PREVIOUS YEAR QUESTION ASKED IN CBSE,BOARD EXAM. CHAPTER … bank of Physics class XII.pdf · CHAPTER-2,ELECTROSTATIC POTENTIAL AND CAPACITANCE 2006 Q. Define the term 'dielectric

PREVIOUS YEAR QUESTION ASKED IN CBSE,BOARD EXAM.

CHAPTER-1, ELECTRIC CHARGE AND FIELD

2006

Q. What is electric flux? Write its S. I. Units. Using Gauss’s theorem, deduce an expression for the electric field at a point due to a uniformly charged infinite plane sheet.(5)

ANS: The electric flux through a given surface area is the total number of electric lines of force passing normally this area. It is given by φE =E.dS .

The SI unit of electric flux = Nm2C-1.

According to Gauss’s theorem, the total flux through a closed surface is1/Ɛ0times the total charge enclosed by the

closed surface. Derivation: Consider a non-conducting sheet of charge with surface charge density .Consider a cylinder of length 2r

and cross - sectional area A as Gaussian surface.referncert book,page38,fig:1.30. From symmetry electric field E points at right angle to the end caps and away from the sheet. There is no contribution from the curved surface because angle between E and dS is 900. At the end faces, angle between E and dsis zero. From Gauss’s law,Φ=∫E.ds=q/ε0=EA+EA=σ A/ε0 ,So, E=A/2ε0

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2007

Q. The electric field due to a point charge at any point near it is defined as E&E =limt F/q q 0

where q is the test charge and F is the force acting on it. What is the physical significance of lim q 0in this expression? Draw the electric filed lines of a point charge Q when (i) Q > 0and (ii) Q <0 .(2) lim ANS: The lim. q 0 indicates that the test charge is so small that its presence does not disturb the distribution of source charge and hence its electric field. The electric fields of the point charge Q are shown in figure 1.11(a)&(b),page-18,NCERT,book. OR

Define electric flux. Write its S.I. Units. A spherical rubber balloon carries a charge that is uniformity distributed over its surface. As the balloon is blown up and increases in size, how does the total electric flux coming out of the surface change? Give reason.(2)

ANS: The electric flux through a given surface area is the total number of electric lines of force passing normally through that area. It is given by. φE =E.dS SI unit of electric flux is Nm2C-1. As the balloon is blown up, the total charge on the balloon surface remains unchanged, so the total electric flux coming out of its surface remains unchanged. Q. Deduce an expression for the electric potential due to an electric dipole at any point on its axis. Mention one contrasting feature of electric potential of a dipole at a point as compared to that due to single charge.(3)

ANS: 13.Let P be an axial point at distance r from the centre of the dipole of length2a.

-q +q P 2a Electric potential at point P will be,V=V1+V2

=1/4∏Ɛ0(-q/r+a + q/r-a )

On simplification we get, =1/4∏Ɛ0(p/r2-a2 ) where p=2aq

For a far away point, r >> a, V =1/4∏Ɛ0(p/r2 )

At large distances, dipole potential falls off as1/r2whereas the potential due to a single charge falls off as 1/r.

Q.A parallel plate capacitor, each with plate area A and separation d is charged to a potential difference V. The battery used to charge it is then disconnected. A dielectric slab of thickness d and dielectric (3) constant K is now placed between the plates. What change, if any, will take place in (i) charge on the plates(ii) electric field intensity between the plates(iii) capacitance of the capacitor Justify your answer in each case. ANS: (i)The charge on the capacitor plates remains same. (ii)The electric field intensity between the capacitor plates decreases due to the introduction of a dielectric. Introduction of dielectric field creates an intrinsic electric field directed opposite to the original electric field. That is why the electric field intensity decreases.

(iii)The capacitance of the capacitor increases due to the introduction of a dielectric. Electric field decreases, therefore, the capacitor can get more charge to bring back the electric field to its original value. This increases the capacity of holding the charge and hence the capacitance increases.

2008 Q.A 500 micro-coulomb charge is at the centre of a square of side 10 cm. Find the work done in moving a charge of 10 micro-coulomb between two diagonally opposite points on the square.(1)

ANS: The 500µCcharge is at the same distance from all the corners of the square. The opposite corners, say A and C, will have the same potential VA=Vc.

Work done in moving a charge q between points A and C is given as: W = q(VC − VA) = q × 0 = 0. Hence, no work is done in moving the charge between two diagonally opposite points on the square. --------------------------------------------------------------------------------------------------------------------------------------- Q.(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 is (I) positive,(ii) negative.(b) A uniformly charged conducting sphere of 2.5 m in diameter has a surface charge density of

100µC/m2. Calculate the(i) Charge on the sphere(ii) Total electric flux passing through the sphere.(5)

ANS: (a) Electric field intensity at any point outside a uniformly charged spherical shell. Figure1.31 (a)&(b),Page:39,NCERT, TEXT BOOK. Consider a thin spherical shell of radius R and with centre O. Let charge + q be uniformly distributed over the surface of the shell.Let P be any point on the Gaussian sphere S1 with centre O and radius r, as shown in the following figure. According to Gauss’s law, we can write the flux through ds as:Φ=∫E.ds=q/ε0

Or, E (4πr2)=q/ε0

Or, E=1/4πε0(q/r2)

At any point on the surface of the shell, r = R,E=1/4πε0(q/R2)

For charge density σ, q=4πR2σ, Substituing, we get E=σ/ε0 .

(b) Diameter of the sphere = 2.5 m So, Radius of the sphere, R=2.5/2=1.25

Charge density,σ=100 micro coulomb per square meter =10-4C/m2

Total charge, q=4πR2σ=1.96 *10-3C. Total electric Flux, φE =q/ε0=2.21*108Nm2C-1

-----------2009

Q.A positive point charge (+q) is kept in the vicinity of an uncharged conducting plate. Sketch electric filed lines originating from the point on the surface of the plate.Derive the expression for the electric field at the surface of a charged conductor.(3)

ANS: Take a charged conductor of any arbitrary shape with charge density 2 σC / m .The total flux through a small

cylindrical Gaussian surface will be given by Gauss’slaw as follows: EA = σA/ε0So, E=σ/ε0n.

The electric field will be normal to the surface at all points of the conductor.

2010

Q.Figure shows three points 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)

+3q

ANS: Electric flux through the surface S will be as per Gauss law:

φE= net charge/ε0=(2q-q)/ ε0 =q/ε0.

2011

Q.A point charge Q is place at point O as shown in the figure. Is the potential difference

VA – VB positive, negative or zero, if Q is (i) positive (ii) negative? (2)

Q A B

O

Ans: Potential at a point: V = kQ/r

For any Q, VA-VB = kQ( 1/rA-1/rB)

Where, rA<rB , So 1/rA>1/rB

And So 1/rA-1/rB> 0.

If Q at O is positive, VA-VB will be positive.

If Q at O is negative, VA-VB will be negative.

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Q. Using Gauss’s law to obtain the expression for the electric field due to a uniformly charged thin spherical shell of

radius R at a point outside the shell. Draw a graph showing the variation of electric field with r, for r > R and r< R.

+2q

-q

ANS:

EdS

r

Consider a spherical Gaussian surface of radius r (›R), concentric with given shell. If Eis electric field outside the shell, then by symmetry, electric field strength has same magnitude Eon the Gaussian surface and is directed radially outward. Alsothe directions of normal at each point is radially outward, so angle between E0 and dS is zero at each

point. Hence, electric flux through Gaussian surface = Φ=∫E.ds

=∫Eds= E*4πr2

Now, Gaussian surface is outside the given charged shell,so charge enclosed by the Gaussian surface

is Q. Hence, by Gauss’s theorem

E*4πr2 = c.

E =Q/4πr2 ε0

Thus, electric field outside a charged thin spherical shell is same as if the wholecharge Q is concentrated at the centre. Graphically,

Y

Emax

E Eα 1/r2

X

r=R r

For r ‹ R, there is no strength of electric field inside a charged spherical shell.

For r › R, electric field outside a charged thin spherical shell is same as if the wholecharge Q is concentrated at the centre.

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2012

Q

R

o .

Q. Why should electrostatic field be zero inside a conductor? (1)

Ans: If the electric field inside the conductor is not zero, the electrons will accelerate due to the electric field and for the electrostatic condition the net field becomes zero due to the redistribution of the charge carries and electrons come at rest (electrostatics).

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2013

Q. What is the geometrical shape of equipotential surfaces due to a single isolated charge? (1)

ANS: The equipotential surfaces due to a single isolated charge are concentric spherical surfaces. As the distance

from the charge increases the electric field strength will decrease and the distance between the spherical surfaces will increase.

DIAGRAM:figure-2.9(a),page=60,ncert book, class-xii.

2014

Q. Why do the electric field lines never cross each other? (1)

Ans: Electric field line is a curve drawn in such a way that the tangent to it at each point is in the direction of the net

field at that point. Two fields can never cross each other. If they did,it means the field at the point of intersection will not have a unique direction, which is meaningless).

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CHAPTER-2,ELECTROSTATIC POTENTIAL AND CAPACITANCE

2006

Q. Define the term 'dielectric constant' of a medium in terms of capacitance of a capacitor.(1)

ANS: Dielectric constant of a medium is defined as the ratio of the capacitance of a capacitor with the dielectric as the medium to its capacitance with vacuum between its plates.

Q. The electric field and electric potential at any point due to a point charge kept in air is 20NC-1 and 10JC-1 respectively. Compute the magnitude of this charge. (2)

ANS: E=1/4πε0(q/r2)=20NC-1

V=1/4πε0(q/r)=10NC-1

And R=V/E=10/20=1/2=0.5

So, q=4πε0rV=10*0.5/9*109

=0.55* 10-9

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Q.11.The given graph shows the variation of charge q versus potential difference V for twocapacitors C1 and C2. The two capacitors have same plate separation but the plate areaof C2 is double than that of C1. Which of the lines in the graph correspond to C1 and C2and why? (2)

ANS: q A

B

V

As q =CV so, C=q/V and graph A has a larger slope than B, so the graph A represents a capacitor of larger

capacitance.Also, C= ε0A/d, hence: C α A.

As the plate area of C2is double of that of C1, so C2 has a larger capacitance. Hence theline A of the graph corresponds to C2.

---------2008

Q. Derive the expression for the electric potential at any point along the axial line of an electric-

dipole? (2)

ANS: FIGURE:

A B P

Let P be an axial point at distance r from the centre of the dipole. Electric potential at point P is given asV= V1+ V2, V1 and V2are the potentials at point P due to charges +q and -q respectively.

V=1/4πε0 (q/r-a +-q/r+a)

=q/4πε0( 2a/r2-a2)=1/4πε0( p/r2-a2)

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

(b) Calculate the work done to dissociate the system of three charges placed on the vertices of an equilateral triangle of side 10 cms.as shown. Here, q = 1.6*10-10C.(5)

q

-4q +2q

ANS:

(a) The figure given below shows an electric dipole of charges +q and –q which are separated by distance 2a.

Refer,Figure :NCERT BOOK Fig no-2.16,Page-66.

A NS: Expression for the torque: The above arrangement forms a couple. The couple exerts a torque which is given by, τ=Force x Perpendicular distance between the two forces

=qE x 2a.sinθ

=pEsinθ(p=2aq,dipole moment)

Since the direction of torque is perpendicular to p and Ewe can rewrite the above equation as,

τ =pX E.

(b) The work done will be equal to the potential energy of the system

U= 1/4πε0[ (q*2q)/0.1+(q*-4q)/0.1+(2q*-4q)/0.1]

=9*109*10(-10q2)

=9*109*10*(-10)*1.6*10-10*1.6*10-10

=-23.04*10-9J.

2009

Q. Draw 3 equipotential surfaces corresponding to a field that uniformly increases in magnitude but remains constant along Z – direction. How are these surfaces different from that of a constant electric field along Z- direction? (2)

ANS: Planes parallel to the x-y plane. If the field increases and equi-potential surfaces are drawn for the same difference in potential then as the field increases the surfaces will become closer to each other.

F IGURE:

X Z

Q.A parallel plate capacitor is charged by a battery. After some time the battery is dis-connected and a dielectric slab

of dielectric constant K is inserted between the plates.

How would (i) the capacitance (ii) the electric field between the plates and (iii) the energystored in the capacitor be affected? Justify your answer. (3)

_ _ _ + + + ANS: (i) On inserting a slab of dielectric constant K between the plates, the capacitance of the capacitor is K times. New capacitance, C =KCo.

(ii) The electric field between the plates of the capacitor decreases. It becomes E = Eo/k

(iii) The energy stored by a capacitor is Q2/2C0 which becomes Q2/2C =Q2/2kC0

So the energy stored becomes 1/K times its original value.

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2010

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

(1)

ANS: Stable position of the dipole: parallel to electric field. Un-stable position: perpendicular to the electricfield. Q.A parallel plate capacitor is charged by a battery. After sometime the battery isdisconnected and a dielectric slabs its thickness equal to the plate separation is inserted between the plates. How will (i) the capacitance of the capacitor. (ii) Potential difference between the plates and (iii) the energy stored in the capacitor be affected?Justify your answer in each case.(3)

ANS: (i) Capacitance of the capacitor increases by a factor K, i.e., it becomes KC.

(ii) Net electric field will get reduced. As potential difference V=-Ed, as E is reduced,potential- difference between the capacitor plates also reduces. (iii) Energy of the capacitor:As the charge Q is fixed on plates,Energy stored in the capacitor,

U =q2/2C=1/k*(energy without di-electric) So, Uα 1/k ,it goes down.

Q. (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 r1 and r2 respectively in the presence of external electric field E. (3)

ANS: a) An equipotential surface is a surface with a constant value of potential at all points on the surface. The Equipotential surfaces for two identical positive charges. Refer figure, Ncert book,Fig.no:2.11(b),page-60.

First, we calculate the work done in bringing the charge q1 from infinity to r1. Work done in this step is q1 V (r1). Next, we consider the work done in bringing q2 to r2. In this step, work is done not only against the external field E but

also against the field due to q1. Work done on q2 against the external field = q2 V (r2) Work done on q2 against the field due to q1 = q1q2/4πε0r12 Where r12 is the distance between q1 and q2. By the superposition principle for fields, we add up the work done on q2 against the two fields (E and that due to q1): Work done in bringing q2 to r2 = q2Vr2+q1q2/4πε0r12

Thus, Potential energy of the system= the total work done in assembling the configuration= q1 V (r1)+q2 V (r2)+ q1q2/4πε0r12. ------------------------------------------------------------------------------------------------------------------------------------------ 2011 Q. Two uniformly large parallel thin plates having charge densities + δ and – δ are kept in the X-Z plane at a distance’d’

apart. Sketch an equi-potential surface due to electric field between the plates. If a particle of mass m and charge '-q' remains stationary between the plates, what is the magnitude and direction of the field? (3) OR Two small identical electrical diploes AB and CD, each of dipole moment 'p' are kept an angle of 120o as shown in the figure. What is the resultant dipole moment of this combination? If this system is subjected to electric field E directed

along +X direction, what will be the magnitude and direction of the torque acting on this?(3) Y

D +q

X 1200 X’

C

-q

Y’

Ans:

+ + + + + +

Here the darkarrows represent the parallel equi-potential surfaces along X-Z plane. If a charge q has to be held stationary between the two plates, it will have to be balanced by two forces. Gravitational force: mg, downwards Electrostatic force= 2qE, acting upwards.

This implies, that in X-Z plane, the upper plate is + charged plate & lower plate is –charged plate. So, E field lines have to be directed along –y axis. OR Resultant dipole moment, pres =p1+p2 =(p1

2 +p22+2 p1p2cos1200 )1/2

=p Direction of resultant dipole moment: tanθ =psin1200/p+pCos1200 =(3)1/2 So, θ =600 That is, 30 degrees with +x axis. Given applied E is along +x axis, So torque on resultant dipole will be ζ=pESin300=pE/2.

Direction will be along -z axis.

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. Q.Figure shows to identical capacitors, C1 and C2, each of 1 F capacitance connected to a battery of 6V.Initially switch ‘S’ is closed. After sometimes ‘S’ is left open and dielectric slabs of dielectric constant K =3 are inserted to fill

completely the space between the plates of the two capacitors. How will the (i) charge and (ii) potential difference between the plates of the capacitors be affected after the slabs are inserted?

ANS: In C2: Charge QD = CDVD will not change. Where CD = K C= increases K times

VD = V/K = decreases K times.

In C1: Charge QD = CDV Potential V remains the same as 6V. Charge QD =KCV= KQ, increases K times.

2012

Q.Draw a plot showing the variation of (i) electric field Eand (ii) electric potential V with distance r due to a point charge Q. (2)

Ans: E at a point varies inversely as the square of its distance from Q. V at a point varies inversely as its distance from Q. Figure 2.4, NCERT Book, Page No- 55.

------------------------------------------------------------------------------------------------------------------------------------------ 2013 Q. What is the geometrical shape of equi-potential surfaces due to a single isolated charge?

- - - - -

ANS: 1. The equi-potential surfaces due to a single isolated charge are concentric spherical surfaces. As the distance from the charge increases the electric field strength will decrease and the distance between the spherical surfaces will increase.

+q -q

.A capacitor has been charged by a dc source. What are the magnitudes of conduction and displacement currents, when it is fully charged? (2)

ANS: Electric flux through the plates of the capacitor, ɸ =q/ . As q is constant after the capacitor is fully charged,

ɸ will also be a constant. So displacement current, Id = ɸ/dt =0 .Conduction current = Ic =C dV/dt =0 as V is

constant.

Ic = Id when the capacitor will be fully charged.

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Q.A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 300 µC.When potential across the capacitor is reduced by 100 V, the charge stored in it becomes 100 µC.Calculate the potential V and the unknown capacitance. What will be the charge stored in the capacitor if the voltage applied had increased by 100 V? (3) OR

A hollow cylindrical box of length 0.5 m and area of cross-section 20 cm2 is placed in a three dimensional coordinate system as shown in the figure. The electric field in the region is given byE=20xi, where Eis inNC-1& x is in metres.Find: (i) Net flux through the cylinder. (ii) Charge enclosed in the cylinder. Y O X 0.5m Z ANS: We know :Q= CV in case1 : 300x10-6= CV........(i)

in case2 :100 x10-6=C(V-100)…….(ii)

from(i) & (ii) : V =150 V.

C=Q/V=2*10-6F=2 micro farad.

If voltage applied have increased by 100 V:

Charge stored will be=Q= CV

in this case: Q=2*10-6*250=500*10-6C.

OR

E=20xi

E1=at the left circular face=10i(putting the value of x)

E2=at the right circular face=20i(putting the value of x)

(i) ɸnet =∫E.ds=∫E1.ds+∫E2.ds+∫E.ds(curve surface)

=-10*20/100*100+-20*20/100*100=0.02Nm2C-1

(ii)Charge enclosed in the cylinder=q/

So,q=

=0.177*10-12 (on simplification, putting the value of ).

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Q.A capacitor has been charged by a dc source. What are the magnitudes of conduction and displacement currents, when it is fully charged?

ANS: 3. Electric flux through the plates of the capacitor, ɸ =q/ .

As q is constant after the capacitor is fully charged, ɸwill also be a constant.

So displacement current,Id = ɸ/dt =0.

Conduction current = Ic =C dV/dt =0 as V is constant.

Ic = Id when the capacitor will be fully charged.

Q.While travelling back to his residence in the car, Dr. Pathak was caught up in a thunderstorm. It became very dark.

He stopped driving the car and waited for thunderstorm to stop? Suddenly he noticed a child walking alone on the road. He asked the boy to come inside the car till the thunderstorm stopped. Dr. Pathak dropped the boy at his residence. The boy insisted that Dr. Pathak should meet his parents. The parents expressed their gratitude to Dr. Pathak for his concern for safety of the child.

Answer the following questions based on the above information:

(a) Why is it safer to sit inside a car during a thunderstorm?

(b) Which two values are displayed by Dr. Pathak in his actions?

(c) Which values are reflected in parents’ response to Dr. Pathak?(d) Give an example of a similar action on your part in the past from everyday life. (4)

ANS: (a) Because the car acts like electric shield. We know that the electric field inside theclosed conductor is zero.

(b) Awareness and humanity or concern.

(c) Gratitude and obligation.

I was struck in severe thunder storm once in an isolated place. I insisted to go out of the car and enjoy the rain. My parents advised not to go out of the car otherwise I may get thunderstruck.

2014

Q. Considering the case of a parallel plate capacitor being charged, show how one is required to generalize Ampere's circuital law to include the term due to displacement current. (2)

Ans: 9. Consider the charging of a capacitor. The electric field between the plates of the capacitor is as follows:If the plates of the capacitor have an area A and a total charge Q, the magnitude of the electric field between the plates is

E=Q/AƐ0

The field is perpendicular to the surface S as shown in the figure.Thus, using Gauss’s law the electric flux through the surface is

ɸE= E A=QA/AƐ0=Q/Ɛ0

Now, if the charge Q on the capacitor is changing with time, there is a current associated with it, so we have,

dɸE/dt = ( 1/Ɛ0) dQ/dt =( 1/Ɛ0)i

or, I = Ɛ0( d ɸE/dt)

This term is the current due to changing electric field and is called displacement current. Thus, the Ampere’s Circuital law is modified to give

∫B.dl ( d ɸE/dt)

Q. A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor. (2)

ANS: The capacitance of two capacitors is same, i.e. C. The voltage across charged capacitor is V1 = V and that across uncharged capacitor is V2= 0. Thus, the initial energy stored in the capacitor is U1=1/2C1V1

2=1/2CV2

When the charged capacitor is connected across the uncharged capacitor, the two capacitors form a parallel combination.Thus, the resultant capacitance is C’ = C + C = 2C. The initial charge on the capacitor is q = CV.The final potential across the combination will be V’=q1+q2/C’=q/2C=CV/2C=V/2. Hence, the final energy in the combination of capacitors is U2=1/2C’V’2= 1/2(2C)(V/2)2 =CV2/4

Thus, the ratio of energy stored in the combined system to that in the initial single capacitor is given as U2/U1=1/2.

Q: Draw a labelled diagram of Van de Graff generator. State its working principle to show ,how by introducing a small charged sphere into a larger sphere, a large amount of charge can be transferred to the outer sphere. State the use of this machine and also point out its limitations. (5) OR

(a) Deduce the expression for the torque acting on a dipole of dipole moment P in the presence of a uniform electric field (b) Consider two hollow concentric spheres S1 and S2, enclosing charges 2Q and 4Q respectively as shown in the figure. (i) Find out the ratio of the electric flux through them. (ii) How will the electric flux through the sphere s1 change if a medium of dielectric constant ' r' is introduced in the space inside s1 in place of air? Deduce the necessary expression. (5)

ANS: Principle:

1) The charge always resides on the outer surface of hollow conductor.

2) The electric discharge in air or gas takes place readily at the pointed ends of the conductors.

Construction:

It consists of a large hollow metallic sphere S mounted on two insulating columns and an endless belt made up of rubber which is running over two pulleys P1 and P2 with the help of an electric motor.B1 and B2 are two sharp

metallic brushes. The lower brush B1 is given a positive potential by high tension battery and is called a spray brush, while the upper brush B2 is connected to the inner part of the sphereS.

Working:

When brush B1 is given a high positive potential then it produces ions due to the action of sharp points. Thus, the positive ions so produced get sprayed on the belt due to repulsion between positive ions and the positive charge on brush B1. Then it is carried upward by the moving belt.The pointed end of B2 just touches the belt, collects the positive charge and makes it move to the outer surface of the sphere S. This process continues and the potential of the shell rises to several million volts.

Uses:

(1) It can be used to separate different charges. (2) It can be used to accelerate particles like protons, α particles, etc. to high speeds and energies. Limitations:

4Q S2

2Q S1

(1) It cannot be used to generate potential more than 7 million volts. (2) There is only one sided movement available for the charges due to series connection. OR

(a) Consider an electric dipole placed in uniform electric field. The axis of dipole makes an angle Ѳ with the direction electric field E . Diagram, NCERT Book.

The force acting on charge +q at B is +qEin the direction of E and the force acting oncharge –q at A is –qE in the direction opposite to E.

These two equal, opposite and parallel non-collinear forces separated by perpendicular distance BP acting on the electric dipole forms a couple.The torque on the dipole is given as

Ţ = Magnitude of force perpendicular distance between two parallel forces

=qE* BP

=qE* 2lsinѲ

=pEsinѲ( Since, p= q* 2l )

Thus, in vector form, we have, Ţ= p * E.

(b) (i) Let Ф1 and Ф1 be the electric flux through the spheres S1 and S2 respectively.

Then, ɸ1 = 2Q/ Ɛ0......(1)

ɸ2=(2Q + 4Q)/Ɛ0= 6Q/ Ɛ0......(2)

From (1) and (2), we get the ratio of the electric flux passing through the spheres S1 and S2 as

ɸ1/ɸ2=1/3.

(ii) Let E be the electric field intensity on the surface of the sphere S1 due to the charge 2Q present inside the sphere. Then, according to Gauss’ theorem, we have

ɸ1= ∫E.dS =2Q/ Ɛ0

On introducing a medium of dielectric constantƐr inside the sphere S1, suppose that electric field becomes E'. Then,

we haveE' =E/Ɛr.

The electric flux through the sphere is now Φ1’, then we have

ɸ1’= ∫ E’.dS = 1/Ɛ0 ∫ E’.dS = 2Q/ Ɛ0Ɛr.

Thus if a medium of dielectric constant Ɛr is introduced in the space S1 instead of air the electric flux through the

sphere S1 becomes 2Q/ Ɛ0Ɛr.

2015

Q. Write a relation for polarisation P of a dielectric material in the presence of an external electricfield E. (1) Ans: The relation for polarisation P of the dielectric medium in the presence of an external electric field Eis P = E, where susceptibility is a constant characteristic of the dielectric and is known as the electric of a dielectric material.

Q.Explain briefly the process of charging a parallel plate capacitor when it is connected across a d.c. battery.A capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time thebattery is disconnected and the distance between the plates is doubled. Now a slab ofdielectric constant,1<k<2,

is introduced to fill the space between the plates. How will the following be affected? (a) The electric field between the plates of the capacitor (b) The energy stored in the capacitor Justify your answer by writing the necessary expressions. [3] ANS: Consider a parallel plate capacitor connected across a d.c. battery as shown in the figure. The electric current will flow through the circuit. As the charges reach the plate, the insulating gap does not allow the charges to move further; hence, positive charges get deposited on one side of the plate and negative charges get deposited on the other side of the plate. As the voltage begins to develop, theelectric charge begins to resist the deposition of further charge. Thus, the current flowing through the circuit gradually becomes less and then zero till the voltage of the capacitor is exactly equal but opposite to the voltage of the battery. This is how the capacitor gets charged when it is connected across a d.c. battery. (a) The electric field between the plates is E = V/D

The distance between plates is doubled, d' = 2d E’=V’/D’=(V/K)*1/2d =1/2(E/K) Therefore, if the distance between the plates is double, the electric field will reduce to one half. As the capacitance of the capacitor,

(b) As the capacitance of the capacitor, C’=E0KA/d’=E0KA/2d=1/2C ……(1)

Energy stored in the capacitor is U=Q2/2C

U’=Q2/2C’ = Q2/2(1/2) C = 2(Q2/2C)2U(from 1)

Therefore, when the distance between the plates is doubled, the capacitance reduces to half. Therefore, energy stored in the capacitor becomes double.

Q .(a) Deduce the expression for the potential energy of a system of two charges q1 and q2 located r1 and r2,respectively, in an external electric field. (b) Three point charges, + Q + 2Q and – 3Q are placed at the vertices of an equilateral triangle ABC of side l. If these charges are displaced to the mid-point A1, B1 and C1,respectively, find the amount of the work done in shifting the charges to the new locations.

A1 C1

B(+2Q) B1 C(-3Q) OR

ANS.(a) Let q1 and q2 be the two charges located at r1 and r2, respectively, in an external electric field. The work done in bringing the chare q1 from infinity to r1 is W1 = q1V (r1), where V(r1) is the potential. Similarly, the work done in

bringing the chare q1 from infinity to r2 can be calculated. Here, the work is done not only against the external field E but also against the field due to q1. Hence, work done on q2 against the external field is W2 = q2V (r2).

Work done on q2against the field due to q1, W12 = q1q2/4 E0r12 where r12 is the distance between q1 and q2. By the principle of superposition for fields, work done on q2 against two fields will add with work done in bringing q2 to r2, which is given as W2+ W12= q2V (r2)+ q1q2/4∏E0r12. Thus, the potential energy of the system U = total work done in assembling the configuration

U= W1+ W2+ W12. = q1V (r1)+ q2V (r2)+ q1q2/4∏E0r12. (b)q1=+Q, q2=+2Q, q3=-3Q r = l (for each side) Intial potential energy of system

U1=1/4∏E0 l [q1*q2+q2*q3+q3*q1 ]

=-7Q2/4∏E0 l ( putting the value of q1,q2,q3 and after simplification) U2=1/4∏E0 l/2 [q1*q2+q2*q3+q3*q1 ] =-7Q2/2∏E0 l ( putting the value of q1,q2,q3 and after simplification) Work done=U2-U1

=-7/4(Q2/2∏E0 l)

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SECTION-B

MINIMUM LEVEL OF LEARNING Unit-I, Electrostatics (CHAPTER 1- Charge and Electric field.CHAPTER 2- Potential and capacitance.) Formulas

Electrostatics is the study of charges at rest. Charging a body can be done by friction, induction and conduction. Properties of charges: 1 Charge on a body is quantized Q=+ ne

2. charge of an isolated system is conserved 3. Charge on a body is speed independent

To measure charge electroscopes are used.

Coulomb’s law: k= = 9X109 Nm2c-2

Principle of superposition: [vector sum of individual forces] Coulomb’s law for multiple charges

Ftotal = F12 + F 13 + …. 1 31 212 132 2

12 13

1 1 ....4 4q qq q r r

r r

Electric field: Force experienced by a unit positive (or test) charge. It is a vector. SI unitNC-1.

0oq

o

FE Ltq

urur

Field due to a point charge:

Variation of E with r for point charge is as shown in the graph

Electric field intensity due to multiple point charges : 1

ntotal ri

E E

ur ur

[vector sum of individual fields]

Dipole: Two equal and opposite charges separated by a small distance.

E

r

Dipole moment: Product of magnitude of charge and distance of separation between them. It is a vector. SI unit: Cm,

=Q.2 ; direction of is along line joining the negative to positive charge.

Electric field due to a dipole (for l <r)

(a)at any point on the axial line: along the direction of dipole moment

(b)at any point on the equatorial line: opposite to the direction of dipole moment.

Dipole in a uniform electric field experiences no net force and instead experiences a torque.

= =

If = 0 stable equilibrium; If = unstable equilibrium.

Electric flux: = = ; It is a scalar; SI unit: NC-1m2 or Vm.

Gauss’ theorem in electrostatics:

Expressions for charge densities for different types of Uniform Charge distributions:

Linear charge density: Unit Cm-1] for linear charge distribution

Surface charge density: Unit Cm-2] for surface charge distribution

Volume charge density: Unit Cm-3] Volume charge distribution Electric Field Intensity on extreme left, In between and on extreme right of

uniformly and oppositely charged thin conducting plates

EI =0 EII = EIII =0 APPLICATION OF GAUSS’S THEOREM

Son.

Charge distribution

Charge density

Types of Gauss’s surfaces Surface area for which

Gauss’s theorem

Electric field Intensity

1 Infinitely long straight uniformly charged conductor

Linear charge density

Cylindrical

Lateral surface

area

2. Infinitely extended plane sheet of Charge

Surface charge density

Plane

Plane surface

=

3

uniformly Charged spherical shell

Surface charge density

Spherical surface

Properties of electric field lines:. 1.The imaginary path along which a unit positive charge placed in the electric field tends to follow is the magnetic line of force 2. The electric lines of force emanate from a positive charge and terminate on a negative charge. The tangent to an electric field line at any point gives the direction of the electric field at that point. 3. No two electric lines of force cross each other. If they do, then at the point of intersection, there will be two tangents. It means there are two values of the electric field at that point, which is not possible. 6. Electric lines of force are closer (crowded) where the electric field is stronger and the lines spread out where the electric field is weaker. 4. Electric lines of force contract lengthwise to represent attraction between two unlike charges and Electric lines of force exert lateral (sideways) pressure to represent repulsion between two like charges.

Electrostatic Potential: Work done per unit positive Test charge to move it from infinity to that point in an electric field against the field direction . It is a scalar. SI unit: J/C or V

V = W / qo

Electric potential at any point at a distance r from a point charge q:

Graphs: Variation of E & V due to a point charge at any point in the field with r (Graph-1) and Variation of V with 1/r

(Graph-2)

Electric field is conservative. This means that the work done is independent of the path followed and the total work

done in a closed path is zero.

Potential due to a system of charges: 1i

iin kq

rtotalv

Potential due to a dipole at any arbitrary point

on its axial line: = (since =0°)

on its equatorial line: = 0 (Since =90°)

Potential difference

Potential energy of charge q1 in the field of q2 or vice versa : U =

Potential energy of a dipole in a uniform electric field: U = = p E [ - Electrostatics of conductors

(i) Inside a conductor Electrostatic field is zero (ii) On the surface E is always Normal (iii) No charge inside the conductor but gets distributed on the surface (iv) Charge distribution on the surface is uniform if the surface is smooth (v) Charge distribution is inversely proportional to ‘r’ if the surface is uneven (vi) Potential is constant inside and on the surface

Equipotential surfaces: The surfaces on which the potential is same at all the points of the surface.

As E= - If Vis constant, E and if E is constant, V

Capacitor: A device to store charges and electrostatic potential energy.

Capacitance: QCV

, Ratio of charge and potential difference. Scalar,

SI unit: farad [F]

Capacitance of a parallel plate capacitor: Capacitance of a parallel plate capacitor with a dielectric medium in between:

Cm = Combination of capacitors:

Capacitors in series:1

1 1n

i ic c

Capacitors in parallel :1

n

ii

c c

Energy stored in capacitors:21 1 12

2 2 2QU CV QVC

Area shaded in the Q-V graph = U =

Energy density : =

Values of Different quantities after Introducing dielectric slab between the plates of the charged capacitor:

Description

When Battery connected When Battery disconnected

V

Q

Charge K Q0 Q0 Potential difference

V0 V0/K

Electric field

E0 E0/K

Capacitance KC0 KC0 Energy

K times [Energy is supplied By battery]

1/K times [Energy used for Polarization]

On connecting two charged capacitors:

Common Potential:

Loss of energy: Heat generated in the capacitors on connecting them is equal to this loss of energy.

CONCEPT MAP

FORCE/FIELD/POTENTIAL/P.E

CONCEPT MAP

CHARGE ITS IMPACT

QUESTION FOR MLL

Very Short Questions(1 mark)

1. Is the force acting between two point electric charges and kept at some distance apart in air, attractive or

repulsive when (i) > 0 (ii) <0 ? (i. Repulsive ii. Attractive)

2. Which physical quantity has its SI unit as ( 3. How does the force between two point charges change if dielectric constant of medium in which they are kept

increases. (decreases) 4. Which orientation of an electric dipole in a uniform electric field would correspond to stable equilibrium? 5. Define electric dipole moment of a dipole. State its SI unit. 6. Why is it necessary that the field lines from a point charge placed in the vicinity of a conductor must be normal to the surface of the conductor at every point? 7.A 500 µC charge is at the Centre of a square of side 10cm.Find the work done in moving a charge of 10 µC between

two diagonally opposite points on the square. (Solution:- The 500 µC charge is placed at the centre of a square. This charge is, therefore, at the same distance from all the corners of the square. The opposite corners, say A and C, will have the same potential i.e., . Work done in moving a charge q between points A and C is given as: W = q(VC − VA) = q × 0 = 0 Hence, no work is done in moving the charge between two diagonally opposite points on the square.)

8. Vehicles carrying inflammable materials usually have metallic ropes touching the ground during motion. Why? (To leak the charge developed on the body of the vehicle due to air friction to the earth to avoid any hazardous incident) 9. Ordinary rubber is an insulator. But the special rubber tires of aircraft are made conducting. Why is this necessary?(During landing , the tires of space craft get charged due to friction between the tyres and the ground. In case the tyres are slightly conducting , the charge developed on the tyres will not stay on them and leak to the earth) 10. In the following fig. calculate the potential difference across capacitor C2. GivenpotentialatAis90V.C1=20µF,C2=30µF,andC3=15µF.

C1 C2 C3

A Resultant capacitance Cs =(20/3)µF Charge on Cs = (20/3)µF*90V =600µC Charge on C2 is also 600µC Potential across C2=600µC/30µF=20V Shorts Questions (2 marks)

1.Deriveanexpressionfortheworkdoneinobtaininganelectricdipolefromits equilibriumpositiontoananglewiththeuniformelectrostaticfield. 2.Showthatthereisalwaysalossofenergywhentwocapacitorscharged todifferentpotentialssharecharge(connectedwitheachother). 3.Four point charges +5 mC, +2 mC, +10mC and +2 mC are kept at the corners of a square of side 10 cm. A charge q=+1mC is placed at its centre. Find the net force on q. 4. Calculate the distance between two protons such that the electrostatic force between them is equal to the weight of either. 5. Two point charges are 0.1 m apart and their combined charge is 9 mC. If they repel each other with a force 18N, then calculate the magnitude of each charge. 6. Calculate the Coulomb force between two alpha particles separated by a distance of 3.2 x 10-15 m 7. A proton moves through a uniform electric field of 5.01 x 10 3 N/C. Calculate (a) the acceleration with which the proton is moving and (b) the time taken by the proton to cover a distance of 4.8 cm. 8.How many electrons would have to be removed from or added to apenny to leave it charged with 1.0 x 10-6 C [Ans: 6.25 x 10 12] 9. What is the Coulomb’s force between two small charged spheres having charges of 2.0 x 10-7 C and 3.0 x 10-7C placed 30 cm in air? [Ans: 6.0 x 10-3N] 10.Twopointcharges–qand+qareplaced metreapart,asshowninfig. GivethedirectionofelectricfieldatpointsA,B,CandD. D

B– qA + qC (along AB at A, along BA at B, along AC at C along AB at D)

11. Calculate the work required to separate two charges4µc and –2µc placed a (-3cm,0,0)and(+3cm,0,0)infinitely awayfrom each other.

12. What is meantby dielectric polarization? Why does the electric field inside adielectricdecreasewhenitisplacedinanexternalfield? 13.Calculatetheworkdoneintakingachargeof1µCinauniformelectric fieldof10N/CfromBtoCgivenAB=5cmalongthefieldandAC=10 cm per pendicular to electricfield.

A B

C 14. The plates of a parallel plate air capacitor are separated by a distance of 1 mm. What mustbe the plate area if the capacitance of the capacitor is to be 1F?

SHORT ANSWER QUESTIONS (3 MARKS)

1.

Find the equivalence capacitance between X and Y.

As the combination is parallel, Cp=(3+3+3)µF = 9µF

2.Assuming earth to be an isolated conducting sphere of radius 6400 km, what is the capacitance of earth?

3.An isolated sphere has a capacitance of 50pF.Calculate its radius. How much charge should be placed on it to raise its potential to 104V?

4.Twenty seven spherical drops, each of radius 3mm and carrying 10–12C of charge are combined to form a single drop. Find the capacitance and potential of the bigger drop.

5. Define electrostatic potential and write its unit. Obtain expression for electrostatic Potential at a point Pin the field due to a point charge. 6.Calculatetheelectrostaticpotentialenergyforasystemofthreepoint chargesplacedatthecornersofanequilateraltriangleofside‘a’. 7.A charge Q is distributed over two concentric hollow sphere of radii r and R(R>r),such that their surface density of charges are equal. Find Potential at the common c entre.

3 µf 3 µf 3 µf Y

X

8. Defineelectricflux.WriteitsSIunit. How many units of electricfluxpasses normallythroughasphericalGaussiansurfaceofradiusr,duetopoint chargeplacedatthecentre? (1)WhatisthechargeenclosedbyGaussiansurface? (2)IfradiusofGaussiansurfaceisdoubled,howmuchfluxwillpass throughit? 9.Whatisanequipotentialsurface?Writethreeproperties.Sketch equipotentialsurfacesof (i)Isolatedpointcharge(ii) Uniformelectricfield(iii) Dipole 10. What are dielectrics?Give some examples of polar and non polarmolecules. Distinguish polar and nonpolar dielectrics.

11.Derive an expression for the electric field due to an electric dipole at a point on (a) the axial line (b) the equatorial line.

12.Derive an expression for the torque acting on an electric dipole placed in a uniform electric field. 13.Show that the work done in rotating an electric dipole of dipole moment p in a uniform electric field

E by an angle ¸ from the equilibrium position

14.State and verify Gauss theorem .Use Gauss theorem to derive an expression for the electric field at a point due to an infinite plane sheet of charge of uniform charge density σ

15. Derive an expression for the electric field at a point due to a thin infinitely long straight conductor of charge of uniform charge density

16.Derive an expression for the electric field at a point due to uniformly charged spherical shell using Gauss’ law.

17.Derive an expression for the capacitance of a parallel plate capacitor.

18.A dielectric slab of thickness t introduced between the plates of a parallel plate capacitor separated by a distance d. (t < d). Derive an expression for the capacitance of the capacitor.

Formula based Nemerical Questions

1. Force between two points electric charges kept at a distance d apart in air is F.If these charges are kept at the same distance in water, how does the force between them get effected ?

2. Two point charges 10µC and 20µC are separated by a distance r in air. If an additional charge of -8µC is given to each, by what factor does the force between the charges change?

3. Calculate the Coulomb force between a proton and an electron separated by a distanceof0.8x10-15m.

4. Two point charges Q are kept at a distance r from each other. A third charge q is place on the line joining the above two charges such that all the three charges are in equilibrium, what is the magnitude, sign and the position of the charge q?

5. A charge q is placed at the centre of the line joining two equal charges Q and Q. Calculate the value of charge q such that all the three charges are in equilibrium. Also mention the nature of this charge.

6. Two point charges of charge values Q and q are placed at a distance of x and x/2 respectively from a third charge of charge value 4q, all charges being in the same straight line. Calculate the magnitude and nature of charge Q such that the net force experienced by the q charge is zero.

7. Two point electric charges of values q and 2q are kept at a distance d apart from each other in

air. A third charge Q is to be kept along the same line in such a way that the net force on q and 2q is zero. Calculate the position of the charge Q in terms of q and d.

8. Force of attraction between two point charges placed at a distance‘d’ apart in a medium is ‘F’. What should be the distance in the same medium so that the force between them becomes 9F?

9. Two similarly and equally charged identical metal spheres A and B repel each other with a force of 2x10-5 N. A third identical uncharged sphere C is touched with A and then placed at the midpoint between A and B. Calculate the net electric force on C.

VALUEBASEDQUESTIONS

1.AnelderlywomanwentalonetotheRegistrar’sofficetodisburseherproperty.WhensheenquiredintheofficeshewasaskedtogetaXeroxcopyofthedocumentwhichworksunderelectrostaticinduction.TheXeroxshopwasfarawayandacrosstheroad.Shetookthehelpofthepasser–byandgothere for getting the Xeroxdone.

a)Whatvaluesdidthepasser-byhave? b)Howdoesaneutralbodygetchargedbyelectrostaticinduction? 2)RamandShyamwenttothetradefair.Theywerebyside of acrowdedcorner. WhereBalloons weresold.Achildwasseentroublinghisparentandcryingforsomething.Onseeingthis,Ramwenttothechildandsaidthathewouldperformatrickwithballoons.RamtooktwoballoonsandShyamhelpedhimtoinflateandtie.Whentheballoonswererubbedwiththesweaterhewaswearing,theywereattracted.Whentakennearertowall,theballoonsgotstuck.Thechildenjoyedandstoppedcrying. a)GivetwovaluesofRamandShyam. b)Howdidtheballoonsgetattracted?Willtheyrepelalso? 3)Arunhadtorepairthiscarwhenhewasremindedbythecarcompanyforhisregularcarservice.Hetoldthemtodospraypaintingofmountaindewcolour.Thecompanyalsorepliedthattheyusuallyperformspraypainting onlyaswastageisminimizedandevenpaintingachieved. a)Whatvaluesdidthecarservicecompanyhave? b)Ifspraypaintingisdonebyelectrostaticinduction,howisevenpaintingachieved?

.4)InAkash’sclassroomthefanabovetheteacherwasrunningveryslowly.Duetowhichhisteacherwassweatingandwasrestlessandtired.Allhisclassmateswantedtorectifythis.Theycalledforanelectricianwhocameandchangedthecapacitoronlyafterwhichthefanstartedrunningfast.

a)WhatvaluesdidAkashandhisclassmateshave? b)Whatenergyisstoredinthecapacitorandwhere? Important Information

1.Van de Graaff is omitted from syllabus.

2. Direct formula based Numericalare asked only

3. To revise solved examples &numericals givenin NCERT Text Book

QUESTION BANK OF PROBABLE QUESTIONS FOR AISSCE 2016

Questions that have been repeated at least three or more times

Long answer questions (5 marks)

UNIT – 1: ELECTROSTATICS

(Chapter – 1: Electric charges and fields, chapter-2: Electrostatic potential and capacitance)

1. Using Gauss’s law obtain the expression for the electric field due to a uniformly charged thin spherical shell of radius R at a point outside, inside and on the surface of the shell. Draw a graph showing the variation of electric field with r, for r>R and r<R.

2. State Gauss theorem in electrostatics. Apply this theorem to obtain the expression for the electric field at a point due to an infinitely long, thin, uniformly charged straight wire of linear charge density λ C/m.

3. Derive an expression for the energy stored in a parallel plate capacitor Charged to a potential difference V. Hence derive an expression for the energy density of a capacitor.


Questions that have been repeated one or two times

Long answer questions (5 marks)

UNIT – 1: ELECTROSTATICS

(Chapter – 1: Electric charges and fields, chapter-2: Electrostatic potential and capacitance)

1. Find an expression for the electric field strength at a distant point situated (i) on the axis and (ii) along the equatorial line of an electric dipole.

2. Find expression for the torque on an electric dipole kept in a uniform electric field. Identify two pairs of perpendicular vectors in the expression.

3. Briefly explain the principle of a capacitor. Derive an expression for the capacitance of a parallel plate capacitor, whose plates are separated by a dielectric medium.

4. Derive the expression for the electric potential at a point due to an electric dipole. Mention the contrasting features of electric potential of a dipole at a point as compared to that due to a single charge.

5. Define electric flux. Write its S.I. unit. Using Gauss’s law, prove that the electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it.How is the field directed if (i) the sheet is positively charged,(ii) negatively charged?

FREQUENTLY ASKED QUESTIONS FOR REVISION

CHAPTER:3 CURRENT ELECTRICITY

ONE MARK QUESTIONS

1 Define the term ‘mobility’ of charge carriers. Write its S.I. unit.

2008

2 V – I graph for a metallic wire at two different temperatures T1 and T2 is as shown in the figure. Which of the two temperatures is higher and why?

2015

3 Two metallic resistors are connected first in series and then in parallel across a d.c. supply. Plot of I – V graph is shown for the two cases. Which one represents a parallel combination of the resistors and why?

2015

4 I – V graph for two identical conductors of different materials A and B is shown in the figure. Which one of the two has higher resistivity?

2015

5 Distinguish between emf and terminal voltage of a cell.

2008

6 Show variation of resistivity of copper as a function of temperature in a graph

2007

7 When electrons drift in a metal from lower to higher potential, does it mean that all the free electrons of the metal are moving in the same direction?

2012

8 Show on a graph the variation of resistivity with temperature for a typical semiconductor?

2012

9 A 10 V battery of negligible internal resistance is connected across a 200 V battery and a resistance as shown in the figure find the value of current in the circuit.

2013

10 Two wires, one of copper and the other of manganin, have same resistance and equal thickness. Which wire is longer? Justify your answer.

2009 2012

11 Two wires, one of copper and the other of manganin, have same resistance and equal thickness. Which wire is thicker? Justify your answer.

2012

12 Two conducting wires X and Y of same diameter but different materials are joined in series across a battery. If the number density of electrons in X is twice that in Y, find the ratio of drift velocity of electrons in the two wires.

2010

13 A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: Current, current density, drift speed, electric field?

2011 2009

14 A wire of resistance 8 R is bent in the form of a circle. What is the Effective resistance between the ends of a diameter AB ?

2010

15 Show on a graph the variation of resistivity of carbon with temperature for a typical semiconductor?

2006

16 The variation of potential difference V with length l in case of two potentiometers P and Q is as shown, which of these two you will prefer for comparing emfs of two primary cells?

2006

TWO MARKS QUESTIONS

1

Calculate the current drawn from the battery by the network of resistors shown in figure

2009, 2015

2 Draw a circuit diagram of a potentiometer .State its working principle. Derive the necessary formula to describe how it is used to compare the emfs of the two cells.

2008

3 With the help of the circuit diagram, explain the working Principle of meter bridge. How it is used to determine the unknown resistance of a given wire? Write the necessary precautions to minimize the error in the result.

2007 2009

4 Using the concept of drift velocity of charge carriers in a conductor, deduce the relationship between current density and resistivity of the conductor.

2009

5 A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor : current, current density, electric field, drift speed ?

2012

6 Use Kirchhoff’s rules to obtain conditions for the balance condition in a Wheatstone bridge.

2009 2013

7 A variable resistor R is connected across a cell of emf E and internal resistance r as shown in the figure. Draw a plot showing the variation of (i) terminal voltage V and (ii) the current I, as a function of R.

2011

8 In the potentiometer circuit shown, the null point is at X. State with reason, where the balance point will be shifted when (a) Resistance R is increased, keeping all other parameters unchanged; (b) Resistance S is increased, keeping R constant.

2012

9 State the two Kirchhoff’s rules used in electric networks. How are these rules justified?

2008

10 Define the term ‘power loss’ in a conductor of resistance R carrying a current I. In what form does this power loss appear? Show that to minimize the power loss in the transmission cables connecting the power stations to homes, it is necessary to have the connecting wires carrying current at enormous high values of voltage.

2011

11 In the circuit diagram shown, AB is a uniform wire of resistance 15 Ω and length 1 m. It is connected to a cell E1 of emf 2 V and negligible internal resistance and a resistance R. The balance point with another cell E2 of emf 75 mV is found at 30 cm from end A. Calculate the value of the resistance R.

2009

12 Use Kirchhoff ’s rules to determine the potential difference between the points A and D when no current flows in the arm BE of the electric network shown in the figure.

2007

13 A potentiometer wire of length 1m has a resistance of 10 Ω . it is connected to a 6V battery in series with a resistance of 5Ω . Determine the emf of the primary cell which gives the balance point at 40 cm

2005

14 (a) State the working principle of a potentiometer. With the help of a circuit diagram, explain how a potentiometer is used to compare the emfs of two primary cells. Obtain the required equation used for the comparing of emfs.

(b) Write two possible causes for one sided deflection in a potentiometer experiment.

2013

15 A cell of emf E and internal resistance r is connected to two external resistances R1 and R2 and a perfect ammeter. The current in the circuit is measured in four different situations:

2012

(i) without any external resistance in the circuit. (ii) with resistance R1 only (iii) with R1 and R2 in series combination (iv) with R1 and R2 in parallel combination. The currents measured in the four cases are 0.42 A, 1.05 A, 1.4 A and 4.2 A, but not necessarily in that order. Identify the currents corresponding to the four cases mentioned above.

16 In the meter bridge experiment, balance point was observed at J with AJ = l. (i) The values of R and X were doubled and then interchanged. What would be the new position of balance point? (ii) If the galvanometer and battery are interchanged at the balance position, how will the balance point get affected?

2011

17 In the given circuit, assuming point A to be at zero potential, use Kirchhoff’s rules to determine the potential at point B.

2011

18 Show that the electric field at the surface of a charged conductor is given by E = 0) n, where is the surface charge density and $ n is a unit vector normal to the surface in the outward direction.

2007

19 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 ?

2008

20 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. Predict from the graph the condition under which ‘V’ becomes equal to ‘E‘.

2009

21 Derive an expression for drift velocity of free electrons in a conductor in terms of relaxation 2009

time.

22 A wire of 15 Ω resistances is gradually stretched to double its original length. It is then cut into two equal parts. These parts are then connected in parallel across a 3 00 volt battery. Find the current drawn from the battery.

2009

23 (a) You are required to select a carbon resistor of resistance 47 k10% from a large collection. What should be the sequence of colour bands used to code it? (b) Write the characteristics of manganin which make it suitable for making standard resistance.

2012

THREE MARKS QUESTIONS

1 In the two electric circuits shown in the figure, determine the readings of ideal Ammeter (A) and the ideal voltmeter (V).

2015

2 In the circuit shown in the figure, find the current through each resistor.

2015

3 (a) Deduce the relation between current I flowing through a conductor and drift velocity d of the electrons. (b) Figure shows a plot of current ‘I’ flowing through the cross-section of a wire versus the time‘t’. Use the plot to find the charge flowing in 10s through

2014

the wire..

4 A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable

load resistor R. Draw the plots of the terminal voltage V versus (i) R and (ii) the current I. It is found that when R = 4 , the current is 1 A and when R is increased to 9 , the current reduces to 0.5 A. Find the values of the emf E and internal resistance r.

2013

5 A potential difference V is applied across a conductor of length L and diameter D. How is the drift velocity, vd, of charge carriers in the conductor affected when (i) V is halved, (ii) L is doubled and (iii) D is halved ? Justify your answer in each case.

2015

6 Two wires X, Y have the same resistivity, but their cross-sectional areas are in the ratio 2 : 3 and lengths in the ratio 1 : 2. They are first connected in series and then in parallel to a d.c. source. Find out the ratio of the drift speeds of the electrons in the two wires for the two cases.

2011

7 Define the electric resistivity of a conductor. Plot a graph showing the variation of resistivity with temperature in the case of a (a) conductor, (b) semiconductor. Briefly explain, how the difference in the behaviour of the two can be explained in terms of number density of charge carriers and relaxation time.

2010

8 Plot a graph showing the variation of current density (j) versus the electric field (E) for two conductors of different materials. What information from this plot regarding the properties of the conducting material, can be obtained which can be used to select suitable materials for use in making (i) standard resistance and (ii) connecting wires in electric circuits ? Electron drift speed is estimated to be of the order of mm s–1. Yet large current of the order of few amperes can be set up in the wire. Explain briefly.

2009

9 A 16 Ω resistance wire is bent to form a square. A source of emf 9 V is connected across one of its sides as shown. Calculate the current drawn from the source. Find the potential difference between the ends C and D. If now the wire is stretched uniformly to double the length and once again the same cell is connected in the same way, across one side of the square formed, what will now be the potential difference across one of its diagonals?

2014

10 When a metallic conductor is subjected to a certain potential V across its ends, discuss briefly how the phenomenon of drift occurs. Hence define the term ‘drift velocity’ of charge carriers and show that the current density j is related to the applied electric field E by the relation j= Ewhere defines the conductivity of the material.

2009

11 State the underlying principle of a potentiometer. Write two factors by which current sensitivity of a potentiometer can be increased. Why is a potentiometer preferred over a voltmeter for measuring the emf of a cell ?

2007

12 Find the relation between drift velocity and relaxation time of charge carriers in a conductor. A conductor of length L is connected to a d.c. source of emf ‘E’. If the length of the conductor is tripled by stretching it, keeping ‘E’ constant, explain how its drift velocity would be affected.

2006

13

Write any two factors on which internal resistance of a cell depends. The reading on a high resistance voltmeter, when a cell is connected across it, is 20 V. When the terminals of the cell are also connected to a resistance of 3as shown in the circuit, the voltmeter reading drops to 15 V. Find the internal resistance of the cell.

2010

14 State Kirchhoff’s rules. Use these rules to write the expressions for the currents I1, I 2 and I 3 in the circuit diagram shown.

2010

15 Prove that the current density of a metallic conductor is directly proportional to the

drift speed of Electrons. 2005

16 A number of identical cells, n, each of emf E, internal resistance r connected in series are charged by a d.c. source of emf E, using a resistor R. (i) Draw the circuit arrangement. (ii) Deduce the expressions for (a) the charging current and (b) the potential difference across the combination of the cells.

2007

17 A potentiometer wire of length 1 m is connected to a driver cell of emf 3 V as shown in the figure. When a cell of 15 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. (i) Calculate unknown emf of the cell. (ii) Explain with reason, whether the circuit works, if the driver cell is replaced with a cell of emf 1 V. (iii) Does the high resistance R, used in the secondary circuit affect the balance point? Justify your Answer.

18 A network of resistors is connected to a 16 V battery of internal resistance of 1 as shown in the Figure.

(a) Compute the equivalent resistance of the network. (b) Obtain the voltage drops VAB and VCD .

19 Calculate the value of the resistance R in the circuit shown in the figure so that the current in the circuit is 0.2 A. What would be the potential difference between points B and E?

2012

20 In the figure a long uniform potentiometer wire AB is having a constant potential gradient along its length. The null points for the two primary cells of emfs 1and 2 connected in the manner shown are obtained at a distance of 120 cm and 300 cm from the end A. Find (i) 1 / 2 and (ii) position of null point for the cell 1. How is the sensitivity of a potentiometer increased?

2012

FOUR MARKS (VALUE BASED)/FIVE MARKS QUESTIONS

1 Ameen had been getting huge electricity bill for the past few months. He was upset 2015

about this. One day his friend Rohit, an electrical engineer by profession, visited his house. When he pointed out his anxiety about this to Rohit, his friend found that Ameen was using traditional incandescent lamps and using old fashioned air conditioner. In addition there was no proper earthing in the house. Rohit advised him to use CFL bulbs of 28 W instead of 1000 W – 220 V and also advised him to get proper earthing in the house. He made some useful suggestion and asked him to spread this message to his friends also. (i) What qualities/values, in your opinion did Rohit possess ? (ii) Why CFLs and LEDs are better than traditional incandescent lamps ? (iii) In what way earthing reduces electricity bill

2 Ajit had a high tension tower erected on his farm land. He kept complaining to the authorities to remove it as it was occupying a large portion of his land. His uncle, who was a teacher, explained to him the need for erecting these towers for efficient transmission of power. As Ajit realized its significance, he stopped complaining. Answer the following questions : (a) Why is it necessary to transport power at high voltage ? (b) A low power factor implies large power loss. Explain. (c) Write two values each displayed by Ajit and his uncle.

2015

3 During a thunderstorm the ‘live’ wire of the transmission line fell down on the ground from the poles in the street. A group of boys, who passed through, noticed it and some of them wanted to place the wire by the side. As they were approaching the wire and trying to lift the cable, Anuj noticed it and immediately pushed them away, thus preventing them from touching the live wire. During pushing some of them got hurt. Anuj took them to a doctor to get them medical aid. Based on the above paragraph, answer the following questions : (a) Write the two values which Anuj displayed during the incident. (b) Why is it that a bird can sit on a suspended ‘live’ wire without any harm whereas touching it on the ground can give a fatal shock ? (c) The electric power from a power plant is set up to a very high voltage before transmitting it to distant consumers. Explain, why.

2014

4 (a) State Kirchhoff ’s rules and explain on what basis they are justified. (b) Two cells of emfs E1 and E2 and internal resistances r1 and r2 are connected in parallel. Derive the expression for the (i) emf and (ii) internal resistance of a single equivalent cell which can replace this combination.

2010

5 Two heating elements of resistances R1 and R2 when operated at a constant supply of voltage V, consumes powers P1 and P2 respectively. Deduce the expressions for the power of their combinations when they are, in turn, connected in (i) Series and (ii) parallel across the same voltage supply.

2011

EXPECTED QUESTIONS FOR REVISION/MLL

CHAPTER:3 CURRENT ELECTRICITY

1 Define the terms I. ‘Mobility’ of charge carriers.

II. Average relaxation time. III. Quantization of charge IV. Drift velocity of electrons V. Temperature co efficient of resistivity. VI. Current density

2 V – I graph for a metallic wire at two different temperatures T1 and T2 is as shown in the figure.

Which of the two temperatures is higher and why?

3 Two metallic resistors are connected first in series and then in parallel across a d.c. supply. Plot of

I – V graph is shown for the two cases. Which one represents a parallel combination of the resistors and why?

4 I – V graph for two identical conductors of different materials A and B is shown in the figure.

Which one of the two has higher resistivity?

5 Distinguish between emf and terminal voltage of a cell.

6 Show variation of resistivity as a function of temperature in a graph for

I. Metals II. Semiconductors

III. Alloys

7 Find the colour code for a resistance 23 KΩ 20%.

8 Write any two limitations of Ohm’s law. 9 Draw a circuit diagram of a potentiometer .State its working principle. Derive the necessary formula to

describe how it is used to compare the emfs of the two cells.

10 Draw a circuit diagram of a potentiometer .State its working principle. Derive the necessary formula to describe how it is used to find internal resistance of a primary cell

11 With the help of the circuit diagram, explain the working Principle of meter bridge. How it is used to determine the unknown resistance of a given wire?

12 Use Kirchhoff’s rules to obtain conditions for the balance condition in a Wheatstone bridge. 13 In the potentiometer circuit shown, the null point is at X. State with reason, where the balance point

will be shifted when (a) Resistance R is increased, keeping all other parameters unchanged; (b) Resistance S is increased, keeping R constant (c) the potential of the driving cell is less than the experimental cell Also write any two possible causes of one-sided deflection.

14 A potential difference V is applied across a conductor of length L and diameter D. How is the drift velocity, vd, of charge carriers in the conductor affected when (i) V is halved, (ii) L is doubled and (iii) D is halved? Justify your answer in each case.

15 In the meter bridge experiment, balance point was observed at J with AJ = l. (i) The values of R and X were doubled and then interchanged. What would be the new position of balance point? (ii) If the galvanometer and battery are interchanged at the balance position, how will the balance point get affected?

16 State the underlying principle of a potentiometer. Write two factors by which current sensitivity of a potentiometer can be increased. Why is a potentiometer preferred over a voltmeter for measuring the emf of a cell ?

17 Deduce the relation between current I flowing through a conductor and drift velocity d of the electrons.

18 A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor : current, current density, electric field, drift speed ?

19 State Kirchhoff’s rules. Use these rules to write the expressions for the currents I1, I 2 and I 3 in the circuit diagram shown.

20 Two cells of emfs E1 and E2 and internal resistances r1 and r2 are connected in parallel. Derive the

expression for the (i) emf and (ii) internal resistance of a single equivalent cell which can replace this combination.

21 Write the characteristics of Manganin which make it suitable for making standard resistance. Why Manganin is used in the Metre Bridge?

22 A battery has an emf E and internal resistance r. A variable resistance R is connected across the terminals of the battery. Find the value of R such that

I. The current is maximum II. The potential difference across the terminals is maximum

III. Plt a graph between V and R. 23 Explain how a meter bridge is used to determine the resistivity of the material of a wire in the

laboratory. Why it is preferred to get a null point almost at the middle of the wire?

FREQUENTLY ASKED QUESTIONS FOR REVISION

CHAPTER:4 MAGNETIC EFFECT OF CURRENT

ONE MARK QUESTIONS

1 Write the expression in a vector form for the Lorentz magnetic force F due to a charge moving with a velocity V in a magnetic field B .What is the direction fo the magnetic force

2013

2 What is the direction of the force acting on a charge particle q, moving with a velocity v in a uniform magnetic field B?

2008

3 An electron does not suffer any deflection while passing through a region of uniform magnetic field. What is the direction of the magnetic field?

2009

4 A beam of particles projected along +x-axis, experiences a force due to a magnetic field along the +y-axis. What is the direction of the magnetic field?

2012 2007

5 Write two factors by which voltage sensitivity of a galvanometer can be increased. 2008 6 Write two properties of a material used as a suspension wire in a moving coil

galvanometer. 2006

7 An electron moving through a magnetic field does not experience a force; under what condition is it possible?

2005

8 Name the physical quantity whose S I unit is Wb-m2, is it ascalar or vector quantity? 2005 9 Two wires of equal length are bent in the form of two loops , One of the loops is square

shaped and another is circular. These loops are suspended in a uniform magnetic field and same current is passed through them. Which loop will experience greater torque?

2005

10 How does the magnetic moment of an electron in a circular orbit of radius ‘r’ and moving with a speed ‘v’ change ,when the frequency of revolution doubled?

2005c

TWO MARKS QUESTIONS

1

A square loop of side 20 cm carrying current 1 A is kept near an infinitely long straight wire carrying current 2 A ,calculate the magnitude and direction of net force on the loop due to the current carrying con doctor.

2015

2 A square shaped plane coil of area 100 cm2 of 200 turns caries a steady current of 5 A . it is placed in a uniform magnetic field of 0.2 T acting perpendicular to the plane of the coil.

2014

Calculate the torque on the coil when its plane makes an angle of 60o with the direction of the field. In which orientation will the coil be in stable equilibrium?

3 An ammeter of resistance 0.80 can measure current upto 1.0 A. (i) What must be the value of shunt resistance to enable the ammeter to measure current upto 5.0 A? (ii) What is the combined resistance of the ammeter and the shunt?

2013 2007

4 Two identical circular wires P and Q each of radius R and carrying current ‘I’ are kept in perpendicular planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net magnetic field at the common centre of the two coils.

2012

5

Two identical circular loops, P and Q, each of radius r and carrying currents I and 2I respectively are lying in parallel planes such that they have a common axis. The direction of current in both the loops is clockwise as seen from O which is equidistant from the both loops. Find the magnitude of the net magnetic field at point O.

2012 2014

5 A wire of length L is bent round in the form of a coil having N turns of same radius. If a steady current I flows through it in a clockwise direction, find the magnitude and direction of the magnetic field produced at its centre

2009

6 A straight wire carrying a current of 12 A is bent into a semi-circular arc of radius 20 cm as

shown. What is the magnetic field B at O due to (i) straight segments (ii) the semi-circular arc?

2010

7 A jet plane is travelling west at 450 ms 1. If the horizontal component of earth’s magnetic field at that place is 4 104 tesla and the angle of dip is 30°, find the emf induced between the ends of wings having a span of 30 m.

2008

8 Write the expression for Lorentz magnetic force on a particle of charge ‘q’ moving with velocity v in a magnetic field B . Show that no work is done by this force on the charged particle.

2012

9 A steady current (I1) flows through a long straight wire. Another wire carrying steady current (I2) in the same direction is kept close and parallel to the first wire. Show with the help of a diagram, how the magnetic field due to the current I1 exerts a magnetic force on the second wire. Write the expression for this force.

2012

10 A rectangular loop of wire of size 4 cm × 10 cm carries a steady current of 2A. A straight long wire carrying 5A current is kept near the loop as shown. If the loop and the wire are coplanar, find (i) the torque acting on the loop and (ii) The magnitude and direction of the force on the loop due to the current carrying wire.

2012

11 A particle of charge ‘q’ and mass ‘m’ is moving with velocity V. It is subjected to a uniform magnetic field B directed perpendicular to its velocity. Show that it describes a circular path. Write the expression for its radius

THREE MARKS QUESTIONS

1 A closely wound solenoid of 2000 turns and cross sectional area 1.6 x10–4

m2 carrying a current of 4.0 A is suspended through its centre allowing it to turn in a horizontal plane. Find the magnetic moment associated with the solenoid, (ii) Magnitude and direction of the torque on the solenoid if a horizontal magnetic field of 7.5x10–2 T is set up at an angle of 30with the axis of the solenoid.

2014

2 State the principle of working of a galvanometer. A galvanometer of resistance G is converted into a voltmeter to measure upto V volts by connecting a resistance R1 in series with the coil. If a resistance R2 is connected in series with it, then it can measure upto V/2 volts. Find the resistance, in terms of R1 and R2, required to be connected to convert it into a voltmeter that can read upto 2 V. Also find the resistance G of the galvanometer in terms of R1 and R2.

2015

3 (a) Why is the magnetic field radial in a moving coil galvanometer? Explain how it is achieved. (b) A galvanometer of resistance ‘G’ can be converted into a voltmeter of range (0-V) volts by connecting a resistance ‘R’ in series with it. How much resistance will be required to change its range from 0 to V/2?

2013

4 Deduce the expression for the torque acting on a planar loop of area A and carrying current I

placed in a uniform magnetic field B, If the loop is free to rotate, what would be its orientation in stable equilibrium?

2010

5 A cyclotron’s oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons? If the radius of its ‘dees’ is 60 cm, calculate the kinetic energy (in MeV) of the proton beam produced by the accelerator.

2006

6 State Biot – Savart law. Deduce the expression for the magnetic field at a point on the axis of a current carrying circular loop of radius ‘R’, distant ‘x’ from the centre. Hence write the magnetic field at the centre of a loop.

2007

7 A uniform magnetic field of 6·5 10– 4 T is maintained in a chamber. An electron enters into the field with a speed of 4·8 106 m/s normal to the field. Explain why the path of the electron is a circle. Determine its frequency of revolution in the circular orbit. Does the frequency depend on the speed of the electron ? Explain.

2008 2011

8 A uniform magnetic field is set up along the positive x-axis. A particle of charge ‘q’ and mass ‘m’ moving with a velocity v enters the field at the origin in X-Y plane such that it has velocity components both along and perpendicular to the magnetic field B Trace, giving reason, the trajectory followed by the particle. Find out the expression for the distance moved by the particle along the magnetic field in one rotation.

2013

9 A wire AB is carrying a steady current of 12 A and is lying on the table. Another wire CD carrying 5A is held directly above AB at a height of 1 mm. Find the mass per unit length of the wire CD so that it remains suspended at its position when left free. Give the direction of the current flowing in CD with respect to that in AB. [Take the value of g = 10 ms–2]

2010

10 Depict the field-line pattern due to a current carrying solenoid of finite length. (i) In what way do these lines differ from those due to an electric dipole? (ii) Why can’t two magnetic field lines intersect each other?

2009

11 A long straight wire AB carries a current I. A proton P travels with a speed v, parallel to the wire, at a distance d from it in a direction opposite to the current as shown in the figure. What is the force experienced by the proton and what is its direction?

2010

12 2010

An -particle and a proton moving with the same speed enter the same magnetic field region at right angles to the direction of the field. Show the trajectories followed by the two particles in the region of the magnetic field. Find the ratio of the radii of the circular paths which the two particles may describe.

FOUR MARKS (VALUE BASED QUESTIONS)

1 Asha’s uncle was advised by his doctor to have an MRI (magnetic resonance imaging) scan of his brain. Her uncle felt that it was too expensive and wanted to postpone it. When Asha learnt about this, she took the help of her family and when she approached the doctor, he also offered a substantial discount. She thus convinced her uncle to undergo the test to enable the doctor to know the condition of his brain. The resulting information greatly helped his doctor to treat him properly. Based on the above paragraph, answer the following questions : (a) What according to you are the values displayed by Asha, her family and the doctor ? (b) What in your view could be the reason for MRI test to be so expensive? (c) Assuming that MRI test was performed using a magnetic field of 0·1 T, find the maximum and minimum values of the force that the magnetic field could exert on a proton (charge = 1·6 x 10–19

C) that was moving with a speed of 104 m/s.

2015

2 Deepika and Ruchika were asked by their teacher to perform an experiment using a galvanometer. Before doing the experiment they were very keen to know the different parts of the galvanometer which was given to them in the form of a small box. They approached the teacher and asked for the permission. The teacher thought it would be a good idea if the galvanometer be opened before the whole class and explained its construction and working to all of them. Based on the above paragraph, answer the following questions : (a) What, in your opinion, were the qualities displayed by Deepika, Ruchika and the teacher? (b) State briefly the working principle of the galvanometer. (c) What is the shape of the magnets used and why is it so designed?

2014

FIVE MARKS QUESTIONS

1 (a) Use Biot-Savart law to derive the expression for the magnetic field due to a circular coil of radius R having N turns at a point on the axis at a distance ‘x’ from its centre. Draw the magnetic field lines due to this coil. (b) A current ‘I’ enters a uniform circular loop of radius ‘R’ at point M and flows out at N as shown in the figure. Obtain the net magnetic field at the centre of the loop.

2010 2015

2 (a) Show how Biot-Savart law can be alternatively expressed in the form of Ampere’s

circuital law. Use this law to obtain the expression for the magnetic field inside a solenoid of length ‘l’, cross-sectional area ‘A’ having ‘N’ closely wound turns and carrying a steady current ‘I’. Draw the magnetic field lines of a finite solenoid carrying current I. (b) A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in therod through the wires. Find the magnitude and direction of the magnetic field which should be set up in order that the tension in the wire is zero.

2003

3 (a) State Ampere’s circuital law. Use this law to obtain the expression for the magnetic field inside an air cored toroid of average radius ‘r’, having ‘n’ turns per unit length and carrying a steady current I. (b) An observer to the left of a solenoid of N turns each of cross section area ‘A’ observes that a steady current I in it flows in the clockwise direction. Depict the magnetic field lines due to the solenoid specifying its polarity and show that it acts as a bar magnet of magnetic moment m = NIA.

2008 2005

4 (a) Draw the magnetic field lines due to a circular loop of area A carrying current I. Show that it acts as a bar magnet of magnetic Moment m =AI . (b) Derive the expression for the magnetic field due to a solenoid of length ‘2 l’, radius ‘a’ having ‘n’ number of turns per unit length and carrying a steady current ‘I’ at a point on the axial line, distant ‘r’ from the centre of the solenoid. How does this expression compare with the axial magnetic field due to a bar magnet of magnetic moment ‘m’?

2013

5 (a) Draw a labelled diagram of a moving coil galvanometer. State its working principle. What is the function of a cylindrical soft iron core used in it ? (b) Define the terms (i) current sensitivity and (ii) voltage sensitivity. (c) Explain the underlying principle used in converting a galvanometer into a (i) voltmeter and (ii) ammeter.

2014

6 Draw a schematic sketch of a cyclotron. Explain its working principle. Obtain the necessary mathematical expression to show how this machine is used to accelerate charged particles

2011

7 (a) State Ampere’s circuital law. Show that the magnetic field B at a distance r outside the straight infinite wire carrying current I is tangential and is given by B = µo I / (2πr). (b) Consider a long straight cylindrical wire of circular cross-section of radius a, as shown in the figure. The current I is uniformly distributed across this cross-section. Calculate the magnetic field B in the region r < a and r > a. Plot a graph of B versus r from the centre of the wire.

2014

8 Two infinitely long straight parallel wires, ‘1’ and ‘2’, carrying steady currents I1 and I2

in the same direction are separated by a distance d. Obtain the expression for the magnetic field due to the wire ‘1’ acting on wire ‘2’. Hence find out, with the help of a suitable diagram, the magnitude and direction of this force per unit length on wire ‘2’ due to wire ‘1’. How does the nature of this force change if the currents are in opposite direction? Use this expression to define the S.I. unit of current

2011

9 Explain, using a labelled diagram, the principle and working of a moving coil galvanometer. What is the function of (i) uniform radial magnetic field, (ii) soft iron core? Define the terms (i) current sensitivity and (ii) voltage sensitivity of a galvanometer. Why does increasing the current sensitivity not necessarily increase voltage sensitivity?

2004 2012

10 a) Derive the expression for the torque on a rectangular current carrying loop suspended in a uniform magnetic field.

b) A proton and a deuteron having equal momentum enter in a region of uniform magnetic field at right angle to the direction of the field. Depict their trajectories in the field.

2008

11 (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. (b) Two small identical circular coils marked 1 and 2 carry equal currents and are placed with their geometric axes perpendicular to each other as shown in the figure. Derive an expression for the resultant magnetic field at O.

2009

12 If a particle of charge q is moving with velocity v along the y-axis and the magnetic field B

is acting along the z-axis, use the expression Fq ( v B) to find the direction of the force F acting on it. A beam of proton passes undeflected with a horizontal velocity v, through a region of electric and magnetic fields, mutually perpendicular to each other and perpendicular to the direction of the beam. If the magnitudes of the electric and magnetic fields are 100 kV/m, 50 mT respectively, Calculate (i) velocity of the beam (ii) Force exerted by the beam on a target on the screen, if the proton beam carries a current of 080 mA.

2009

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

2007 2010

14 If a particle of charge q is moving with velocity v along the y-axis and the magnetic field B isacting along the z-axis, use the expression F q ( v x B) to find the direction of the force F acting on it. A beam of proton passes undeflected with a horizontal velocity v, through a region of electric and magnetic fields, mutually perpendicular to each other and perpendicular to the direction of the beam. If the magnitudes of the electric and magnetic fields are 100 kV/m, 50 mT respectively, calculate (i) Velocity of the beam v. (ii) force exerted by the beam on a target on the screen, if the proton beam carries a current of 080 mA

2008

15 (a) State the principle of the working of a moving coil galvanometer, giving its labelled diagram. (b) “Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity.” Justify this statement. (c) Outline the necessary steps to convert a galvanometer of resistance RG into an ammeter of a given range.

2011

16 a) Using Ampere’s circuital law, obtain the expression for the magnetic field due to a long Solenoid at a point inside the solenoid on its axis. (b) In what respect is a toroid different from a solenoid? Draw and compare the pattern of the magnetic field lines in the two cases. (c) How is the magnetic field inside a given solenoid made strong?

2011

EXPECTED QUESTIONS FOR REVISION/MLL

CHAPTER:5 MAGNETISM

1 Write the magnetic properties of materials used preparing I. permanent magnets

II. electromagnets III. Core of the transformer

Give one example each.

2 The horizontal component of the earth’s magnetic field is equal to the vertical component at a place. Find the angle of dip?

3 Define the three elements to describe Earth’s magnetism at a place,show them in a diagram.

4 A uniform magnetic field gets modified as shown below when two specimens X and Y are placed in it. Identify whether specimens X and Y are diamagnetic, paramagnetic or ferromagnetic.

5 Which of the following substances are diamagnetic? Bi, Al, Na, Cu, Ca and Ni

6 How does angle of dip change as one goes from magnetic pole to magnetic equator of the Earth?

7 The permeability of a magnetic material is 0.9983. Name the type of magnetic materials it represents. 8 The susceptibility of a magnetic material is 1.9 × 10–5. Name the type of magnetic materials it represents. 9 The susceptibility of a magnetic materials is –4.2 × 10 6 . Name the type of magnetic materials it represents.

10 In what way is Gauss’s law in magnetism different from that used in electrostatics? Explain briefly.

The Earth’s magnetic field at the Equator is approximately 0.4 G; Estimate the Earth’s magnetic dipole moment. Given: Radius of the Earth = 6400 km.

11 How the following magnetic materials behave with the rise of temperature Para,Ferro,Dia-magnetic substances

12 Distinguish between Para, Ferro Dia-magnetic substances, give one example each 13 Deduce the expression for magnetic dipole moment of an electron revolving around the

Nucleus in a circular orbit of radius ‘r’. Indicate the direction of the magnetic dipole moment.

14 Deduce the expression for magnetic field due to a magnetic dipole at any point on the I. Axial line

II. Equatorial line Describe the expression for torque experienced by a dipole in a uniform magnetic field.

15 How magnetic field lines are different from electric field lines? Write any two properties of magnetic field lines.

16 Define the terms

I. Magnetic permeability II. Retentively

III. Coercively IV. Susceptibility

What do the area of the Hysteresis loop and slope of the graph between I and H signify?


CHAPTER – 6 (ELECTROMAGNETIC INDUCTION)

Questions that have been asked one time

VERY SHORT ANSWER QUESTIONS (1 MARK)

1. How does the mutual inductance of a pair of coils change when

(i) distance between the coils is increased and

(ii) number of turns in the coils is increased? [CBSE (AI) 2013]

Ans. (i) Decreases (ii) Increases

2. The motion of copper plate is damped when it is allowed to oscillate between the two poles of a magnet. What is the cause of this damping? [CBSE (AI) 2013]

Ans. As the plate oscillates, the changing magnetic flux through the plate produces a strong eddy current in the direction which opposes the cause. Also, copper being diamagnetic substance, it gets magnetized in the opposite direction, so the plate motion gets damped.

3. The closed loop PQRS is moving into a uniform magnetic field acting at right angles to the plane of the paper as shown. State the direction of the induced current in the loop. [CBSE (AI) 2012]

X X X X X P Q

X X X X X

X X X X X

X X X X X

X X X X X

X X X X X R S

Ans. along PSRQP

4. When current in a coil changes with time, how is the back emf induced in the coil related to it? [CBSE (AI) 2008]

Ans. The back emf induced in the coil opposes the change in current.

5. Write Faraday’s laws of electromagnetic induction[CBSE (AI) 2009]

Ans.(i) whenever the amount of magnetic flux linked with a closed circuit changes, an emf is induced in the circuit which lasts as long as the change in flux lasts.(ii) The magnitude of the induced emf in a circuit is equal to the time rate of change of magnetic flux through circuit.

SHORT ANSWER QUESTIONS (2, 3 MARKS)

1. Two identical loops, one of copper and the other of aluminium, are rotated with the same angular speed in the same magnetic field. Compare (i) the induced emf and (ii) the current produced in the two coils. Justify your answer. [CBSE (AI) 2010]

Ans.

(i) Induced emf is same in both loops (B,A and ω are same for both loops)

(ii) As area A, length l and emf E are same for both loops but the resistivity of copper is less than aluminium therefore current induced is larger in copper loop.

2. Define self-inductance of a coil. Obtain an expression for the energy stored in a solenoid of self-inductance L when the current through it grows from zero to I. [CBSE (AI) 2015]

Ans. Self-inductance of a coil is numerically equal to the magnetic flux linked with the coil when a unit current flows through it.

Energy stored in an inductor = ½ LI2

3. Define the term mutual inductance between the two coils. Obtain the expression for mutual inductance of a pair of long co-axial solenoids each of length l and radii r1and r2.Total number of turns in the two solenoids are N1 and N2 respectively.

[CBSE (AI) 2014, 2009]

Ans. When current flowing in one of two nearby coil, the coil, in which current is changed is called primary coil and the coil in which emf is induced is called the secondary coil.

The si unit of mutual inductance is henry.

Mutual Inductance: Suppose there are two coils C1 and C2. The current I1 flowing in primary coil c1 ; due to which an effective magnetic flux Φ2 is linked with secondary coil C2 .

Φ2=M21I1 , M21 is the mutual inductance of coil 2 w.r.t. coil 1

Mutual inductance between two coils (M21) is numerically equal to the flux linkage with secondary coil, when current flowing in primary coil is 1 ampere.

Mutual inductance of two co-axial solenoids: Consider two long coaxial solenoids each of length l with number of turns N1 and N2 wound one over the other. I1 is the current flowing in outer solenoid and B1 is the magnetic field produced within this solenoid.

B1= µ0n1I1 n1 is the number of turns per unit length of outer solenoid

Φ2= n2lB1A2= µ0n1I1 n2lA2 , n2 is the number of turns per unit length of inner solenoid, A2 is the cross-sectional area of inner solenoid, Φ2 is the flux linkage with inner solenoid.

M21 = µ0n1 n2lA2 , Similarly M12 = µ0n1 n2lA2

LONG ANSWER QUESTIONS (5 MARKS)

1. State Faraday’s law of electromagnetic induction. Figure shows a rectangular conductor PQRS in which the conductor PQ is free to move in a uniform magnetic field B perpendicular to the plane of the paper. The field extends from x=0 to x=b and is zero for x>b. Assume that only the arm PQ possesses resistance r. When the arm PQ is pulled outward from x=0 to x=2b and is then moved backward to x=0 with constant speed v, obtain the expression for the flux and the induced emf. Sketch the variations of these quantities with distance 0≤x≤2b. [CBSE (AI) 2010]

. . . . . . . .

.S . . . . . . .

. . . . . . P.

. . . . . . .

. . . . . . Q.

R. . . . . . . .

. x=0. . . x=b. x=2b

ANS. When the magnetic flux linked with a coil or circuit changes, an emf is induced in the coil. The emf and current last so long as the change in magnetic flux lasts

The magnitude of induced emf is proportional to the rate of change of magnetic flux linked with the circuit.

NCERT TEXT BOOK PART 1 page no. 217, Example 6.8

Questions that have been repeated two times

LONG ANSWER QUESTIONS (5 MARKS)

1. What are eddy currents? How are they produced? In what sense eddy currents are considered undesirable in a transformer? How can they be minimized? Give two applications of eddy currents.

[CBSE (AI) 2006, 2011]

ANS. Eddy currents are the currents induced in conductors when they are placed in changing magnetic flux region.

When a metallic plate is placed in a time varying magnetic field, the magnetic flux linked with the plate changes, the induced currents are set up in the plate, and these currents are called eddy currents

Production: For diagram Refer NCERT TEXT BOOK PART 1 page No. 218

In transformer, there is a huge loss of energy due to production of eddy currents, so these currents are undesirable in transformer.

Eddy currents may be minimized by using laminated core of soft iron.

APPLICATIONS: Induction furnace, Electromagnetic braking in trains, Electric power meters, Electromagnetic damping

2. State the working of a.c. generator with the help of a labelled diagram. The coil of an ac. Generator having N turns, each of area A, is rotated with a constant angular velocity. Deduce the expression for the alternating emf generated in the coil. What is the source of energy generation in this device?

[CBSE (AI) 2008C, 2011]

ANS. AC generator: A dynamo or generator is a device which converts mechanical energy into electrical energy.

Principle: It works on the principle of electromagnetic induction. When a coil rotates continuously in a magnetic field with its axis perpendicular to the magnetic field, the magnetic flux linked with the coil changes and an induced emf and hence a current is set up in it.

Construction:

(i) Field Magnet: It produces the magnetic field. In the case of a low power dynamo. The magnetic field is generated by a permanent magnet, while in the case of large power dynamo, the magnetic field is produced by an electromagnet.

(ii) Armature: It consists of a large number of tums of insulated wire in the soft iron drum or ring. It can revolve round an axle between the

two poles of the field magnet. The drum or ring serves the two purposes: (i) It serves as a support to coils and (ii) It increases the magnetic field due to air core being replaced by an iron core.

(iii) Slip rings: The slip rings are the two metal rings to which the ends of armature coil are connected. These rings are fixed to the shaft which rotates the armature coil so that the rings also rotate along with the armature.

(iv) Brushes: These are two flexible metal plates or carbon rods which are fixed and constantly touch the revolving rings. The output current in external load is taken through these brushes.

Diagram: Refer NCERT TEXT BOOK PART-1 page NO. 225

Working: when the armature coil is rotated in the strong magnetic field, the magnetic flux linked with the coil changes and the current is induced in the coil, its direction being given by Fleming’s right hand rule,

Expression for Induced. emf: If N is the number of

Turns in coil, f the frequency of rotation, A area of coil

And B the magnetic induction, then induced emf

e = - / t

= d/dt (NBA (cos 2πft))

= 2 sin 2πft

The source of energy generation is the mechanical energy of rotation of armature coil.

Expected Questions for MLL

1. State Lenz’s law (1)

ANS. The polarity of the induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it.

2. Write S.I unit of magnetic flux. Is it a scalar or vector quantity? (1)

ANS. Weber (wb). Scalar.

3. Write an expression for the energy stored in an inductor of inductance L, when a steady current is passed through it. Is the energy electric or magnetic? (1)

ANS. ½ LI2 , Magnetic energy.

4. Show that Lenz’s law is in accordance with the law of conservation of energy. (2)

ANS. When the north pole of a coil is brought near a close to coil, the direction of current induced in the coil is such as to oppose the approach the North Pole. For this the nearer face of coil behaves as North Pole. This necessitates an anticlockwise current in the coil when seen from the magnet side. (Fig a)

Similarly where North Pole of the magnet is moved away from coil the direction of current in the coil will be such as to attract the magnet. For this the nearer face of coil behaves as South Pole. The necessitates a clock wise current in the coil when seen from the magnet. (Fig b)

FIG. (a) Anticlockwise FIG. (b) Clockwise

5. Derive expression for self-inductance of a long air-cored solenoid of length l, cross-sectional area A and having number of turns N.

(3)

ANS. Consider a long air solenoid having ‘n’ number of turns per unit length. If current in solenoid is I, the magnetic field inside the solenoid, B = µ0nI

If A is cross-sectional area of solenoid, then effective flux linked with the solenoid of length ’l’; Φ = (NBA), where N=nl is the number of turns in length ‘l’ of solenoid.

Φ = (nlBA)

Substituting the value of B from (i)

Φ = nl (µ0nI ) A = µ0n2AlI

S N

N S N

S

Self-inductance of air solenoid

L = Φ/I = µ0n2Al

If N is total number of turns in length l, then

n= N/l

Self-inductance L = µ0(N/l)2Al

= µ0N2A/l

Q. 1. What do you mean by mutual inductance of two nearby coils? Find an expression for mutual inductance of two co-axial solenoid. (5)

[CBSE (F) 2013, 2010]

Ans. When current flowing in one of two nearby coils is changed, the magnetic flux linked with the other coil changes; due to which an emf is induced in it (other coil). This phenomenon of electromagnetic induction is called the mutual induction. The coil, in which current is changed is called primary coil and the coil in which emf is induced is called the secondary coil.

The si unit of mutual inductance is henry.

Mutual Inductance: Suppose there are two coils C1 and C2. The current I1 flowing in primary coil c1 ; due to which an effective magnetic flux Φ2

is linked with secondary coil C2 .

Φ2=M21I1 , M21 is the mutual inductance of coil 2 w.r.t. coil 1

Mutual inductance between two coils (M21) is numerically equal to the flux linkage with secondary coil, when current flowing in primary coil is 1 ampere.

Mutual inductance of two co-axial solenoids: Consider two long coaxial solenoids each of length l with number of turns N1 and N2 wound one over the other. I1 is the current flowing in outer solenoid and B1 is the magnetic field produced within this solenoid.

B1= µ0n1I1 n1 is the number of turns per unit length of outer solenoid

Φ2= n2lB1A2= µ0n1I1 n2lA2 , n2 is the number of turns per unit length of inner solenoid, A2 is the cross-sectional area of inner solenoid, Φ2 is the flux linkage with inner solenoid.

M21 = µ0n1 n2lA2 , Similarly M12 = µ0n1 n2lA2


CHAPTER – 6 (ALTERNATING CURRENT)



1. Mention the two characteristic properties of the material suitable for making core of a transformer. [ CBSE (AI) 2012]

ANS. (i) Low hysteresis loss (ii) Low coercivity.

2. In a series LCR circuit, the voltage across an inductor, a capacitor and a resistor are 30 volt, 30 volt and 60 volt respectively. What

is the phase difference between the applied voltage and current in the circuit? [ CBSE (AI) 2007]

Ans. tanΦ = ( VL - VC ) / VR

Φ = 00

3. The instantaneous current and voltage of an a.c circuit are given by i= 10 sin 314t ampere, v= 50 sin 314t volt. What is the power dissipation in the circuit? [ CBSE (AI) 2008]

Ans. Power = p = ½ V0 I0 cosΦ = 250 watt. Here Φ=00


1. (a) For a given a.c, i= i0sinωt, Show that the average power dissipated in a resistor R over a complete cycle is ½( i0 )

2 R.

(b) A light bulb is rated at 100 watt for a 220 volt a.c supply. Calculate the resistance of the bulb. [CBSE (AI) 2013]

Ans. (a) Derivation of average power

Average power = ½( i0 )2 R

(b) Average power = ( irms)2R = (Vrms )

2 /R Vrms =220 volt

R = 484 ohm.

2. State the principle of working of a transformer. Can a transformer be used to step up or step down a d.c voltage? Justify your answer [CBSE (AI) 2011]

Ans. Mutual induction, No, because there is no change in magnetic flux.

When d.c voltage is applied across a primary coil of a transformer, the current in primary coil remain same, so there is

no change in magnetic flux and hence no voltage is induced across the secondary coil.

3. How is the large scale transmission of electric energy over long distances done with the use of transformers? [CBSE (AI) 2012]

Ans. At the power generating station. The step up transformers step up the output voltage which reduces the current through the cables and hence reduce resistive power loss. Then at the consumer end, a step down transformer step down the voltage. Hence in this way the large scale transmission of electric energy over long distances can be done by transformer.

4. An a.c voltage V= V0sin wt is applied across a

(a) Series RC circuit in which capacitive reactance is a times the resistance of the circuit.

(b) Series RL circuit in which inductive impedance is ‘b’ times the resistance in the circuit.

Find the value of power factor of the circuit in each case.

ANS. Power factor cosΦ = (R/Z), when Z=√ (R2+X2)

(i) X=XC=aR, Z= √(R2+(aR2)) = R√(1+a2)

CosΦ = R/ (R√1+a2)) = 1/√ (1+a2)

(ii)X=XL=bR

(iii) Z=√(R2+(bR2)) = R√(1+b2)

CosΦ = R/ (R√1+b2)) =1/√ (1+b2)

5. An AC source of voltage V= Vmsin wt is applied across a series LCR circuit. Draw the phasor diagrams for the circuit, when

(i) Capacitive reactance exceeds the inductive reactance.

(ii) Inductive reactance exceeds capacitive reactance.

[CBSE (AI) 2008C]

ANS. When XC>XL: the phasor diagram is shown in fig. (a).

V - axis

VL

VR I0 I - axis

Φ

VC - VL

VC

Fig (a)

(iii) When XL>Xc, the phasor diagram is shown in fig. (b).

V - axis

VL

VL - VC

Φ

VR I0 I - axis

VC

FIG (b)

6. A voltage V= Vosin wt is applied to a series LCR circuit. Derive the expression for the average power dissipated over a cycle. Under what condition is (i) no power dissipated even though the current flows through the circuit. (ii) Maximum power dissipated in the circuit. [CBSE (AI) 2014]

Ans. Average power = p = ½ V0 I0 cosΦ

(i) When Φ = 900 or -900 , purely inductive or purely capacitive circuit

(ii) When Φ = o0 , at resonance(behaves like purely resistive circuit)

7. You are given three circuit elements X,Y and Z. When the element X is connected across an a.c. source of a given voltage, the current and the voltage are in the same phase. When the element Y is connected in series with X across the source, voltage is ahead of the current in phase by π/4. But the current is ahead of the voltage in phase by π/4 when Z is connected in series with X across the source. Identify the circuit elements X, Y and Z. When all the three elements are connected in series across the same source, determine the impedance of the circuit. Draw a plot of the current versus the frequency of the applied source and mention the significance of this plot. [CBSE (AI) 2015]

Ans. X= resistor, Y= inductor, Z= capacitor

Impedance = R2 + (XL - XC) 21/2

For plotting of current versus frequency refer NCERT text book part 1 page no. 248

LONG ANSWER QUESTIONS (5 marks)

1. Define the term capacitive reactance. Show graphically the variation of capacitive reactance with frequency of applied alternating voltage.

An ac voltage V= Vosinwt is applied across a pure capacitor of capacitance C. Find an expression for current flowing through it. Show mathematically the current flowing through it leads the applied voltage by angle (π/2). [CBSE (AI) 2008C]

ANS. Capacitive Reactance: The resistance offered by capacitor alone to the flow of alternating current is called the capacitive reactance.

It is denoted by XC. Its value is XC = (1/ωC) = (1/2πfC)

XC is inversely proportional to capacitance.

Phase Difference between current and applied voltage in purely Capacitive Circuit:

Circuit Containing Pure Capacitance: Consider a capacitor of capacitance C; its plates are connected to the terminals of a source of alternating voltage.

C

V= V0sinωt

V= Vo sinωt , q= cVo sinωt

I= dq/dt = cωV0 coswt

I = V0/(1/ωC) cos ωt = I0 sin(ωt + π/2)

Where I0= V0/XC Here XC= 1/ωC

Current leads the applied emf by an angle of π/2.

2. State the condition for resonance to occur in series LCR a.c circuit and derive an expression for resonant frequency. Draw a plot showing the variation of the peak current with the frequency of the a.c source used. Define quality factor Q of the circuit. [CBSE (AI) 2008]

Ans. For resonance the current produced in the circuit and emf applied must always be in the same phase.

For resonance Φ = 00, XC = XL

1/ω0C = ω0L ω0 = resonant angular frequency

ω0 = 1/√LC f0 = resonant frequency

Quality factor is defined as the ratio of resonant frequency to the band width of the circuit.

Q= ω0L/R

For graph refer NCERT TEXT BOOK PART 1 page NO. 248

3. Draw a schematic diagram of a step-up transformer. Explain its working principle. Deduce the expression for the secondary to primary voltage in terms of the number of turns in the two coils. In an ideal transformer, how is the ratio related to the currents in the two coils? How is the transformer used in large scale transmission and distribution of electrical energy over long distances?

Ans. Transformer is a device by which an alternating voltage may be decreased or increased. It is based on the principle of mutual induction.

Construction: It consists of laminated core of soft iron on which two coils of insulated copper wire are separately wound. These coils are kept insulated from each other and from the iron core, but are coupled through mutual induction. The number of turns in these coils are different. Out of these coils one coil is called primary coil and the other is called the secondary coil. The terminals of primary coils are connected to A.C mains and the terminals of the secondary coil are connected to external circuit in which alternating current of desired voltage is required. Transformers are of two types:

1. Step up transformer: It transforms the alternating low voltage to alternating high voltage and in this the number of turns in secondary coil is more than that in primary coil

2. Step down transformer: It transforms the alternating high voltage to alternating low voltage and in this the number of turns in secondary coil is less than that in primary coil

Diagram: Refer NCERT TEXT BOOK PART 1 PAGE NO- 260

Working: When alternating current source is connected to the ends of primary coil, the current changes continuously in the primary coil, due to which the magnetic flux linked with the secondary coil changes continuously, therefore the alternating emf of same frequency is developed across the secondary.

NS/NP = VS/VP

NS is the number of turns in secondary coil

NP is the number of turns in primary coil

VP is the alternating voltage applied to primary coil

VS is the alternating voltage across the secondary coil

IS/IP = NP/NS

In an ideal transformer input power = output power

VPIP=VSIS

NS/NP = VS/VP = IP/IS

At the power generating station. The step up transformers step up the output voltage which reduces the current through the cables and hence reduce resistive power loss. Then at the consumer end, a step down transformer step down the voltage. Hence in this way the large scale transmission of electric energy over long distances can be done by transformer.

Expected questions for MLL

1. What is the phase difference between the voltages across the inductor and a capacitor in an AC circuit? (1)

ANS. 1800 .

2. What is phase difference between voltage and current in a LCR series circuit at resonance? (1)

ANS. 00.

3. The peak value of e.m.f. in ac is E0. Write its (i) rms (ii)average value over a complete cycle. [CBSE (F) 2011] (1)

ANS. E0= peak value of emf

(i) rms value [Erms] =( E0/√2)

(ii) (ii) average value [Eav]= zero.

4. An electrical element X when connected to an alternating voltage source, has a current through it leading the voltage by (π/2)rad. Identify X and write an expression for its reactance . (1)

ANS. Capacitor, XC= 1/wc .

5. What will be the effect on inductive reactance and capacitive reactance if frequency of AC source increased? (1)

ANS. Inductive reactance will increase with the increase of frequency and capacitive reactance will decrease with the increase of frequency.

6. What is wattless current? [CBSE (DELHI) 2011] (1)

ANS. when pure inductor or pure capacitor is connected to AC source the current flows in the circuit but with no power loss. Such a current is called wattless current.

7. Define power factor? State the conditions under which it is maximum and minimum. [CBSE (DELHI) 2010] (2)

ANS. Power factor is the ratio of resistance and impedance of an AC circuit.

When Z=R, power factor in maximum (purely resistive).

Power factor is minimum (zero) when circuit is purely inductive or purely capacitive.

8. An air cored coil L and a bulb B are connected in series to the AC mains. The bulb closed with brightness. How would the glow of the bulb change if an iron rod were inserted in the coil? give reasons in support of your answer. (2)

ANS. When iron rod is inserted in the coil, the inductance of coil increases; so impedance of circuit increases and hence, current in circuit I = ( V/√(R2+(wL)2 ) decreases.

Consequently, the glow of bulb decreases.

9. Explain why the reactance provided by a capacitor to an alternating current decreases with increasing frequency. (2)

ANS. A capacitor does not allow flow of direct current through it as the resistance across the gap is infinite. When an alternating voltage is applied across the capacitor plates, the place are alternately charged and discharged. The current through the capacitor is a result of this charging voltage(or charge). Thus, a capacitor will pass more current through it if the voltage is changing at a faster rate, i.e., if the frequency of supply is higher. This implies that the reactance offered by a capacitor is less with increasing frequency; it is given by 1/wC .


CHAPTER – 6 (ELECTROMAGNETIC WAVES)



1. What are the directions of electric and magnetic field vectors relative to each other and relative to the direction of propagation of electromagnetic waves? [CBSE(AI)2012]

ANS.They are perpendicular to each other and also perpendicular to the direction of propagation.

2. Identify the part of the electromagnetic spectrum to which the following wavelengths belong:

(i) 10-1m (ii) 10-12 m [CBSE (AI) 2008]

ANS. (i) short radio waves (ii) gamma rays

3. Identify the part of the electromagnetic spectrum to which the following wavelengths belong:

(i) 1 mm (ii) 10-11 m [CBSE (AI) 2008]

ANS. (i) microwaves (ii) gamma rays.

4. Welders wear special goggles or face masks with glass windows to protect their eyes from electromagnetic radiations. Name the radiations and write the range of their frequency. [CBSE(AI)2013]

ANS. Ultraviolet radiations, frequency range: 1015-1o17 Hz

5. Name the electromagnetic radiations used for studying the crystal structure of solids and write its frequency range

[CBSE (AI) 2007, 2009]

ANS. X- rays, frequency range 1017 to 1020 HZ

6. The speed of an electromagnetic wave in a material medium is given by v = 1/√µε, µ being the permeability of the medium and € its permittivity. How does its frequency change?

[CBSE (AI) 2012]

ANS. No change

7. How are X-rays produced? [CBSE(AI)2011]

ANS. X-rays are produced when high energetic electron beam is made incident on a metallic target of high melting point and high atomic weight.

8. The frequency of oscillation of the electric vector of a certain electromagnetic wave is 5x1014 Hz. What is the frequency of oscillation of the corresponding magnetic field vector and to which part of the electromagnetic spectrum does it belong?

[CBSE (AI) 2008C]

ANS. 5x1014 Hz, visible region.

9. Which of the following has the shortest wavelength?

Microwaves, Ultraviolet rays, X-rays [CBSE (AI) 2010]

ANS. X-rays

10. To which part of the electromagnetic spectrum does a wave of frequency 5x1019 Hz belong? [CBSE (AI) 2014]

Ans. Gamma rays.


1. What is meant by the transverse nature of electromagnetic waves? Draw a diagram showing the propagation of an electromagnetic wave along X-direction, indicating clearly the

directions of oscillating electric and magnetic fields associated with it. [CBSE (AI) 2008]

ANS. In an electromagnetic wave, the electric and magnetic field vectors oscillate, perpendicular to the direction of propagation of wave. This is called transverse nature of electromagnetic wave

Diagram: Refer NCERT TEXT BOOK page NO. 275

Accordingly if a wave is propagating along z-axis, the electric vector oscillates along x- axis and magnetic field vector oscillates along y-axis.

2. Identify the following electromagnetic radiations as per the wavelengths given below.

(a) 10-3 nm (b) 10-3m (c) 1 nm

Write one application of each. [CBSE (AI) 2008]

ANS. (a) gamma radiation

Radio therapy or to initiate nuclear reactions.

(b) Microwaves

In radar for aircraft navigation.

(c) X-ray

In medical science for detection of fractures, stones in kidneys, gall bladder etc.

3. Identify the following electromagnetic radiations as per the frequencies given below:

(a) 1020 HZ (b) 109 HZ (c) 1011 HZ

Write one application of each. [CBSE (AI) 2008]

ANS. (a) gamma radiation, for treatment of cancer

(b) Radio waves, for broadcasting radio programmes to long distances.

(c) Micro waves, for cooking in microwave oven.

4. Write the order of frequency range and one use of each of the following electromagnetic radiations

(a)Microwaves (b) Ultraviolet rays (c) Gamma rays

[CBSE (AI) 2006]

ANS. (a) Microwaves: 3X 1011- 1X 108Hz. These are suitable for the radar systems, used in aircraft navigation.

Ultraviolet rays: 1X106 - 8X1014Hz. They are used to detect invisible writing, forged documents and finger prints.

Gamma rays: 5X 1023- 3X1019Hz. For the treatment of cancer cells.

5. A capacitor of capacitance of ‘C’ is being charged by connecting it across a dc source along with an ammeter. Will the ammeter show a momentary deflection during the process of charging? If so, how would you explain this momentary deflection and the resulting continuity of current in the circuit? Write the expression for the current inside the capacitor. [CBSE (AI) 2012]

ANS. Yes, because of the production of displacement current between the plates of capacitor on account of changing electric field.

Current inside the capacitor

Id= ε0 ( dφE/dt)

6. A capacitor, made of two parallel plates each of plate area A and separation d, is being charged by an external ac source. Show that the displacement current inside the capacitor is the same as the current charging the capacitor. [CBSE (AI) 2013]

ANS.

+q -q

E

Ic = dq/dt Ic is the conduction current.

Id= ε0 ( dφE/dt) φE is the electric flux

φE = q/ ε0, so Id = dq/dt Id is the displacement current.

Both conduction current and displacement current are equal.

7. Considering the case of a parallel plate capacitor being charged, show how one is required to generalize Ampere’s circuital law to include the term due to displacement current. [CBSE (AI) 2014]

ANS. = µ0IC + µ0ε0 dɸE/dt

Here Id= ε0 ( dφE/dt) = displacement current

IC = conduction current.

8. Arrange the following electromagnetic eaves in the order of their increasing wavelength:

Gamma rays, microwaves, x rays, radio waves.

How are infra-red waves produced? What role does infra-red radiation play in (i) maintaining the Earth’s warmth and (ii) physical therapy? [CBSE (AI) 2015]

ANS. Gamma rays, x rays, microwaves, radio waves.

Infra-red waves are produced by the vibration of atoms and molecules

(i) The earth radiates infrared waves which are reflected by the gases in the lower atmosphere. This phenomenon, called greenhouse effect, keeps the earth warm.

(ii) Infrared lamps in the treatment of muscular complaints.

Expected questions for MLL

1. Name the electromagnetic waves, which (i) maintain Earth’s warmth and (ii) are used in aircraft navigation.[CBSE (F) 2012]

(1)

ANS. (i) Infrared rays.

(ii)Microwaves.

2. Why are infra-red radiations referred to as heat waves? Name the radiations which are next to these radiations in the electromagnetic spectrum having (i) shorter wavelength (ii) longer wavelength. [CBSE (F) 2013] (2)

ANS. Infrared waves are produced by hot bodies and molecules, so are referred to as heat waves.

(i)Em wave having short wavelength than infrared waves are

visible, UV, X-rays and ϒ-rays.

(ii) Em wave having longer wavelength than infrared waves are microwaves, short radio waves, television and FM radio.

3. What do electromagnetic waves consist of? Explain as what factors does its velocity in vacuum depend? (2)

ANS. Electromagnetic waves consist of mutually perpendicular electric and magnetic field vectors. Its velocity in vacuum is given by

C= (1/√µ0ε0) = same for electromagnetic waves.

In other words its velocity in vacuum does not depend on any factor.

4. Give two characteristics of electromagnetic waves. Write the expression for velocity of electromagnetic waves in terms of permittivity and permeability of the medium. (2)

ANS. Characteristics of electromagnetic waves:

(i)Electromagnetic waves travel in free space with speed of light c= 3X 108m/s.

(ii) Electromagnetic waves are transverse in nature.

Expression for velocity of em waves in vacuum, c= (1/√µ0ε0)

5. (a)How are electromagnetic waves produced by oscillating charges?

(b)State clearly how a microwave oven works to heat up a food item containing water molecules.

6. (c)Why microwaves are found useful for the radar systems in aircraft navigation? [CBSE (F) 2013] (3)

ANS. (a) if a charge particle oscillates with some frequency, produces an oscillating electric field in space, which produces an oscillating magnetic field, which in turn is a source of electric field, and so on. Thus oscillating electric fields and magnetic fields regenerate each other, and an electromagnetic wave propagates in the space.

(b) In microwave oven, the frequency of the microwaves is selected to match the resonant frequency water molecules so that energy from the waves get transferred efficiently to the kinetic energy of the molecules. This kinetic energy raises the temperature of any food containing water.

(c)Microwaves are short wave length radio waves with frequency of order GHz. Due to short wave length, they have high penetrating power with respect to atmosphere and less diffraction in the atmospheric layers. So these waves are suitable for the radar systems used in aircraft navigation.

RAY OPTICS AND OPTICAL INSTRUMENTS QUESTIONS HAVE BEEN ASKED ONE TIME

SL. NO.

QUESTIONS

M.M. YEAR

1 An object is held at the principal focus of a concave lens of focal length f. Where is the image formed?

1 2008

2 A converging lens is kept co-axially in contact with a diverging lens – both the lenses being of equal focal lengths. What is the focal length of the combination?

1 2010

3 An astronomical telescope uses two lenses of power 10 D and 1 D. what is its magnifying power in normal adjustment?

1 2010

4 The image of a candle is formed by a convex lens on a screen. The lower half of the lens is painted black to make it completely opaque. Draw the ray diagram to show the image formation. How will this will be different from the one obtained when the lens is not painted black?

2 2006

5 A convex lens of refractive index 1.5 has a focal length of 18 cm in air. Calculate the change in its focal length when it is immersed in water of refractive index 4/3.

2 2007

6 The focal length of the objective and eye-lens of a compound microscope are 2 cm, 6.25 cm respectively. The distance between the lenses is 15 cm. (i) How far from the objective lenses, will the object be kept, so as to obtain the final image at the near point of the eye? (ii) also calculate its magnifying power.

2 2008

7 Define refractive index of a transparent medium. A ray of light passes through a triangular prism. Plot a graph showing the variation of the angle of deviation with the angle of incidence.

2 2009

8 An object AB is kept in front of a concave mirror as shown in the figure.

(i) Complete the ray diagram showing the formation of the image.

(ii) How will the position and intensity of the image be affected if the lower half of the mirror`s

2 2012

B

A

F C

reflecting surface is painted black? 9

(a) Write the necessary conditions for the phenomenon of total internal reflection to occur. (b)Write the relation between the refractive index and critical angle for a given pair of optical media.

2 2013

10 When monochromatic light travels from rarer to denser medium, explain the following, giving reasons :

(i) Is the frequency of reflected and refracted light same as the frequency of incident light?

(ii) Does the decrease in speed imply a reduction in energy carried by light wave

2 2013

11 A convex lens of focal length 25 cm is placed coaxially in contact with a concave lens of focal length 20 cm. Determine the power of the combination. Will the system be converging or diverging in nature?

2 2013

12 Two monochromatic rays of light are incident normally on the face AB of an isosceles right-angled prism ABC. The refractive indices of the glass prism for the two rays ‘1’ and ‘2’ are respectively 1.35 and 1.45. Trace the path of these rays after entering through the prism.

1

2

2 2014

13 A biconvex lens of glass of refractive index 1.5 having focal length of 20 cm is placed in a medium of refractive index 1.65. Find its focal length. What should be the

2 2015

A

C B

value of refractive index of the medium in which the lens should be placed so that it acts as a plane sheet of glass?

14 A ray of light incident on an equilateral glass prism propagates parallel to the base line of the prism inside it. Find the angle of incidence of this ray. Given refractive index of material of glass prism is √3.

2 2015

15 You are given two converging lenses of focal lengths 1.25 cm and 5 cm to design a compound microscope. If it is desired to have a magnification of 30, find out the separation between the objective and the eyepiece.

2 2015

16 A small telescope has an objective lens of focal length 150 cm and eyepiece of focal length 5 cm. What is the magnifying power of the telescope for viewing distant objects in normal adjustment? If this telescope is used to view a 100 m tall tower 3 km away, what is the height of the image of the tower formed by the objective lens?

2 2015

17 Use mirror equation to show that an object placed between f and 2f of a concave mirror produces a real image beyond 2f.

2 2015

18 A figure divided into squares, each of size 1 mm2 , is being viewed at a distance of 9 cm through a magnifying lens of focal length 10 cm, held close to the eye.

(a) Draw a ray diagram shoeing the formation of the image.

(b) What is the magnification produced by the lens? How much is the area of each square in the virtual image?

(c) What is the angular magnification of the lens?

3 2006

19 Define the term ‘resolving power’ of an astronomical telescope. How does it get affected on

(i) Increasing the aperture of the objective lens?

(ii) Increasing the wavelength of the light used?

Justify your answer in each case.

3 2007

20 In the figure given below, light rays of blue, green, red wavelength are incident on an isosceles right-angle prism. Explain with reason. Which rays of light will be transmitted through the face AC. The refractive index of the prism for red, green, blue light are 1.39, 1.424, 1.476 respectively

3 2008

21 Write three distinct advantages of a reflecting type telescope over a refracting type telescope. A convex lens of focal length 10 cm is placed coaxially 5 cm away from a concave lens of focal length 10 cm. If an object is placed 30 cm in front the convex lens, find the position of the final image formed by the combined system.

3 2009

22 With the help of a suitable diagram, derive the mirror formula for a concave mirror.

3 2009

23 Why must both the objectives and the eye-piece of a compound microscope have short focal lengths? The image obtained with a convex lens is erect and its length is four times the length of the object. If the focal length of the lens is 20 cm, calculate the object and image distances.

3 2010

24 A convex lens is used to obtain a magnified image of an object on a screen 10m from the lens. If the magnification is 19, find the focal length of the lens.

3 2010

A

C B

25 A convex lens lens made up of glass of refractive index

1.5 is dipped, in turn, in (i) a medium of refractive index 1.65, (ii) a medium of refractive index 1.33.

Will it behave as a converging or a diverging lens in the two cases?

How will its focal length change in the two media?

3 2011

26 Use the mirror equation to show that

(a) An object placed between 혧 and 2혧 of a

concave mirror produces a real image beyond

2혧.

(b) A convex mirror always produces a virtual image independent of the location of the object.

(c) An object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.

3 2011

27 A compound microscope uses an objective lens of focal length 4 cm an eyepiece lens of focal length 10 cm. an object is placed at 6 cm from the objective lens. Calculate the magnifying power of the compound microscope. Also calculate the length of the microscope.

3 2011

28 A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece lens of focal length 1.0 cm is used, find the angular magnification of the telescope. If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.42 x 106 m and the radius of the lunar orbit is 3.8 x 108 m.

3 2011

29 A converging lens has a focal length of 20 cm in air. It is 3 2011

made of a material of refractive index 1.6. it is immersed in a liquid of refractive index 1.3. Calculate its new focal length.

30 You are given three lenses L1, L2 and L3 each of focal length 15 cm. An object is kept at 20 cm in front of L1 , as shown. The final image is formed at the focus ‘I’ of L3. Find the separations between L1, L2 and L3.

3 2012

31 Draw a ray diagram showing the image formation by a compound microscope. Hence obtain expression for total magnification when the image is formed at infinity.

3 2013

32 A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The two are kept at 15 cm from each other. A point object lies 60 cm in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and position of the image formed.

3 2014

33 A convex lens of focal length 20 cm is placed coaxially with a concave mirror of focal length 10 cm at a distance of 50 cm apart from each other. A beam of light coming parallel to the principal axis is incident on the convex lens. Find the position of the final image formed by this combination. Draw the ray diagram showing the formation of the image.

3 2014

34 a) A ray of light is incident normally on the face AB of a right angled glass prism of refractive index aµg= 1.5 . The prism is partly immersed in a liquid of unknown refractive index. Find the value of refractive index of the liquid so that the ray grazes

3 2015

15 cm

I

L3

20 cm

L2 L1

along the face BC after refraction through the prism.

b) Trace the path of the ray if it were incident normally on the face AC.

35 (i) A concave mirror produces real and magnified image of an object kept in front of it. Draw a ray diagram to show the image formation and use it derive mirror equation.

(ii) A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is

(a) a convex lens of focal length 20 cm,

(b) a concave lens of focal length 16 cm?

5 2015

36 (a) A ray PQ of light is incident on the face AB of a glass prism ABC and emerges out of the face AC. Trace the path of ray. Show that

/i +/e = /A + /δ Where δ and e denote the angle of deviation and angle of emergence respectively.

5 2015

C

A B 60o

Plot a graph showing the variation of angle of deviation as a function of angle of incidence. State the condition under which /δ is minimum. (b) Find out the relation between the refractive index(µ) of the glass and /A for the case when the angle of prism (A) is equal to the angle of minimum deviation. Hence obtain the value of the refractive index for angle of prism A = 60o.

37 A point object O is kept in a medium of refractive index n1 in front of a convex spherical surface of radius of curvature R which separates the second medium of refractive index n2 from the first one. Draw the ray diagram showing the formation of image and deduce the relationship between the object distance and the image distance in terms of n1, n2 and R. When the image formed above acts as virtual object for a concave spherical surface separating the medium n2 from n1 (n2 > n1), draw this ray diagram and write the similar relation. Hence obtain the expression for lens maker’s formula.

5 2015

C B

A

i

Q P

SL. NO.

QUESTIONS

M.M. YEAR

1 For the same value of angle incidence, the angles of refractive in three media A, B and C are 15o , 25o and 35o respectively. In which medium would the velocity of light be minimum?

1 [2012, 2015]

2 Draw a labeled ray diagram of a compound microscope and write an expression for its magnifying power.

2 [2008, 2010]

3 Draw a labeled ray diagram to show the formation of image in an astronomical telescope for a distant object.

2 [2008, 2009]

4 Draw a neat labeled ray diagram of an astronomical telescope in normal adjustment. Explain briefly its working.

2

5 Draw a labeled ray diagram of an astronomical telescope, in normal adjustment position and write the expression for its magnifying power. An astronomical telescope uses an objective lens of focal length 15 m and eye lens of focal length 1 cm. What is the angular magnification of the telescope? If this telescope is used to view moon, what is diameter of the image of moon formed by objective lens? (Diameter of moon =3.5X106 m, radius of lunar orbit=3.8X108 m).

5 [2008, 2011]

RAY OPTICS AND OPTICAL INSTRUMENTS EXPECTED QUESTIONS FOR MLL

SL. NO.

QUESTIONS

M.M.

1 An object AB is kept in front of a concave mirror as shown in the figure.

(iii) Complete the ray diagram showing the formation of the image.

(iv) How will the position and intensity of the image be affected if the lower half of the mirror`s reflecting surface is painted black?

2

2 When monochromatic light travels from rarer to denser medium, explain the following, giving reasons :

(iii) Is the frequency of reflected and refracted light same as the frequency of incident light?

(iv) Does the decrease in speed imply a reduction in energy carried by light wave

2

3 In the figure given below, light rays of blue, green, red wavelength are incident on an isosceles right-angle prism. Explain with reason. Which rays of light will be transmitted through the face AC. The refractive index of the prism for red, green, blue light are 1.39, 1.424, 1.476 respectively

3

B

A

F C

A

A small telescope has an objective lens of focal length 150 cm and eyepiece of focal length 5 cm. What is the magnifying power of the telescope for viewing distant objects in normal adjustment? If this telescope is used to view a 100 m tall tower 3 km away, what is the height of the image of the tower formed by the objective lens?

4 Use the mirror equation to show that

(d) An object placed between 혧 and 2혧 of a concave

mirror produces a real image beyond 2혧.

(e) A convex mirror always produces a virtual image independent of the location of the object.

(f) An object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.

3

5 A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The two are kept at 15 cm from each other. A point object lies 60 cm in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and position of the image formed.

3

6 A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece lens of focal length 1.0 cm is used, find the angular magnification of the telescope.

3

If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.42 x 106 m and the radius of the lunar orbit is 3.8 x 108 m.

7 Draw a neat labeled ray diagram of an astronomical telescope in normal adjustment. Explain briefly its working. Derive the expression for its magnifying power

5

8 Draw a labeled ray diagram of a compound microscope and derive the expression for its magnifying power.

3

9 Define the term ‘resolving power’ of an astronomical telescope. How does it get affected on

(iii) Increasing the aperture of the objective lens? (iv) Increasing the wavelength of the light used?


3

10 Define the term ‘resolving power’ of a compound microscope. telescope. Write its expression. How does it get affected on

(i) Increasing the aperture of the objective lens? (ii) Increasing the focal length of the objective?


3

11 Derive lens maker’s formula 3 12 For refraction at a spherical surface derive the relation

3

13 (a) A ray PQ of light is incident on the face AB of a glass prism ABC and emerges out of the face AC. Trace the path of ray. Show that

/i +/e = /A + /δ Where δ and e denote the angle of deviation and angle of emergence respectively. Plot a graph showing the variation of angle of deviation as a function of angle of incidence. State the condition under which

5

C B

A

i

Q P

/δ is minimum. (b) Find out the relation between the refractive index(µ) of the glass and /A for the case when the angle of prism (A) is equal to the angle of minimum deviation. Hence obtain the value of the refractive index for angle of prism A = 60o.

WAVE OPTICS QUESTIONS HAVE BEEN ASKED ONE TIME

SL. NO.

QUESTION M.M. YEAR

1 What is the geometrical shape of the wave front when a plane wave passes through a convex lens?

1 2008

2 How would the angular separation of interference fringes in Young’s double slit experiment change when the distance between the slits and screen is doubled?

1 2009

3 How does the fringe width, in Young’s double-slit 1 2012

experiment, change when the distance of separation between the slits and screen is doubled?

4 Compare and contrast the pattern which is seen with two coherently, illuminated narrow slits in Young’s experiment with that seen from coherently illuminated single slit producing diffraction.

2 2006

5 Define the term ‘linearly polarised light’. When does the intensity of transmitted light become maximum, when a Polaroid sheet is rotated between two crossed Polaroids?

2 2009

6 A beam of light consisting of two wavelengths, 800 nm and 600 nm is used to obtain the interference fringes in a Young’s double slit experiment on a screen placed 1.4 m away. If the two slits are separated by 0.28 mm, calculate the least distance from the central bright maximum where the bright fringes of the two wavelengths coincide.

2 2012

7 Two wavelengths of sodium light 590 nm and 596 nm are used, in turn, to study the diffraction taking place at a single slit of aperture 2 x 10-4 m. The distance between the slit and the screen is 1.5 m. Calculate the separation between the positions of the first maxima of the diffraction pattern obtained in the two cases.

2 2013

8 State clearly how an unpolarised light gets linearly polarised when passed through a Polaroid. a) Unpolarised light of intensity Io is incident on Polaroid P1 which is kept near another Polaroid P2 whose pass axis is parallel to that of P1. How will the intensities I1 and I2, transmitted by the Polaroids P1 and P2 respectively change on rotating P1 without disturbing P2? b) Write the relation between the intensities I1 and I2.

3 2015

9 Use Huygens` principle to show how a plane wave front propagates from a denser to rarer medium. Hence verify snell s law of refraction.

3 2015

10 Answer the following : (a) When a tiny circular obstacle is placed in the

path of light from a distance source, a bright spot is seen at the centre of the shadow of the

2 2015

obstacle. Explain, why? (b) How does the resolving power of a microscope

depend on (i) the wave length of the light used and (ii) the medium between the object and the objective lens?

11 In Young’s doubled slit experiment , monochromatic light of wavelength 630 nm illuminates the pair of slits and produces an interference pattern in which two consecutive bright fringes are separated by 8.1 nm. another source of monochromatic light produces the interference pattern in which the two consecutive bright fringes are separated by 7.2 nm . Find the wave length of light from the second source. What is the effect on the interference fringes if the monochromatic source is replaced by a source of white light?

3 2009

12 How does an unpolarised light get polarized when passed through polaroid? Two polaroids are set in crossed positions. A third

polaroid is placed between the two making an angle

with the pass axis of the first polaroid. Write the expression of the intensity of light transmitted from the second polaroid. In what orientations will the transmitted intensity be (i) minimum and (ii) maximum?

3 2010

13 (a) State Huygens` principle. Using this principle explain how a diffraction pattern is obtained on a screen due to a narrow slit on which a narrow beam coming from a monochromatic source of light is incident normally. (b) Show that the angular width of the first diffraction

fringe is half of that of the central fringe. (c) If a monochromatic source of light is replaced by white light, what change would you observe in the

3 2011

diffraction pattern? 14

(a) Using the phenomenon of polarisation, show how transverse nature of light can be demonstrated.

(b)Two polaroids P1 and P2are placed with their pass axes perpendicular to each other. Unpolarised light of intensity I0is incident on P1 . A third polaroid P3is kept in between P1and P2 such that its pass axis makes an angle of 300 with that of P1. Determine the intensity of light transmitted through P1,P2 and P3.

3 2014

15 (a) The light from a clear blue portion of the sky shows a rise and fall of intensity when viewed through a Polaroid which is rotated. Describe, with the help of a suitable diagram, the basic phenomenon/process which occurs to explain this observation.

(b) Show how light reflected from a transparent medium gets polarized. Hence deduce Brewster’s law

3 2015

16 (a) Define a wave front.

(b) Using Huygens` principle, draw diagrams to show the nature of the wave fronts when an incident plane wave front gets

(i) reflected from a concave mirror,

(ii) refracted from a convex lens.

3 2015

17 What are coherent sources? Why are coherent sources required to produce interference of light? Give an example of the interference of light in everyday life. In Young’s double slit experiment, the two slits are 0.03 cm apart and the screen is placed at a distance of 1.5 m away from the slits. The distance between the central bright fringe and fourth bright fringe is 1 cm. Calculate the wavelength of light used.

5 2007

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

5 2007

light at a single slit. A slit if width ‘a’ is illuminated by a monochromatic light of wavelength 700 nm at normal incidence. Calculate the value of ‘a’ for position of

(i) First minimum at an angle of diffraction of 30o.

(ii) First maximum at an angle of diffraction of 30o.

19 (a) In a single slit diffraction experiment, a slit of which ‘d’ is illuminated by red light of wavelength 650 nm. For what value of ‘d’ will:

(i) The first minimum fall at an angle diffraction of 30o, and

(ii) The first maximum fall at an angle of diffraction 30o? (b) Why does the intensity of the secondary maximum become less as compared to the central maximum?

5 2009

20 In Young’s double slit experiment, the two slits 0.15 mm apart are illuminated by monochromatic light of wavelength 450 nm. The screen is 0.1 m away from the slits.

(a) Find the distance of the second (i) bright fringe, (ii) dark fringe from the central maximum.

(b) How will the fringe pattern change if the screen is moved away from the slits?

5 2010

21 State the importance of coherent sources in the phenomenon of interference. In Young’s double slit experiment to produce interference pattern, obtain the conditions for constructive and destructive interference. Hence deduced the expression for the fringe width. How does the fringe width get affected, if the entire experimental apparatus of Young is immersed in water?

5 2011

22 1. How does an unpolarised light incident on a polaroid get polarised?

Describe briefly, with the help of the necessary

5 2012

diagram, the polarisation of light by refection from a transparent medium. 2. Two polaroids ‘A’ and ‘B’ are kept in crossed position. How should a third Polaroid ‘C’ be placed between them so that the intensity of polarised light transmitted by Polaroid ‘B’ reduces to 1/8th of the intensity of unpolarised light incident on A?

23 (a) In Young’s double slit experiment, describe briefly how bright and dark fringes are obtained on the screen kept in front of a double slit. Hence obtain the expression for the fringe width. (b) The ratio of the intensities at minima to the maxima in the Young’s double slit experiment is 9:25. Find the ratio of the widths of the two slits.

5 2014

24 (a) Describe briefly how a diffraction pattern is obtained on a screen due to a single narrow slit illuminated by a mono-chromatic source of light. Hence obtain the conditions for the angular width of secondary minima. (b) Two wave lengths of sodium light of 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture 2x 10-6 m. The distance between the slit and the screen is 1.5 m. Calculate the separation between positions of first maxima of the diffraction pattern obtained in the two cases.

5 2014

25 Consider two coherent sources S1 and S2 producing monochromatic waves to produce interference pattern. Let the displacement of the wave produced by S1 be given by Y1 = a cosωt and the displacement by S2

be Y2 = a cos (ωt+ϕ). Find out the expression for the amplitude of the resultant displacement at a point and show that intensity at that point will be

I =4a2cos2ϕ/2. Hence establish the condition for constructive and destructive interference. What is the effect on the interference fringes in Young’s double slit experiment when (i) the width of

5 2015

the slit is increased ; (ii) the monochromatic source of light is replaced by a source of white light?

26 (a) Using Huygens` construction of secondary wavelets explain how a diffraction pattern is obtained on a screen due to a narrow slit on which a narrow beam coming from a monochromatic source of light is incident normally. (b) Show that the angular width of the first diffraction

fringe is half of that of the central fringe.

(c) Explain why the maxima at becomes weaker and weaker with increasing n.

5 2015

SL. NO.

QUESTIONS HAVE BEEN ASKED TWO TIMES

M.M. YEAR

1 In what way is diffraction from each slit related to the interference pattern in a double slit experiment?

1 [2013, 2015]

2 In Young’s double slit experiment, derive the condition for (i) Constructive interference and (ii) Destructive interference at a point on the screen.

3 [2011, 2012]

SL. NO.

QUESTIONS HAVE BEEN ASKED THREE TIMES OR MORE

M.M. YEAR

1 State Huygens’ principle. With the help of a suitable diagram, prove Snell’s law of refraction using Huygens’ principle.

3 [2006, 2013, 2015]

2 In Young’s double slit experiment, deduce the conditions for

(i) constructive, and (ii) destructive interference at a point on the screen. Draw a graph showing variation of the resultant intensity in the interference pattern against position ‘x’ on the screen.

3 [2006, 2011, 2012]

WAVE OPTICS EXPECTED QUESTIONS FOR MLL

SL. NO.

QUESTIONS

M.M.

1 State Huygens’ principle. With the help of a suitable diagram, prove Snell’s law of refraction using Huygens’ principle.

3

2 State Huygens’ principle. With the help of a suitable diagram, prove the laws of reflection using Huygens’ principle.

3

3 In Young’s double slit experiment, deduce the conditions for (ii) constructive, and (ii) destructive interference at a point on the screen. Draw a graph showing variation of the resultant intensity in the interference pattern against position ‘x’ on the screen.

4 State the importance of coherent sources in the phenomenon of interference. In Young’s double slit experiment to produce interference pattern, obtain the conditions for constructive and destructive interference. Hence deduced the expression for the fringe width. How does the fringe width get affected, if (i) the entire experimental

apparatus of Young is immersed in water? (ii) The wavelength of light

is increased? (iii) Separation between the

two slits decreased? (iv) Monochromatic light is

replaced by white light? (v) Distance of the screen is

increased?

5 (d) Using Huygens` construction of secondary wavelets explain how a diffraction pattern is obtained on a screen due to a narrow slit on which a narrow beam coming from a monochromatic source of light is incident normally. (e) Show that the angular width of the first diffraction fringe

5

is half of that of the central fringe.

(f) Explain why the maxima at becomes weaker and weaker with increasing n.

6 3. How does an unpolarised light incident on a polaroid get polarised?

Describe briefly, with the help of the necessary diagram, the polarisation of light by refection from a transparent medium. 4. Two polaroids ‘A’ and ‘B’ are kept in crossed position. How should a third Polaroid ‘C’ be placed between them so that the intensity of polarised light transmitted by Polaroid ‘B’ reduces to 1/8th of the intensity of unpolarised light incident on A?

5

7 (a) The light from a clear blue portion of the sky shows a rise and fall of intensity when viewed through a Polaroid which is rotated. Describe, with the help of a suitable diagram, the basic phenomenon/process which occurs to explain this observation.

(b) Show how light reflected from a transparent medium gets polarized. Hence deduce Brewster’s law

8 (a) Define a wave front.

(b) Using Huygens` principle, draw diagrams to show the nature of the wave fronts when an incident plane wave front gets

(i) reflected from a concave mirror,

(ii) refracted from a convex lens.

QUESTIONS THAT HAVE BEEN ASKED ONE TIME FROM CHAPTER -11 DUAL NATURE OF RADIATION AND MATTER

1. An electron, an alpha-particle and a proton have the same kinetic energy. Which one of these

particles has the largest de-Broglie wave length? (1)(2007)

2. In an experiment on photoelectric effect, the following graphs were obtained between the photoelectric current (I) and the anode potential (V). Name the characteristic of the incident radiation that was kept constant in this experiment. (1) (2005)

3. Write the expression for the de Broglie wavelength associated with a charged particle having charge ‘q’ and mass ‘m’, when it is accelerated by a potential V.(1)(2013) 4. (a) Draw the energy level diagram showing the emission of β-particles followed by γ-rays by a Co6027 nucleus.(b) Plot the distribution of kinetic energy of β- particles and state why the energy spectrum is continuous. (3) (2005)

5. Write Einstein’s photoelectric equation and point out any two characteristic properties of photons on which this equation is based. Briefly explain the three observed features which can be explained by this equation.(3)(2013)

6. Define the terms threshold frequency and stopping potential in relation to the phenomenon of photoelectric effect. How is the photoelectric current affected on increasing the (i) frequency (ii) intensity of the incident radiations and why? (3) (2006)

QUESTIONS THAT HAVE BEEN ASKED TWO TIMES FROM DUAL NATURE OF RADIATION AND MATTER.

1. A proton and an electron have same velocity. Which one has greater de-Broglie wavelength and why?(1) (2007,2012) 2. The graph shows variation of stopping potential V0 versus frequency of incident radiation v for two photosensitive metals A and B. Which of the two metals has higher threshold frequency and why?(1) (2005,2014)

3. The graph shows the variation of stopping potential with frequency of incident radiation for two photosensitive metals A and B. Which one of the two has higher value of work-function? Justify your answer.(1) (2005,2014)

4. A proton and an electron have same kinetic energy. Which one has greater de-Broglie wavelength and why?(1)(2007,2012)

5. Define the term ‘stopping potential’ in relation to photoelectric effect.(1) (2006,2011)

6. The stopping potential in an experiment on photoelectric effect is 1 .5 V. What is the maximum kinetic energy of the photoelectrons emitted? (1) (2008, 2009)

7. The maximum kinetic energy of a photoelectron is 3eV.What is its stopping potential?(1)(2008,2009)

8. With what purpose was famous Davisson-Germer experiment with electrons performed.(1) (2005,2006)

9. An α-particle and a proton are accelerated from rest by the same potential. Find the ratio of their de-Broglie wavelengths.(2) (2005,2010)

10.Set up Einstein’s photoelectric equation using the photon picture of electromagnetic radiation. Explain briefly how this equation accounts for all the observations in the photoelectric effect.(3)(2013,2015)

11. Define the term ‘intensity of radiation’ in photon picture of light. Ultraviolet light of wavelength

2270 Å from 100 W mercury source irradiates a photo cell made of a given metal. If the stopping potential is – 1·3 V, estimate the work function of the metal. How would the photo cell respond to a high intensity (~ 105 Wm–2 ) red light of wavelength 6300 Å produced by a laser ? (3) (2013, 2014)

12. An electron microscope uses electrons accelerated by a voltage of 50 kV. Determine the de-Broglie wavelength associated with the electrons. Taking other factors, such as numerical aperture etc. to be same, how does the resolving power of an electron microscope compare with that of an optical microscope which uses yellow light? (3) (2013, 2014)

13. In a plot of photoelectric current versus anode potential, how does (i) the saturation current vary with anode potential for incident radiations of different frequencies but same intensity? (ii) the stopping potential vary for incident radiations of different intensities but same frequency ? (iii) photo electric current vary for different intensities but same frequency of incident radiations ? Justify your answer in each case.(3) (2005,2007)

QUESTIONS THAT HAVE BEEN ASKED THREE TIMES FROM DUAL NATURE OF RADIATION AND MATTER

1.Draw a plot showing the variation of photoelectric current with collector plate potential for two different frequencies, v 1 >v 2 , of incident radiation having the same intensity. In which case will the stopping potential be higher? Justify your answer.(3) (2005,2007,2011)

ADDITIONAL IMPORTANT QUESTIONS FRCM TEXT BOOK.

1. What is the de Broglie wavelength associated with (a) an electron moving with a speed of 5.4×106 m/s, and (b) a ball of mass 150 g travelling at 30.0 m/s?

2. An electron, an α-particle, and a proton have the same kinetic energy. Which of these particles has the shortest de Broglie wavelength?

3. What is the de Broglie wavelength associated with an electron, accelerated through a potential difference of 100 volts?

4. The work function of caesium metal is 2.14 eV. When light of frequency 6 ×1014Hz is

incident on the metal surface, photoemission of electrons occurs. What is the (a) maximum kinetic energy of the emitted electrons?

(b) Stopping potential, and

(c) Maximum speed of the emitted photoelectrons?

5. In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is found to be 4.12 × 10–15 V s. Calculate the value of Planck’s constant.

6. The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm?

7. An electron and a photon each have a wavelength of 1.00 nm. Find (a) their momenta,

(b) the energy of the photon, and (c) the kinetic energy of electron.

8. Calculate the (a) momentum, and

(b) de Broglie wavelength of the electrons accelerated through a potential difference of 56 V.

TOPICS TO BE COVERED IN M.L.L FROM;-

I. Dual nature of matter and radiation

(1) Definition of de-Broglie wave/ matter wave

(2) de-Broglie wavelength

a) General formula, λ= or , λ=

b)In terms of kinetic energy( E) , λ=

c) In term of potential difference (V),λ=

d) For electron accelerating in potential difference (V), λ= =, λ= A0

e) For a molecule of gas at absolute temperature (T), λ=

3) Most of the questions are asked to compare wavelength

a) When velocity is same but mass is different (Hint :λ= or λα )

b) When mass is same velocity is different (Hint: λ= or λα )

c) Kinetic energy is same but masses are different (Hint: λ= or λα ).

d) Kinetic energy is different but masses are same (Hint: λ= or λα ).

E ) Same charge accelerating in different potential (Hint :λ= or λα ).

f) Different charge accelerating in same potential (Hint: λ= or λα ).

g) For an electron accelerating in potential difference V (Hint: λ= A0 or λα A0

h) Molecule of same gas at different temperatures (Hint: λ= or λα ).

i) Molecule of different gases at same temperatures (Hint: λ= or λα ).

3) Conclusion of Davission- Germer’s experiment (Hint: It proves dual nature of matter and

radiation.)

II. Photo -electric Effect

1) Definition of work function ( , Threshold frequency ( ) and Threshold wavelength ( ).

2) Dependence of work function on Threshold frequency ( ) and Threshold wavelength ( ).(Hint :

3) Graph between photo current and anode potential at constant intensity of light. From that part

a) Relation between frequencies for different curves

b) Which one has high stopping potential and why (Hint : )

4) Graph between photocurrent and Anode potential at constant frequency. From that part

a) Comparison between intensities i.e., which one is less or more or ratio.

b) Why is stopping potential same for two different intensities? (Hint: but

does not depend upon intensity).

c) Why saturation current are different at different intensities? (Hint: photocurrent α photoelectrons

and photoelectrons α intensity, it means photocurrent intensity).

5) Graph between kinetic energy and frequency and its three applications as

a) Calculation of threshold frequency.

b) Calculation of work function from intercept

c) Calculation of Plank’s constant by slope of graph.

QUESTIONS THAT HAVE BEEN ASKED ONE TIME FROM CHAPTER -12(ATOM)

1. Define ionisation energy. What is its value for a hydrogen atom?(1)(2010)

2. Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its: (i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.(1)(2010)

3. The ground state energy of hydrogen atom is – 13.6 eV. What are the kinetic and potential energies of electron in this state?(2) (2010)

2. Using Bohr’s postulates of the atomic model, derive the expression for radius of n th electron orbit. Hence obtain the expression for Bohr’s radius. (2) (2014)

1. Using Rutherford model of the atom, derive the expression for the total energy of the electron in hydrogen atom. What is the significance of total negative energy possessed by the electron? (2)(2014)

1. Determine the value of the de Broglie wavelength associated with the electron orbiting in the ground state of hydrogen atom(Given En =–13·6/n2) eV and Bohr radius ro = 0·53 Å). How will the de Broglie wavelength change when it is in the first excited state ? (2)(2015)

1. Show that Bohr’s second postulate, ‘the electron revolves around the nucleus only in certain fixed orbits without radiating energy' can be explained on the basis of de-Broglie hypothesis of wave nature of electron.(3)(2008)

1. Draw a schematic arrangement of the Geiger-Marsden experiment. How did the scattering of a-particles of a thin foil of gold provide an important way to determine an upper limit on the size of the nucleus? Explain briefly.(3) (2009)

1. Using Bohr’s postulates, derive the expression for the frequency of radiation emitted when electron in hydrogen atom undergoes transition from higher energy state (quantum number ni ) to the lower state, (nf ). When electron in hydrogen atom jumps from energy state ni =4 to nf =3, 2,1, identify the spectral series to which the emission lines belong.(5)(2013)

QUESTIONS THAT HAVE BEEN ASKED TWO TIMES FROM CHAPTER -12 ATOM

1. (a) Using de Broglie’s hypothesis, explain with the help of a suitable diagram, Bohr’s second postulate of quantization of energy levels in a hydrogen atom. (b) The ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential energies of the electron in this state?(3) ( 2010,2011)

1. In a Geiger– Marsden experiment, calculate the distance of closest approach to the nucleus of Z =75, when an a-particle of 5 MeV energy impinges on it before it comes momentarily to rest and reverses its direction. How will the distance of closest approach be affected when the kinetic energy of the a-particle is doubled?(5) (2009,2012)

QUESTIONS THAT HAVE BEEN ASKED THREE TIMES FROM CHAPTER -12

2. The ground state energy of hydrogen atom is –13.6 eV. If an electron makes a transition from an energy level – 0.85 eV to – 1.51 eV, calculate the wavelength of the spectral line emitted. To which series of hydrogen spectrum does this wavelength belong?(5) (2010,2011,2012)

2. Given the value of the ground state energy of hydrogen atom as –13·6 eV, find out its kinetic and potential energy in the ground and second excited states. (3) (2010,2011,2012,2015).

TOPICS TO BE COVERED IN M.L.L

I. Atoms and Nuclei

Rutherford experiment and its limitation.

Bohr’s postulates derivation for radius of orbits and total energy.

Energy level diagram and region of spectral series.

Radius of Nucleus.

Binding energy per nucleon versus Mass Number (A) graph.

Inference of graph(Fission and Fusion)

Graph showing the variation of Nuclear force versus separation between Nucleons; specify the region in the graph showing attraction and repulsion nature of Nuclear forces.

Numericals based on Binding Energy and Binding Energy per Nucleon.

Characteristics of Nuclear force, Graph showing the variation of potential energy versus separation between Nucleons.

Properties of rays.

Derivation of and graph showing the variation of N and t.

Derivation .

Define Activity and it’s S.I. unit.

Numericals based on group displacement law and half life.

Conversion from Nickel to Cobalt emission of ray.

Components of Nuclear reactor(Moderator,Coolant,Control rod, Nuclear fuel)

Concept of Slow neutron.

QUESTIONS THAT HAVE BEEN ASKED ONE TIME FROM CHAPTER -13, NUCLEI

1. The radioactive isotope D decays according to the sequence

β-particle α-particle

D------------------D1-------------------D2

If the mass number and atomic number of D2 are 176 and 71 respectively,

what is (i) the mass number (ii)atomic number of D? (1) (2007)

2.What is the nuclear radius of 125 Fe, if that of 27Al is 3.6 fermi? (1) (2008)

3. Why is it found experimentally difficult to detect neutrinos in nuclear β-decay? (1) (2014)

4. 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) (2007)

5. A radioactive sample contains 2.2 mg of pure C which has half-life period of 1224 seconds. Calculate

(i) the number of atoms present initially. .(ii) the activity when 5 µg of the sample will be left. (3) (2005)

6. The half-life of U against α-decay is 4.5 X 109 years. Calculate the

activity of 1 g sample of U. (3) (2005)

7. Explain, with the help of a nuclear reaction in each of the following cases, how the neutron to proton ratio changes during (i) alpha- decay (ii) beta-decay? (3) (2006)

8. Why is the mass of a nucleus always less than the sum of the masses of its constituents, neutrons and protons? If the total number of neutrons and protons in a nuclear reaction is conserved, how then is the energy absorbed or evolved in a reaction? Explain.(3) (2006)

9. Draw a graph showing the variation of binding energy per nucleon with mass number for different nuclei. Explain, with the help of this graph, the release of energy by the process of nuclear fusion.(3) (2006)

10. State the law of radioactive decay. If N0 is the number of radioactive nuclei in the sample at some initial time, t 0 , find out the relation to determine the number N present at a subsequent time. Draw a plot of N as a function of time. (3) (2008)

11. Distinguish between isotopes and isobars. Give one example for each of the species. A radioactive isotope has a half-life of 5 years. How long will it take the activity to reduce to 3.125%? (3) (2008)

12. (a) Write symbolically the β - decay process of 15 P32 .

(b) Derive an expression for the average life of a radionuclide. Give its relationship with the half- life.(3) (2010)

QUESTIONS THAT HAVE BEEN ASKED TWO TIMES FROM CHAPTER -13, NUCLEI

1. Two nuclei have mass numbers in the ratio 1 : 8. What is the ratio of their nuclear radii?(1) (2008,2009)

2. Two nuclei have mass numbers in the ratio 8 : 125. What is the ratio of their nuclear radii? (1) (2008,2009)

3. Two nuclei have mass numbers in the ratio 27 : 125. What is the ratio of their nuclear radii? (1) (2008,2009)

4. Define the activity of a given radioactive substance. Write its S.I. unit.(1) (2009,2013)

5. (a) The mass of a nucleus in its ground state is always less than the total mass of its constituents – neutrons and protons. Explain.(2) (2006,2009)

6. Draw a plot of the binding energy per nucleon as a function of mass number for a large number of nuclei. Explain the energy release in the process of nuclear fission from the above plot. Write a typical nuclear reaction in which a large amount of energy is released in the process of nuclear fission.(3) (2006,2008)

7. Define the activity of a radionuclide. Write its S.I. units. Give a plot of the activity of a radioactive species versus time. How long will a radioactive isotope, whose half life is T years, take for its activity to reduce to 1/8th of its initial value? (3) (2008,2009)

8. Draw a plot of potential energy of a pair of nucleons as a function of their separations. Mark the regions where the nuclear force is (i) attractive and (ii) repulsive. Write any two characteristic features of nuclear forces.(3) (2007,2012)

QUESTIONS THAT HAVE BEEN ASKED THREE TIMES FROM CHAPTER -13, NUCLEI

1. Write any two characteristic properties of nuclear force.(1) (2008,2009,2011)

2. Draw a plot showing the variation of binding energy per nucleon versus the mass number A. Explain with the help of this plot the release of energy in the processes of nuclear fission and fusion.(3) (2006,2008,2009)

3. Draw a plot showing the variation of binding energy per nucleon versus the mass number A. Explain with the help of this plot the release of energy in the processes of nuclear fission and fusion.(3) (2006,2008,2009)

4.Draw a plot of potential energy of a pair of nucleons as a function of their separation. Write two important conclusions which you can draw regarding the nature of nuclear forces.(3) (2007,2009,2010)

5.Draw a plot of the binding energy per nucleon as a function of mass number for a large number of nuclei, 2≤ A ≤ 240. How do you explain the constancy of binding energy per nucleon in the range 30 < A< 170 using the property that nuclear force is short-ranged? Nuclear forces are short ranged, so every nucleon interacts with their neighbours only; so binding energy per nucleon remains constant.](3) (2006,2008,2009,2010)

6. 1. Using the curve for the binding energy per nucleon as a function of mass number A, state clearly how the release in energy in the processes of nuclear fission and nuclear fusion can be explained.(3) (2006,2008,2009,2010,2011)

2. (a) Draw the plot of binding energy per nucleon (BE/A) as a function of mass number A. Write two important conclusions that can be drawn regarding the nature of nuclear force. (b) Use this graph to explain the

release of energy in both the processes of nuclear fusion and fission. (c) Write the basic nuclear process of neutron undergoing b–decay. Why is the detection of neutrinos found very difficult?(5) (2006,2008,2009,2010,2011,2013)

Text Book : PHYSICS PART II ( NCERT)

Chapter 14: Semiconductor Electronics: Materials, devices and Simple circuits

Frequency : ( Asked three times or more ) Sl.No. Question Marks Year 1 Draw a simple circuit of a CE transistor amplifier. Explain its working.

Show that the voltage gain AV, of the amplifier is given by

,where is the current gain, RL is the load resistance and ri is the input resistance of the transistor. What is the significance of the negative sign in the expression for the voltage gain?

5

2012(D) Questions of similar nature asked in 2008, 2009

Explain the function of base region of a transistor. Why is this region made thin and lightly doped?

Draw a circuit diagram to study the input and output characteristics of n-p-n transistor in a common emitter (CE) configuration. Show these characteristics graphically. Explain how current amplification factor of the transistor is calculated using output characteristics.

OR

2006, 2013

2

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

5

2009(D)

3 (i) With the help of circuit diagrams distinguish between forward biasing and reverse biasing of a p-n junction diode.

(ii) Draw V-I characteristics of a p-n junction diode in (a) forward bias, (b) reverse bias.

3

2009, 2010, 2014(D)

(a) Why is zener diode fabricated by heavily doping both p-and n-sides of the junction?

(b) Draw the circuit diagram of zener diode as a voltage regulator and briefly explain its working. OR

2008, 2009,2010(F) 2012, 2014(F)

How is a zener diode fabricated so as to make it a special purpose diode? Draw I-V characteristics of zener diode and explain the significance of breakdown voltage. OR

3

2009(D)

4

Name the semiconductor device that can be used to regulate an unregulated dc power supply.With the help of I-V characteristics of this device, explain its working principle.

2 2011(D)

5 Draw a circuit diagram of a full-wave rectifier. Explain its working principle. Draw the input/output wave-forms indicating clearly the functions of the two diodes used.

3

2007, 2008,2012

6 Explain, with the help of suitable diagram, the two important processes that occur during the formation of p-n junction. Hence define the terms : depletion region and barrier potential.

3 2009, 2010, 2012, 2015

Draw the circuit diagram of an illuminated photodiode in reverse bias. How is photodiode used to measure light intensity? OR

2 2010

Explain, with the help of a circuit diagram, the working of a photo-diode. Write briefly how it is used to detect the optical signals. OR

2 2013(D)

7

(a) How is photodiode fabricated? (b) Briefly explain its working. Draw its V–I characteristics for two different intensities of illumination.

3 2014(F)

(i) Identify the logic gates marked P and Q in the given logic circuit.

(ii) Write down the output at X for the inputs A = 0, B = 0 and A =1, B

=1. OR

2 2010(AI) 8

The given inputs A, B are fed to a 2-input NAND gate. Draw the output wave form of the gate.

2 2008(D)

OR (iii) Identify the logic gates marked P and Q in the given logic circuit.

(ii) Write down the output at X for the inputs A = 0, B = 0 and

A =1, B =1. OR

2 2010(AI)

Write the truth table for the logic circuit shown below and identify the logic operation performed by this circuit.

2 2011(D)

In the circuit shown in the figure, identify the equivalent gate of the circuit and make its truth table.

OR

2 2013(AI)

Write the truth table for the combination of the gates shown. Name the gates used.

OR

2 2014(D)

Identify the logic gates marked ‘P’ and ‘Q’ in the given circuit. Write the truth table for the combination.

2 2014(D)

Frequency : ( Asked two times ) Sl.No. Question Marks Year 1 (a) Draw the circuit diagram of a base-biased n-p-n transistor in C-E

configuration. Explain how this circuit is used to obtain the transfer characteristic (Vo –Vi characteristics).

(b) The typical output characteristics (IC –VCE ) of an n-p-n transistor in C-E configuration is shown in the figure. Calculate (i) the output resistance r0 and (ii) the current amplification factor ac .

5 2010, 2013

2 Explain, with the help of a circuit diagram, the working of a p-n junction diode as a half-wave rectifier.

3 2006, 2014

3 The current in the forward bias is known to be more (~mA) than the current in the reverse bias (~µA). What is the reason, then, to operate the photodiode in reverse bias?

2 2008 ,2012

Mention the important considerations required while fabricating a p-n junction diode to be used as a Light Emitting Diode (LED). What should be the order of band gap of an LED if it is required to emit light in the visible range? OR

2 2013, 2015

4

How is a light emitting diode fabricated ? Briefly state its working. Write any two important advantages of LEDs over the conventional incandescent

3 2015(Bhubaneswar)

low power lamps. OR Explain, with the help of a schematic diagram, the principle and working of a Light Emitting Diode. What criterion is kept in mind while choosing the semiconductor material for such a device ? Write any two advantages of Light Emitting Diode over conventional incandescent lamps.

3 2007(D)

What are energy bands? How are these formed? Distinguish between a conductor, an insulator and a semiconductor on the basis of energy band diagram. OR

5 2006(AI)

Draw energy band diagrams of an n-type and p-type semiconductor at temperature T > 0 K. Mark the donor and acceptor energy levels with their energies. OR

2

5

Distinguish between a metal and an insulator on the basis of energy band diagrams.

2

2014(F)

6 What happens to the width of depletion layer of a p-n junction when it is (i) forward biased, (ii) reverse biased?

2 2011(AI),2008(AI)

Frequency : ( Asked Once ) Sl.No. Question Marks Year 01 Draw a circuit diagram for use of NPN transistor as an amplifier in common

emitter configuration. The input resistance of a transistor is 1000Ω. On changing its base current by 10µA, the collector current increases by 2 mA. If a load resistance of 5kΩ is used in the circuit, calculate:

(i) The Current gain (ii) voltage gain of the amplifier

3 2006(D)

(a) Differentiate between three segments of a transistor on the basis of their size and level of doping. (b) How is a transistor biased to be in active state? (c) With the help of necessary circuit diagram, describe briefly how n-p-n transistor in CE configuration amplifies a small sinusoidal input voltage. Write the expression for the ac current gain.

5 2014(D)

Chapter : Communication Systems

Frequency: Asked Three Times or more Sl. No.

Question Marks Year

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

2 2009, 2010(F) 2014(F)

Write briefly any two factors which demonstrate the need for modulating a signal. Draw a suitable diagram to show amplitude modulation using a sinusoidal signal as the modulating signal. OR

3 2011(AI),2012(D), 2013(D),

Why are high frequency carrier waves used for transmission? OR

2 2009(D)

02

Write two factors justifying the need of modulation for transmission of a signal.

2 2009(AI)

Name the type of waves which are used for line of sight (LOS) communication. What is the range of their frequencies? A transmitting antenna at the top of a tower has a height of 20 m and the height of the receiving antenna is 45 m. Calculate the maximum distance between them for satisfactory communication in LOS mode. (Radius of the Earth = 6.4 × 106 m) OR

3 2013(AI)

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). OR

2 2008(D)

What does the term ‘LOS communication’ mean ? Name the types of waves that are used for this communication. Give typical examples, with the help of a suitable figure, of communication systems that use space wave mode propagation. OR

3 2008(AI)

03

(i) Why is communication using line of sight mode limited to a frequencies above 40 MHz? (ii) A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in line of sight mode?

3 2010(D)

Name the three different modes of propagation of electromagnetic waves. Explain, using a proper diagram the mode of propagation used in the frequency range above 40 MHz. OR

3 2012(D)

Name the three different modes of propagation of electromagnetic waves. Explain, using a proper diagram the mode of propagation used in the frequency range from a few MHz to 40 MHz.

3 2012(D)

04

Mention three ‘different modes of propagation used in communication system. Explain with the help of a diagram how long distance communication can be achieved by ionospheric reflection of radio waves.

3 2012(AI)

05 Explain briefly the following terms used in communication system: 3 2012(AI)

(i) Transducer (ii) Repeater (iii) Amplification OR

2014(AI)

Mention the function of any two of the following used in communication system: (i) Transducer (ii) Repeater (iii) Transmitter (iv) Bandpass Filter

2 2012(D)

Frequency: Asked two times Sl. No.

Question Marks Year

Distinguish between ‘sky wave’ and ‘space wave’ modes of propagation. Why is the sky wave mode of propagation restricted to frequencies upto 40 MHz ? OR

2 2015(Bhuban eswar)

01

Describe briefly, by drawing suitable diagrams, the (i) sky wave and (ii) space wave modes of propagation. Mention the frequency range of the waves in these modes of propagation.

3 2014(F)

02 Draw a block diagram of a simple modulator for obtaining amplitude modulated signal. A carrier wave of peak voltage 12 V is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index of 75% ?

3 2015(Bhuban eswar) 2010(AI)

Which mode of propagation is used by short wave broadcast services having frequencies range from a few MHz upto 30 MHz? Explain diagrammatically how long distance communication can be achieved by this mode. Why is there an upper limit to frequency of waves used in this mode?

3 2010(AI) 2011(AI)

03

In standard AM broadcast, what mode of propagation is used for transmitting a signal? Why is this mode of propagation limited to frequencies upto a few MHz?

2 2010(F)

04 In the given block diagram of a receiver, identify the boxes labelled as X and Y and write their functions.

2 2012(AI) 2013(D)

Frequency: Asked once Sl. No.

Question Marks Year

01 (a) Define the terms (i) ‘amplitude modulation’ and (ii) ‘modulation index’. 3 2009(F)

(b) If a low frequency signal in the audio frequency range is to be transmitted over long distances, explain briefly the need of translating this signal to high frequencies before transmission.

02 What is meant by detection of a signal in a communication system? With the help of a block diagram explain the detection of AM signal.

3 2009(F)

03 (i) Define modulation index. (ii) Why is the amplitude of modulating signal kept less than the amplitude of carrier wave?

2 2011(D)

04 Draw a schematic diagram showing the (i) ground wave (ii) sky wave and (iii) space wave propagation modes for e m waves. Write the frequency range for each of the following: (i) Standard AM broadcast (ii) Television (iii) Satellite communication

3 2011(D)

05 Distinguish between ‘Analog and Digital signals’. 2 2012(D) 06 In the block diagram of a simple modulator for obtaining an AM signal, shown in the

figure, identify the boxes A and B. Write their functions.

2 2013(AI)

07 The carrier wave is given by C(t) = 2 sin (8t) volt. The modulating signal is a square wave as shown. Find modulation index.

1 2014(D)

08 Why is frequency modulation perferred over amplitude modulation for transmission

of music ?

1

2007(D)

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PREVIOUS YEAR QUESTION ASKED IN CBSE,BOARD EXAM. CHAPTER … bank of Physics class XII.pdf · CHAPTER-2,ELECTROSTATIC POTENTIAL AND CAPACITANCE 2006 Q. Define the term 'dielectric