy ,treating cancer and tumours.

8. How are the following e.m radiations produced, Mention one used of them. i) radio waves ii ) infra red rays iii) x rays

a. i) radio waves :produced by oscillating circuits having inductor and capacitor. Used in radio and TV communication. ii)infra red rays: produced by all hot bodies treating muscular strains/ solar appliances etc., iii) gamma rays: produced when high energy electrons bombards metals. . to detect fracture in bones/ study crystal structure

CLASS –12 PHYSICS ASSIGNMENT –1 TOPIC- ELECTROSTATICS, CURRENT ELECTRICITY 1..What is the angle between the directions of electric field at any (i) axial point and (ii) equatorial point due to an electric dipole ? 2. Name the physical qantity whose unit is(i) coulomb /volt. (ii) newton/coulomb (iii)joule/coulomb. 3.The I-V characterstics of a resistor are observed to deviate from a straight line for higher values of current. Why? 4. Name the materials used for making standard resistances. Give reasons. 5.(i)Is the electrostatic potential nessarily be zero at a point where electric field strength is zero?Give example to illustrate your answer. (ii)Does the electric potential rise or fall along the electric line of force? 6..Define dielectric constant of a medium? What is the value of dielectric constant for a metal? .7. Are the paths of electrons straight lines between successive collisions with the positive ions of the metal in the a) absence of electric field b) presence of electric field? 8.Define resistivity of a conductor ? a) How does it vary with increase in temp. for a metallic conductor? b) What is the unit of resistivity? 9.Two wires Aand B are of the same material, have the same area of cross section and their lengths in the ratio 2 : 1. What will be the ratio of current flowing through them when the same potential difference is applied across length of each of them. 10. At a point due to point charge , the values of electric field intensity and potentials are 25N/C and 10J/C respectively. Calculate a) the magnitude of charge? b)distance of the charge from the point of observation. 11.A battery of e m f E and internal resistance r gives a current of 0.5A with an external resistor of 12 ohm. And a current of 0.25 A with an external resistor of 25 ohm. Calculate the internal resistance of the cell and e m f of the cell? 12. Two cells of emf 1V,2V and internal resistances 2 ohm and 1 ohm respectively are connected in (i) series (ii) parallel. What should be the external resistance in the circuit so that the current through the resistance be the same in the two cases ?In which case more heat is generated in the coils?

13.The lengths of three conducting wires are in the ratio 1:2:3. All the wires are of same metal and their radii are equal. If we join them in parallel across a battery, what will be the rato of currents in them ? 14.A cell of emf 4V and internal resistance 0.5 ohm is connected across a load resistance (i)7.5 ohm (ii)11.5 ohm. Calculate (i) the ratio of differences in emf of the cell and potential drop across the load (ii)ratio of currents in two cases ? 15 .A small sphere of radius R1 and charge Q1 is enclosed by a spherical shell of radius R2and charge Q2. Show that if Q1 is positive , charge will necessarily flow from the sphere to the shell when the two are connected by a wire, no matter , what the charge Q2 on the shell is? 16. A potentiometer wire of length 100cm has a resistance of 10 ohm. It is connected in series with a resistance and an accumulator of emf 2 V and negligible resistance . A source of emf 10 mV is balanced against a length of 40 cm of potentiometer wire . What is the value of external resistance? . 17.A battery of emf 2 V and internal resistance 0.1 ohm is being charged by current of 5 A. what is the direction of current inside the battery?. What is the potential difference between the terminals of the battery? 18.An electric field is uniform between two points separated by a distance of 0.12m . 2.88 x 10 –4 J of work has to be done in carrying a charge of 80/3 x 10 –9 C from one point to another. Find the intensity of electric field ? . 19 . Two resistances of 3 ohm and 6 ohm are connected in parallel in the right gap of a meter bridge with a known resistance of 1.5 ohm in the left gap. Find the position of the null point when the bridge is balanced? 20.In a potentiometer a standard cell of emf 5V and negligible resistance maintain a steady current through the potentiometer wire of length 5m. The two primary cell of emf`s E1 and E2 are joined in series with (i) same polarity (ii) opposite polarity. The combination is connected through a galvanometer and jockey to the potentiometer. The balancing length in two cases are found to be equal to 350 cm and 50cm respectively. (i) draw the circuit diagram (ii) Find the value of the emf`s of the two cells.. ------------------------------------------------------------------------------------------------------------

ASSIGNMENT-2

TOPIC- MAGNETIC EFFECTS OF ELECTRIC CURRENT, MAGNETISM ELECTROMAGNETIC INDUCTION

1. Which physical quantity has unit of Wb/m2 ? Is it a scalar or vector quantity ?

. 2.Name materials, one in each case , which are suitable for (i)permanent magnet (ii)core of electric transformer. Justify your answer ?

3.Draw diagrams to depict the behaviour of magnetic field lines near a bar of (i)copper (ii)aluminium (iii) Mercury ,cooled to very low temperatur (4.2 k).

4. .As soon as the current is switched on in a high voltage wire, the bird sitting on it flies away. Why? 5. An ammeter and a milliammeter are converted from the same galvanometer. Out of the two , which current measuring instrument has higher resistance ?

6..what is the basic difference between the atoms or molecules of a diamagnetic and paramagnetic material? Why are elements with even atomic number more likely to be diamagnetic ?

7. .How does the self inductance of an air core coil change when (i)the number of turns in the coil is increased (ii) an iron rod is introduced in the coil ? 8.. How doeds the mutual inductance of a pair of coils change when (i) distance between the coils is increased (ii) number of turns in each coil is decreased?

9.How does the a) pole strength b) magnetic moment of each part of a bar magnet change if it is cut into two equal parts transverse to length ?

10. An electron is moving in a circle in a auniform magnetic field. By what factor will the radius of the path change if the velocity of electron is doubled and the magnetic field is halved? 11. In a hydrogen atom the clectron revolves round the nucleus 6.8 x 10 15 times per second in an orbit of radius 0.53 A� .Calculate the equivalent magnetic dipole moment . 12. A proton and an alpha particle of the same velocity enter in turn a region of uniform magnetic field acting perpendicular to the magnetic field . find the ratio of the radii of the circular paths described. Explain why the kinetic energy of the particle after emerging from the magnetic field remains unchanged? 13. . What is the magnetic moment associated with a coil of 1 turn , area of cross section 10 –4 m 2, carrying a current of 2A 14. Distinguish between dia, para and ferro magnetic materials on the basis of

a) behaviour in a non- uniform magnetic field b) intensity of magnetization c) susceptibility

d) permeability

15.A conducting rod of length l, with one end pivoted , is rotated with uniform angular speed � in a vertical plane, normal to a uniform magnetic field B. Deduce an expression for the emf induced in this rod? 16.. A galvanometer has a resistance 30 ohm and gives full scale deflection for a current of 2 mA. How much resistance in what way must be connected to convert it into

i) an ammeter of range 0.3A ii) a voltmete of range 0.2V.

17..A short bar magnet of magnetic moment M= 0.32 J/T is placed in a uniform magnetic field of 0.15T. If the bar is free to rotate in the plane of the field, which orientation correspond to (i) stable (ii) unstable equiliburium ? What is the potential energy of the magnet in each case ? 18 Where on the earth`s surface is the value of vertical component of the earth`s magnetic field zero? The horizontal component of earth`s magnetic field at a given place is 0.4x10 –4

Wb/m2 and angle of dip is 30� . calculate the value of a) vertical component b) total intensity of magnetic field ?

19. A bar magnet having a magnetic moment of of 10 4 J/T is free to rotate in a horizontal plane . A horizontal magnetic field of B= 5x10 –4 T exists in space. Calculate the work done to rotate the magnet by 60 � from the direction of the magnetic field? 20 . Two circular coils XandYhaving radii R and R/2 respectively are placed in a horizontal plane with their centers coinciding with each other . Coil X has current I flowing through it in the clock wise direction. What must be the current in coil Y to make the total magnetic field at the common center of the two coils , zero? ----------------------------------

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