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Preface

The study of Physics helps to understand basic laws of nature and their manifestation in different

physical phenomena. It facilitates the development of experimental, observational, manipulative,

decision making and investigatory skills in the learners.

Learning Physics aims at:

developing conceptual competence in the learners and make them realize and appreciate the interface of Physics with other disciplines.

exposing the learners to different processes used in Physics-related industrial and technological applications.

The basic aim of Ready Reckoner is to provide the students with a ready to absorb material, which can

be very helpful at the time of revising the syllabus. Questions included at the end of each chapter are in

accordance with CBSE guidelines.

Each chapter has been divided into three sections:

Section A: Synopsis of the chapter emphasizing all the value points

Section B: Concept Based Exercises which includes Very Short, Short and Long Answer Questions

Section C: Enhancement exercises which includes HOTS and Value based questions

Practice sample papers

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Index

CHAPTER NO. CHAPTER NAME PAGE NO.

SYLLABUS AND MARKS DIVISION 3-5

DESIGN OF QUESTION PAPER 6-7

CH-1&2 Electric Charges and Fields; Potential & Capacitance

8-25

CH- 3 Current Electricity 26-40

CH-4&5 Magnetic Effects of current & Magnetism 41-55

CH-6&7 Electromagnetic Induction and Alternating Current 56-71

CH-8 Electromagnetic Waves 72-78

CH-9,10 Ray Optics And Wave Optics 79-91

CH-11 Dual nature of Matter and Radiation 92-101

CH-12 & 13 Atom and Nuclei 102-115

CH-14 Semiconductor devices 116-129

Sample papers 130-184

Subject tips 185

Bibliography 194

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SYLLABUS & MARKS DIVISION PHYSICS COURSE STRUCTURE CLASS XII

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Unit I: Electrostatics 22 Periods

Chapter–1: Electric Charges and Fields Electric Charges; Conservation of charge, Coulomb's law-force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field. Electric flux, statement of Gauss's theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside).

Chapter–2: Electrostatic Potential and Capacitance Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field. Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor.

Unit II: Current Electricity 20 Periods

Chapter–3: Current Electricity Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current; Ohm's law, electrical resistance, V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity, Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance. Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel, Kirchhoff's laws and simple applications, Wheatstone bridge, metre bridge. Potentiometer - principle and its applications to measure potential difference and for comparing EMF of two cells; measurement of internal resistance of a cell.

Unit III: Magnetic Effects of Current and Magnetism 22 Periods

Chapter–4: Moving Charges and Magnetism Concept of magnetic field, Oersted's experiment. Biot - Savart law and its application to current carrying circular loop. Ampere’s law and its applications to infinitely long straight wire. Straight and toroidal solenoids (only qualitative treatment), force on a moving charge in uniform magnetic and electric fields, Cyclotron. Force on a current-carrying conductor in a uniform magnetic field, force between two parallel current-carrying conductors-definition of ampere, torque experienced by a current loop in uniform magnetic field; moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter.

Chapter–5: Magnetism and Matter Current loop as a magnetic dipole and its magnetic dipole moment, magnetic dipole moment of a revolving electron, magnetic field intensity due to magnetic dipole (bar magnet) along its axis and

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perpendicular to its axis, torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; earth's magnetic field and magnetic elements. Para-, dia- and Ferro - magnetic substances, with examples. Electromagnets and factors affecting their strengths, permanent magnets.

Unit IV: Electromagnetic Induction and Alternating Currents 20

Periods Chapter–6: Electromagnetic Induction Electromagnetic induction; Faraday's laws, induced EMF and current; Lenz’s Law, Eddy currents. Self and mutual induction.

Chapter–7: Alternating Current Alternating currents, peak and RMS value of alternating current/voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, power factor, wattless current.AC generator and transformer.

Unit V: Electromagnetic waves 04

Periods Chapter–8: Electromagnetic Waves Basic idea of displacement current, Electromagnetic waves, their characteristics, their Transverse nature (qualitative ideas only).Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses.

Unit VI: Optics 27 Periods

Chapter–9: Ray Optics and Optical Instruments Ray Optics: Reflection of light, spherical mirrors, mirror formula, refraction of light, total internal reflection and its applications, optical fibres, refraction aspherical surfaces, lenses, thin lens formula, lens maker’s formula, magnification, power of a lens, combination of thin lenses in contact, refraction of light through a prism. Scattering of light - blue colour of sky and reddish appearance of the sun at sunrise and sunset. Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.

Chapter–10: Wave Optics Wave optics: Wave front and Huygens’s principle, reflection and refraction of plane wave at a plane

surface using wave fronts. Proof of laws of reflection and refraction using Huygens’s principle. Interference, Young's double slit experiment and expression for fringe width, coherent sources and sustained interference of light, diffraction due to a single slit, width of central maximum, resolving power of microscope and astronomical telescope, polarisation, plane polarised light, Brewster's law, uses of plane polarised light andPolaroids.

Unit VII: Dual Nature of Radiation and Matter 08 Periods

Chapter–11: Dual Nature of Radiation and Matter

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Dual nature of radiation, Photoelectric effect, Hertz and Lenard's observations; Einstein’s photoelectric equation-particle nature of light. Matter waves-wave nature of particles, de-Broglie relation, Davisson Germer experiment (experimental details should be omitted; only conclusion should be explained).

Unit VIII: Atoms and Nuclei 15 Periods

Chapter–12: Atoms Alpha-particle scattering experiment; Rutherford's model of atom; Bohr model, energy levels, hydrogen spectrum.

Chapter–13: Nuclei Composition and size of nucleus, Radioactivity, alpha, beta and gamma particles/rays and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear fission, nuclear fusion.

Unit IX: Electronic Devices 12

Periods Chapter–14: Semiconductor Electronics: Materials, Devices and Simple Circuits Energy bands in

conductors, semiconductors and insulators (qualitative ideas only) Semiconductor diode ( I-Characteristics in forward and reverse bias, diode asa rectifier; Special purpose p-n junction diodes: LED, photodiode, solar cell and Zenerdiode and their characteristics, zener diode as a voltage regulator.

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QUESTION PAPER DESIGN CLASS XII (2019-20)

(THEORY) Time: 3 hrs. Max Marks: 70

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CHAPTER-1 ELECTRIC CHARGES AND FIELDS

SYNOPSIS

1. Electrostatics is the study of charges at rest.

2. The charging done by rubbing two insulating objects with each other is called charging by friction.

3. The process of charging a neutral body by bringing charged body near it without making contact

between the two bodies is known as charging by induction.

4. Properties of charges: a. Like charges repel and unlike charges attract. b. Charges are additive in nature i.e., Q=∑ 𝑞𝑖

𝑛𝑖=1

c. Charges are quantized. i.e., Q= ± ne [n=1,2,3,…& e=1.602 X10-19 C] means that charge on an object is always an integral multiple of the basic unit of charge which is electron.

d. Conservation of charge

5. Coulomb’s law states that the magnitude of force exerted by one point charge q1 on another point charge q2 is directly proportional to the magnitude of the charges and inversely proportional to the square of distance between the charges.

=𝑘𝑞1𝑞2

𝑟2 , k=1

4𝜋𝜀0 = 9X109 Nm2C-2, where 𝜀0= permittivity of free space.

6. Principle of superposition: According to it, the net force on charge q1 due to surrounding charges

is 𝐹total = ∑ 𝐹𝑖𝑛

𝑖=1 [vector sum of individual forces] 1 31 212 132 2

12 13

1 1 ....4 4

q qq qr r

r r

7. Electric field: due to a point charge is the space around the charge in which its influence (force)

can be felt by a unit positive test charge placed at that point. It is a vector quantity. SI unit is NC-1.

=𝑘𝑄

𝑟2

0oqo

FE Lt

q

8. Properties of electric field lines:

starts from positive charge and end at negative charge,

Continuous, but never form closed loops, never intersect each other,

Relative closeness of the field lines represents the magnitude of the field strength.

9. A system of two equal and opposite charges separated by a very small distance forms an electric dipole. The strength of an electric dipole is measured by a quantity called electric

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dipole moment. It is equal to the product of magnitude of either of the charges and the dipole length. SI unit of Dipole moment is Cm.

=Q.2, direction of is from negative to positive charge.

10. A line joining the centres of the two charges of an electric dipole is known as the axial line of the electric dipole. The electric field at any arbitrary point on the axial line of the electric dipole

is given by 2𝑘

𝑟3 for r>>a, along the direction of dipole moment.

11. A line which is perpendicular to the axial line of an electric dipole and passes through the

centre of the dipole is known as equatorial line of the electric dipole. The electric field at any

arbitrary point on the equatorial line of the dipole is given by 𝑘

𝑟3for r>>a, opposite to the

direction of dipole moment.

12. When an electric dipole is placed in a uniform electric field, the torque acting on the electric dipole is given by τ=pEsinθ.

13. A system which consists of a large number of charges along its length, area or volume is known

as continuous charge distribution.

Linear charge distribution: 𝜆 =∆𝑞

∆𝑙 [𝜆 ⇒ linear charge density Unit Cm-1]

Surface charge distribution: 𝜎 =∆𝑞

∆𝑆 [𝜎 ⇒ surface charge density Unit Cm-2]

Volume charge distribution: 𝜌 =∆𝑞

∆𝑉 [𝜌 ⇒ Volume charge density Unit Cm-3]

14. The number of electric field lines crossing a surface normally is known as electric flux.

Mathematically ∅=∆𝑆 . =|||∆𝑆 | 𝑐𝑜𝑠 𝜃. SI unit of flux is Nm2/ C.

15. According to Gauss’s law, the total electric flux enclosed inside a closed surface is 1/𝜀0times

the charge enclosed within the surface. ∅𝑡𝑜𝑡𝑎𝑙 =𝑞𝑡𝑜𝑡𝑎𝑙

𝜀0 = ∮ 𝐸. 𝑑𝑆

16. The electric field due to an infinitely long, uniformly charged straight line at a point that is at a

radial distance r from the line is given by the relation E= 𝜆

2𝜋𝑟𝜀0.

17. The electric field intensity due to an infinite plane sheet of charge is given by the relation E=

𝜎

2𝜀0, directed away from the sheet for positive charge and towards for negative charge.

18. The electric field due to a charged spherical shell is given by (i) for a point inside the shell E= 0,

(ii) for a point on the surface of the shell E= 𝜎

𝜀0, (iii) for a point outside the shell E =

𝑘𝑄

𝑟2 .

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CHAPTER-2 ELECTROSTATIC POTENTIAL AND CAPACITANCE

SYNOPSIS

1. The work done by the electrostatic force is path-independent. 2. Electric potential energy difference between two points is defined as the work done by an

external force in moving a charge q0 from one point to another point in an electric field. 3. The electric potential at a point is equal to the amount of work done in bringing a unit positive

test charge from infinity to that point without acceleration. SI unit is volt and it is a scalar quantity. V=W/q0

4. The electric potential V due to a particle of charge q at any radial distance from the particle is

given by 𝑉 =𝑘𝑞

𝑟

5. The electric potential due to an electric dipole is given by V=kpcosθ/r2. The electric potential depends on the angle between the position vector r and the dipole moment.

6. The relation between electric field and electric potential E=-dV/dr.

7. The electric potential energy of a pair of point charges q1 and q2 separated by distance r is given

by: U = 𝑘𝑞1𝑞2

𝑟

8. Potential due to a dipole at a point

i. on its axial line: 𝑉𝑎𝑥𝑖𝑎𝑙 = 𝑘 ||

𝑟2

ii. on its equatorial line:𝑉𝑒𝑞 = 0

9. Potential difference: 𝑉𝐴 − 𝑉𝐵 = 𝑘𝑞 [1

𝑟𝐴−

1

𝑟𝐵]

10. Potential energy of two charges: U = 𝑘𝑞1𝑞2

𝑟

11. Potential energy of a dipole : U = 𝑝 . = p E [𝑐𝑜𝑠𝜃0 - 𝑐𝑜𝑠𝜃1 ]

12. Electrostatics of conductors

(i) Inside a conductor Electrostatic field is zero

(ii) On the surface of a charged conductor E is always Normal

(iii) No charge exists 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 of a charged conductor.

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13. Equipotential surfaces: The surfaces on which the potential is same everywhere.

(i) Work done in moving a charge over an equipotential surface is zero.

(ii) No two equipotential surfaces intersect.

(iii) Electric field lines are always perpendicular to the equipotential surfaces. 15. Equipotential surfaces

(a)Due to electric dipole.

(b) Due to two equal positive charges.

16. Dielectrics are insulating materials such as plastics. (i) Dielectrics in which centres of positive and negative charges do not coincide because of

the asymmetric shape of the molecules are known as polar dielectrics. Eg: H2O (ii) Dielectrics in which centre of positive charge coincide with the centre of negative charge

are known as non-polar dielectrics. Eg: CO2 (iii) The ratio of polarisation to 𝜖𝑜 times the electric field intensity is called electric

susceptibility. 𝜒= 𝑃/𝜖𝑜𝐸. The dielectrics with constant 𝜒 are called linear dielectrics. (iv) The maximum external electric field the dielectric can withstand without dielectric

beakdown is called dielectric strength. SI unit Vm-1. (v) Behaviour of dielectric material in absence and presence of electric field :

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17. A capacitor consists of two conductors of any shape placed near one another without touching. It is device used to store charge and electric potential energy.

18. Capacitance: Q

CV

, Ratio of charge and potential difference. Scalar quantity, its SI unit is farad

[F].

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

Cm = 𝜖𝑜 𝐴

(𝑑−𝑡+𝑡

𝑘)

If t=0 =>C0 = 𝜖𝑜 𝐴

(𝑑)

If t=d =>C0 =k 𝜖𝑜 𝐴

(𝑑)=>Cm = k C0.

The capacitance of a parallel plate capacitor increases k times if the space between the plates

of the capacitor is completely filled with a dielectric having dielectric constant K.

20. Combination of capacitors:

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Capacitors in series:1

1 1n

i ic c

Capacitors in parallel :1

n

i

i

c c

20. The capacitance of a spherical conductor of radius R is C = 4𝜋𝜖𝑜𝑅.

21. Potential Energy stored in capacitors:21 1 12

2 2 2

QU CV QV

C

22. Introducing dielectric slab between the plates of the charged capacitor with:

Property Battery connected Battery disconnected

Charge K Q0 Q0

Potential difference

V0 V0/K

Electric Field

E0 E0/K

Capacitance KC0 KC0

Energy K times1

2𝜀0𝐸2[Energy is supplied

By battery]

1/K times1

2𝜀0𝐸2 [Energy used

for Polarization]

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CONCEPT BASED EXERCISES

VSA QUESTIONS (1 Mark)

1. Sketch field lines due to (i) two equal positive charges placed near each other (ii) a dipole.

2. Name the physical quantity whose SI unit is volt/meter. Is it a scalar or a vector quantity? (Electric field, vector quantity).

3. Electric dipole moment of CuSO4 molecule is 3.2 × 10–32 Cm. Find the separation between copper and sulphate ions.

4. Two charges Q1 and Q2 are separated by distance r. Under what conditions will the electric field be zero on the line joining them (i) between the charges (ii) outside the charge?

5. An electron and proton are released from rest in a uniform electrostatic field. Which of them will have larger acceleration? (electron)

6. If a dipole of charge 2μC is placed inside a sphere of radius 2m, what is the net flux linked with the sphere. (zero)

7. Two point charges repel each other with a force F when placed in water of dielectric constant 81. What will the force between them when placed the same distance apart in air? (81F)

8. Why an electric dipole placed in a uniform electric field does not undergoes acceleration? (Net F=0)

9. If a body contains n1 electrons and n2 protons then what is the total charge on the body? Q= (n2-n1)e

10.Find the ratio of electric field lines starting from a proton kept first in vacuum and then in a medium of dielectric constant 6. (6:1) 11.Draw schematically an equipotential surface of a uniform electrostatic field along x-axis. 12.What is the work done in rotating a dipole from its unstable equilibrium to stable equilibrium? Does the energy of the dipole increase or decrease? (U = - 2PE, decreases) 13.Is it possible that the electric field 𝐸 at a point is zero, while there is a finite electric potential at that point. Give an example. (at the mid-point of system of two equal charges placed near each other) 14.Can two equipotential surfaces intersect? Justify your answer. 15.Compare the electric flux in a cubical surface of side 10 cm and a spherical surface of radius 10 cm, when a charge of 5μC is enclosed by them. (same) 16.Explain why the electric field inside a conductor placed in an external electric field is always zero. 17.A charge Q is distributed over a metal sphere of radius R. What is the electric field and electric potential at the centre?

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18.Draw schematically the equipotential surface corresponding to a field that uniformly increases in magnitude but remains in a constant (say z) direction.

19.An uncharged conductor A placed on an insulating stand is brought near a charged insulated conductor B. What happens to the charge and potential of B? (Q remains same, Potential difference decreases due to charge induced on A). 20.A point charge Q is placed at point O shown in Fig. Is the potential difference VA- VB, positive, negative or zero, if Q is (i) positive (ii) negative charge.

NUMERICALS LEVEL I

1.What is the charge acquired by a body when 1 million electrons are transferred to it? 2. An attractive force of 5N is acting between two charges of +2.0 μC & -2.0 μC placed at some distance. If the charges are mutually touched and placed again at the same distance, what will be the new force between them? 3. A charge of +3.0 x 10-6 C is 0.25 m away from a charge of -6.0 x 10-6C. a. What is the force on the 3.0 x 10-6 C charge? b. What is the force on the -6.0 x 10-6 C charge? 4. An electric dipole consist of a positive and a negative charge of 4μC each placed at a distance of 5mm. Calculate dipole moment. 5. Three capacitors of capacitances 2μF, 3μF and 4μF are connected in parallel. What is the equivalent capacitance of the combination? Determine charge on each capacitor, if the combination is connected to 100V supply? 6. An electric dipole with dipole moment 4x10-9C-m is aligned at 300 with direction of electric field of magnitude 5x104N/C. Calculate the magnitude of the torque acting on the dipole. 7. A point charge of 2μC is at the centre of cubic Gaussian surface 9.0 cm in edge. What is the net electric flux through the surface? 8. What is the amount of work done in moving a 200nC charge between two points 5 cm apart on an equipotential surface? 9. How much work must be done to charge a 24 μF capacitor, when the potential difference between the plates is 500 V? 10. What is the equivalent capacity of the network given below

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LEVEL II 1. What is the work done in moving a charge of 100μC through a distance of 1cm along the equatorial line of dipole? 2. The given graph shows that variation of charge q versus potential difference V for two capacitors C1 and C2. The two capacitors have same plate separation but the plate area of C2 is double than that of C1. Which of the lines in the graph correspond to C1 and C2 and why?

3. Two point charges 5μC and – 4 μC are separated by a distance of 1 m in air. At what point on the line joining the charges is the electric potential zero? 4. Two charges +5μC and +20μC are placed 15 cm apart. At what point on the line joining the two charges is the electric field zero? 5. Two charges +16μC and −9μC are placed 8 cm apart. At what point on the line joining the two charges is the electric field zero? 6. A 600 pF capacitor is charged by a 200 V supply. It is then disconnected and from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process. 7. Keeping the voltage of the charging source constant, what will be the percentage change in the

energy stored in a parallel plate capacitor if the separation between its plates were to be decreased by

10% .

8. Four charges are placed at the vertices of a square of side d as shown in the figure. (i) Find the work

done to put together this arrangement. (ii) A charge q0is brought to the center E of the square, the

four charges being held fixed at its corners. How much extra work is needed to do this?

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9. If S1 and S2 are two hollow spheres enclosing charges Q and 2Q respectively as shown in the figure

(i) What is the ratio of the electric flux through S1 and S2?

(ii) (ii) How will the flux through the sphere S1 change, if a medium of dielectric constant 5 is

filled in the space inside S1.

10. A charge of 24μC is given to a hollow sphere of radius 0.2m. Find the potential

(i) at the surface of the sphere, and

(ii) at a distance of 0.1 m from the centre of the sphere.

(iii) at the centre

LEVEL III

1. A slab of material of dielectric constant K has the same area as the plates of a parallel plate

capacitor but has a thickness 3d / 4, where d is the separation of the plates. How is the capacitance

changed when the slab is inserted between the plates?

2. A parallel plate capacitor with air between the plates has a capacitance of 8μF. What will be the

capacitance if the distance between the plates is doubled and the space between them is filled with a

substance of dielectric constant K=6?

3. Two dipoles, made from charges ±q and ±Q, respectively, have equal dipole moments. Give the (i)

ratio between the ‘separations’ of these two pairs of charges (ii) angle between the dipole axis of these

two dipoles.

4. The capacitors C1, and C2, having plates of area A each, are connected in series, as shown. Compare

the capacitance of this combination with the capacitor C3, again having plates of area A each, but

‘made up’ as shown in the figure.

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5. A point charge +10μC is at a distance 5cm directly above the centre of a square of side 10cm as

shown in fig. What is the magnitude of flux through the square?

6. Calculate equivalent capacitance of the given network and determine the charge and voltage

across each capacitor.

7. Two identical charges ,Q each are kept at a distance r from each other. A third charge q is placed on

the line joining the two charges such that all the three charges are in equilibrium. What is magnitude,

sign and position of the charge q?

8. ABCD is a square of side 5m. Charges of +50C, -50C and +50C are placed at A,C and D respectively .

Find the magnitude of resultant electric field at B.

9. A cube with each side a is kept in electric field given by E = Cx as shown in the figure where C is a

positive dimensional constant. Find

(i) The electric flux through the cube, and

(ii) The net charge inside the cube.

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ENRICHMENT EXERCISES 1.A metallic spherical shell has an inner radius R1 and outer radius R. A charge Q is placed at the centre of the spherical cavity. What will be the surface charge density on the inner and the outer surface. 2.Two small identical electric dipoles AB and CD each of dipole moment p are kept at an angle of 1200. What is the resultant dipole moment of this combination? If this system is subjected to electric field directed along the +x direction, what will be the magnitude and direction of torque acting on this? C(–q) A(+q) X

D(+q)

B(-q)

3.Does the maximum charge given to a metallic sphere of radius R depend on whether it is hollow or solid? Give reason for your answer. Ans : No charge resides on the surface of conductor. 4.The electric field component in the figure are Ex = 2î,Ey = 0, Ez= 0. Calculate the flux through, (1,2,3) the square surfaces of side 5m.

5. A pendulum bob of mass 80 mg and carrying charge of 3 × 10–8 C is placed in an horizontal electric field. It comes to equilibrium position at an angle of 37° with the vertical. Calculate the intensity of electric field.(g = 10m/s2) (2 × 104 N/C) 6. What is the electric field at O in Figures (i), (ii) and (iii) ABCD is a square of side r.

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7.An infinite number of charges, each equal to q are placed along the x-axis at x=1, x=2, x=4 and so on. (i) Find the potential at the point x=0 due to this set of charges. (ii) What will be the potential if in the above set up the consecutive charges have opposite signs? (q/2πεo, q/6πεo) 8.N spherical droplets, each of radius r, have been charged to have a potential V each. If all these droplets were to coalesce to form a single large drop, what would be the potential of this large drop? (Ans: N2/3 V; Hint: Volume of large drop = N X volume of each drop, Charge on all droplets Q=N X charge on each drop). 9.If the metallic conductor shown in the figure is continuously charged from which of the points A,B,C or D does the charge leak first. Justify. ( Ans. A)

10.Two charge –q and +q are located at points A (0, 0, –a) and B(0, 0, +a).How much work is done in moving a test charge from point (b, 0, 0) to Q (–b, 0, 0)? Ans : Zero 11. What is dielectric strength? Write the value of dielectric strength of air. Ans : 3x106 Vm–1 12.The electric potential V at any point in space is given V = 20x3 volt, where x is in meter. Calculate the electric intensity at point P (1, 0, 2). 13 .A 5 MeVα particle is projected towards a stationary nucleus of atomic number 40. Calculate distance of closest approach. 14. Figure shows three circuits, each consisting of a switch and two capacitors initially charged as indicated. After the switch has been closed, in which circuit (if any) will the charges on the left hand capacitor (i) increase (ii) decrease (iii) remain same?

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15 Three concentric spherical metallic shells A < B < C of radii a, b, c (a <b < c) have surface densities σ,-σ, σ and respectively. Find the potential of three shells A, B and (ii). If shells A and C are at the same potential, obtain relation between a, b, c. 16.Four point charges are placed at the corners of the square of edge a as shown in the figure. Find the work done in disassembling the system of charges.

17.Two identical parallel plate capacitors connected to a battery with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with dielectric of dielectric constant 3. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of dielectric.

18.Calculate the work done in taking a charge of 1 μC in a uniform electric field of 10 N/C from B to C given AB = 5 cm along the field and AC = 10 cm perpendicular to electric field.

19.Find the equivalence capacitance between X and Y.

20.Three point charges +q, +q and Q are placed at the three vertices of an equilateral triangle. Find the value of charge Q (in terms of q), so that the electric potential energy of the system is zero. 21Two point charges 20X10-6 C and -4X10-6C are separated by a distance of 50cm in air. (i) Find the point on the line joining the charges, where the electrostatic potential is zero. (ii) Also find the electrostatic potential energy of the system

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22.In the following fig. calculate the potential difference across capacitor C2. Given potential at A is 90 V. C1 = 20 μF, C2 = 30 μF, and C3 = 15 μF.

23..A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 360μC. When potential across capacitors is reduced by 120V, the charge stored in it becomes 120V. Calculate (i) the potential V and unknown capacitance, (ii) What will be the charge stored in the capacitor, if the voltage applied has increased by 120V 24.Find the potential at A and C in the following circuit :

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ELECTRIC CHARGES AND FIELDS -1

(i) Multiple Choice Questions Two charges 3x10-5 C and 5x 104C are placed at a distance 10 cm from each other. Find the value of electrostatic force acting between them.

(a) 13.5x 1011 N (b) 40 x1011 (c) 180 X 10 9 N (d) 13.5X1010 N 2.When a Piece of Polythene is rubbed with wool, a charge of –2 x 10–7C is developed on polythene. The mass transferred to polythene is ..... kg.

Ans-A 3.A copper sphere of mass 2 gm contains about 22 X 1022 atoms. The charge on the nucleus of each atom is 29e. The fraction of electrons removed.

Ans- D 4.Given that q1 + q2 = q if the between q1 and q2 is maximum,then q1/q is

(A) 1 (B) 0.75 (C) 0.25 (D) 0.5 Ans-D 5. Three charges, each of value Q, are placed at the vertex of an equilateral triangle. A fourth charge q is placed at the centre of the triangle. If the charges remains stationery then,q = ...............

Ans-B 6.For a point charge, the graph between electric field versus distance is given by : -

Ans (b)

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7.A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be (A) 200 % (B) 33.3 % (C) 400 % (D) 66.6 % Ans (D) 8. Two identical capacitors 1 and 2 are connected in series to a battery as shown in figure. Capacitor 2 contains a dielectric slab of constant K. Q1 and Q2 are the charges stored in 1 and 2. Now, the dielectric slab is removed and the corresponding charges are Q’1 and Q’2. Then

Ans © 9. An electric circuit requires a total capacitance of 2μF across a potential of 1000 V. Large number of 1μF capacitances are available each of which would breakdown if the potential is more than 350 V. How many capacitances are required to make the circuit ? (A) 24 (B) 12 (C) 20 (D) 18 Ans (D) 10.A parallel plate capacitor has plate of area A and separation d. It is charged to a potential difference Vo. The charging battery is disconnected and the plates are pulled apart to three times the initial separation. The work required to separate the plates is

Ans (A)

Read the assertion and reason carefully to mark the correct option out of the options given below : (a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. (e) If assertion is false but reason is true.

11 Assertion: The Coulomb force is the dominating force in the universe.

Reason: The Coulomb force is weaker than the gravitational force. Ans-D

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12. Assertion: Electric lines of force cross each other. Reason: Electric field at a point superimposes to give one resultant electric field. Ans-E 13. Assertion: If a proton and an electron are placed in the same uniform electric field. They experience different acceleration. Reason: Electric force on a test charge is independent of its mass. Ans-B 14. Assertion: Dielectric breakdown occurs under the influence of an intense light beam. Reason: Electromagnetic radiations exert pressure. Ans-B 15. Assertion: When charges are shared between any two bodies, no charge is really lost, But some loss of energy does occur.

Reason: Some energy disappears in the form of heat, sparking etc Ans-B

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CHAPTER-3

CURRENT ELECTRICITY

SYNOPSIS

1. Electric current is the flow of electric charge. Mathematically, it can be expressed as I=dq/dt. SI

unit of electric current is ampere (A). 1 A= 1 coulomb/ 1 second.

2. Conductors are the substances which allow electricity to pass through them. Insulators are the

substances which do not allow electricity to pass through them.

3. Ohm’s law: It states that the current flowing through a conductor is directly proportional to the potential difference across the ends of the conductor provided the physical conditions such as temperature, pressure etc. remains constant.

V α I i.e. V = IR, Where R is the resistance of the conductor, R=V/I A conductor that obeys Ohm’s law is called Ohmic conductor and that does not obey Ohm’s law is called a non-ohmic conductor.

4. Resistance is the opposition offered by the conductor to the flow of current. Resistance R = ρl/A where ρ is the resistivity of the material of the conductor- length and A area of cross section of the conductor. If l is increased n times, new resistance becomes n2R. If A is increased

n times, new resistance becomes Rn2

1

5. Resistivity (ρ) is a measure of how strongly a material opposes the flow of current. ρ = m/ne2τ, Where m, n, e are mass, number density and charge of electron respectively, τ-relaxation time of electrons. ρ is independent of geometric dimensions. Relaxation time (τ) is the average time interval between two successive collisions. Conductance of the material G =1/R and conductivity σ=1/ρ

6. Current density (J) is the electric current per unit area of cross section. It is a vector quantity.

7. Drift velocity is the average velocity of all electrons in the conductor under the influence of applied electric field. Drift velocity Vd= (eE/m)τ, also I = neAvd

8. Mobility (μ) of a charge carrier is the ratio of its drift velocity to the electric field applied across the

ends of the conductor. It is given by dV

E

The SI unit of mobility is m2/Vs and its value is always positive.

9. Effect of temperature on resistance: Resistance of a conductor increase with the increase of

temperature of conductor (1 )T oR R T , where α is the temperature coefficient of resistance of the

conductor. α is positive for conductors and alloys, negative for semiconductors and insulators.

10. Combination of resistors: 1 2 ...series nR R R R , 1 2

1 1 1 1...

Parallel nR R R R

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11. Electric cell is a device that delivers electric current as a function of a chemical reaction. The

potential difference between the terminals of a cell when no current is drawn from it (open

circuit) is called as emf of a cell. The potential difference between the terminals of a cell in closed

circuit is called Terminal potential difference.

12. The opposition offered by the electrolyte of a cell to the flow of electric current through it is

called internal resistance of the cell. Internal resistance ‘r’ of a cell is given by

r= RV

E

1

, where E is the emf, V is the terminal potential difference and R is the external

resistance.

14. Grouping of cells :

i) In series grouping circuit current is given by s

nEI

R nr

,

ii) In parallel grouping circuit current is given by p

mEI

r mR

where n, m are number of cells in series

and parallel connection respectively.

15. Kirchhoff’s Laws:

First law or Junction Law:-The algebraic sum of currents meeting at a point is zero. 0I

This law is based upon the conservation of charge.

Second law or Loop law :- The algebraic sum of potential difference around a closed loop is zero.

V o .This law is based upon the conservation of energy.

16. Wheatstone bridge is an arrangement of four resistors arranged in four arms of the bridge and is used to determine the unknown resistance in terms of other three resistances. For balanced Wheatstone

Bridge,P R

Q S

.

17. Slide Wire Bridge or Metre Bridge is based on Wheatstone bridge and is used to measure unknown

resistance. If unknown resistance S is in the right gap, Rl

ls

100

18. Potentiometer is considered as an ideal voltmeter of infinite resistance.

Principle of potentiometer: The potential drop across any portion of the uniform wire is proportional to the length of that portion of the wire provided steady current is maintained in it i.e. V α l

19. Potentiometer is used to

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(i) compare the e.m.f.s of two cells :2

1

2

1

l

l

where

21, ll are the balancing lengths of

potentiometer wire for e.m.fs 1 and 2 of two cells.

(ii) determine the internal resistance of a cell : r= Rl

ll

2

21

,

Where 1l is the balancing length

of potentiometer wire corresponding to e.m.f of the cell, 2l that of terminal potential

difference of the cell when a resistance R is connected in series with the cell whose internal resistance is to be determined.

(iii) measure small potential differences.

20. Joule’s law of heating states that the amount of heat produced in a conductor is proportional to (i) square of the current flowing through the conductor,(ii) resistance of the conductor and (iii) time for which the current is passed. Heat produced is given by the relation H=I2Rt.

21. Electric power: It is defined `as the rate at which work is done in maintaining the current in electric circuit. P =VI = I2R =V2/R. Power P is the product of V & I.

22. Electrical energy: The electrical energy consumed in a circuit is defined as the total work done in

maintaining the current in an electrical circuit for a given time. Electrical energy = V*I*t = I2Rt = (V2/R)t = Pt.

23. Colour coding : Black Brown Red Orange Yellow Green Blue Violet Gray White

0 1 2 3 4 5 6 7 8 9

Tolerance (i) Gold 5% (ii) Silver 10% (iii) No Color 20%

Example: if colour code on carbon resister is Red Yellow and Orange with tolerance colour as silver,

the resistance is: (24×103 ± 10%)Ω

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CONCEPT BASED EXERCISES

VERY SHORT ASNWER QUESTIONS (1 Mark)

1. How does the relaxation time of electron in the conductor change when temperature of the

conductor decreases? (decrease) 2. The emf of the driver cell (Auxillary battery) in the potentiometer experiment should be greater

than emf of the cell to be determined. Why? (in order to maintain null point on the potentiometer wire)

3. Two wires, one of copper and other of manganinhas same resistance and equal length. Which wire is thicker? (manganin)

4. Out of V – I graph for parallel and series combination of two metallic resistors, which one represents parallel combination of resistors? Justify your answer. (A: series, B: parallel)

5. In the figure, what is the potential difference between A and B? ( VA-VB = -8V)

6. If potential difference V is applied across a conductor is increased to 2V, how will the drift

velocity of the electrons change? (twice) 7. State two factors on which sensitivity of a potentiometer depends. 8. Two bulbs whose resistances are in the ratio 1:2 are connected in parallel to a source of

constant voltage. What will be the ratio of power dissipation in the bulbs? (2:1) 9. A heating element is marked 210V, 630W. Find the resistance of the element when connected

to 210V dc source. (70 Ω) 10. Which of the two has greater resistance- 1KW electric heater or a 100W filament bulb, both

marked for 220V. (100 W)

NUMERICALS LEVEL - I

1. What happens to the power dissipation if the value of electric current passing through a conductor of constant resistance is doubled? 2. A cell of emf 2 V and internal résistance 0.1 Ω is connected to a 3.9 Ω external resistance. What will be the current in circuit? 3. Calculate the resistivity of a material of a wire 1 m long, 0.4 mm in diameter and having a resistance of 2 ohm.

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4. In a potentiometer arrangement; a cell of emf 1.25 V gives a balance point at 35.0 cm length of the wire. If the cell is replaced by another cell and the balance point shifts to 63.0 cm, what is the emf of the second cell? 5. A current is maintained in a conductor of cross-section 10-4 m2. If the number density of free electrons be 9 x 1028 m-3and the drift velocity of free electrons be 6.94 x10 – 9 m/s, calculate the current in the conductor. 6. A silver wire has a resistance of 2.1Ω at 27.5 0C, and a resistance of 2.7 Ω at 100 0C. Determine the temperature coefficient of resistivity of silver. 7. Three resistors 1 Ω, 2 Ω and 3 Ω are combined in series. (a) What is the total resistance of the combination? (b) If the combination is connected to a battery of emf 12 V and negligible internal resistance, determine the total current drawn from the battery. 8. (a) Three resistors 2 Ω, 4 Ω and 5 Ω are combined in parallel. What is the total resistance of the combination? (b) If the combination is connected to a battery of emf 20 V and negligible internal resistance and the total current drawn from the battery. 9.A Voltage of 30V is applied across a carbon resistor with first second and third rings of blue, black and yellow colours respectively. Calculate the value of current in mA, through the resistor. 10.In a meter bridge the balance point is found to be 39.5 cm from one end A, when the resistor Y is of 12.5 Ω . Determine the resistance of X.

LEVEL - II 1. A cell of emf 2 V and internal résistance 0.1Ω is connected to a 3.9 Ω external resistance. What will be the p.d. across the terminals of the cell? 2. Out of the two bulbs marked 25W and 100W, which one has higher resistance. 3. A cell of 6 V and internal resistance 2Ω is connected to a variable resistor. For what value of current does maximum power dissipation occur in the circuit? 4. What is the largest voltage you can safely put across a resistor marked 98 Ω - 0.5 W? 5. Two heater wires of the same dimensions are first connected in series and them in parallel to a source of supply . What will be ratio of heat produced in two cases? 6. Using data given in graph determine (i) emf (ii) internal resistance of the cell.

(iv) For what current, does maximum power dissipation occur in the circuit?

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7. You are given ‘n’ resistors each of resistance ‘r’. These are first connected to get of minimum possible resistance. In the second case these are again connected differently to get maximum possible resistance. Compute the ratio between the maximum and minimum values resistance so obtained.

8. Two primary cells of emf E1 and E2 (E1 > E2) are connected to the potentiometer wire as shown in the figure. If the balancing lengths for the cells are 250 cm and 400 cm. Find the ratio of E1 and E2.

9. Two identical cells of emf 1.5V each are joined in parallel providing supply to an external circuit consisting of two resistors of 13Ω each joined in parallel . A very high resistance voltmeter reads the terminal voltage of the cells to be 1.4V. Find the internal resistance of each cell. 10. Three cells of emf 2V, 1.8V and 1.5V are connected in series. Their internal resistances are 0.05Ω, 0.7Ωand 1Ω respectively. If this battery is connected to an external resistance of 4Ω, calculate : (i) the total current flowing in the circuit. (ii) the p.d. across the terminals of the cell of emf 1.5V.

NUMERICALS: LEVEL - III 1. What is the current flowing in the arm BD of this circuit.

2. A cylindrical metallic wire is stretched to increase its length by 5%. Calculate the percentage change in its resistance. 3. Two cells of EMF 1V, 2V and internal resistances 2Ω and 1Ω respectively are connected in (i) series, (ii) parallel. What should be the external resistance in the circuit so that the current through the resistance be the same in the two cases? In which case more heat is generated in the cells?

34

4. Calculate the temperature at which the resistance of a conductor becomes 20% more than its resistance at 270C. The value of the temperature coefficient of resistance of the conductor is 2 x 10-4 / K. 5. Two metallic wires of the same material have the same length but cross sectional area is in the ratio of 1:2. They are connected (i) in series and (ii) in parallel. Compare the drift velocities of electrons in the two wires in both the cases. 6. Two wires X, Y have the same resistivity but their cross-sectional areas in the ratio 2:3 and lengths in the ratio 1:2. They are first connected in series and then in parallel to a dc source. Find out the ratio of the drift speeds of the electrons in the two wires for the two cases. 7. A room has AC run for 5 hours a day at a voltage of 220V. The wiring of the room consists of Cu of 1 mm radius and a length of 10m. Power consumption per day is 10 commercial units. What fraction of it goes in the joule heating in the wires? What would happen if the wiring is made of Al of the same dimensions? [ρCu = 1.7 x 10-8 Ωm, ρAl = 2.7 x 10-8 Ωm] 8. Two cells of emf 1.5 V and 2V and internal resistance 1 Ω and 2 Ω are connected in parallel to pass a current in the same direction through an external resistance of 5 Ω. (a) Draw Circuit Diagram. (b) Using Kirchhoff’s laws, calculate the current through each branch of the circuit and p.d. across the 5 Ω resistor.

9. E2 =1.02V, PQ=1m. When switch S open, null position is obtained at a distance of 51 cm from P. Calculate (i) potential gradient (ii) emf of the cell E1 (iii) when switch S is closed, will null point move towards P or Q. Give reason for your answer.

10.AB=100 cm, RAB=10Ω. Find the balancing length AC.

35

11. Find the value of the unknown resistance X in the circuit, if no current flows through the section AO. Also calculate the current drawn from the battery of emf 6V.

12. E1 = 2V, E2 = 4V, r1 = 1Ω, r2 = 2Ω, R = 5Ω Calculate (i) current (ii) p.d. between B and A (iii) p.d. between A and C.

13.12 cells, each of emf 1.5V and internal resistance 0.5Ω, are arranged in m rows each containing n cells connected in series, as shown. Calculate the values of n and m for which this combination would send maximum current through an external resistance of 1.5Ω

14.The given figure shows the experimental set up of a meter bridge. The null point is found to be 60cm away from the end A with X and Y in position as shown. When a resistance of 15Ω is connected in series with ‘Y’, the null point is found to shift by 10cm towards the end A of the wire. Find the position of null point if a resistance of 30Ω were connected in parallel with ‘Y’.

36

15. A cell of unknown emf E and internal resistance r, two unknown resistances R1 and R2 (R2>R1) and a perfect ammeter are given. The current in the circuit is measured in five different situations : (i) Without any external resistance in the circuit, (ii) With resistance R1 only, (iii) With resistance R2 only, (iv) With both R1 and R2 used in series combination and (v) With R1 and R2 used in parallel combination. The current obtained in the five cases are 0.42A, 0.6A, 1.05A, 1.4A, and 4.2A, but not necessarily in that order. Identify the currents in the five cases listed above and calculate E, r,, R1 and R2.

ENRICHMENT EXERCISES

1. The variation of potential difference V with length l in case of two potentiometers X and Y as

shown. Which one of these will you prefer for comparing emfs of two cells and why? ( Y is more

sensitive)

2. While doing an experiment with potentiometer, it was found that the deflection is one sided

and (i) the deflection decreased while moving from one end A of the wire to the end B; (ii) the

deflection increased while the jockey was moved towards the end B.

(i) Which terminal +or –ve of the cell E1, is connected at X in case (i) and how is E1related to E

?(ii) Which terminal of the cell E1 is connected at X in case (ii)?

(i) Positive terminal of E1 is connected at X and E1>E.

(ii) Negative terminal of E1 is connected at X.

37

3. In the figure, if the potential at point P is 100V, what is the potential at pointQ?

4 A part of a circuit in steady state, along with the currents flowing in the branches and the resistances,

is shown in the figure. Calculate energy stored in the capacitor of 4μF capacitance [Ans. : VAB = 20V, U

= 8 × 10–4 J]

5.A voltmeter with resistance 500 is used to measure the emf of a cell of internal resistance 4 . What will be the percentage error in the reading of the voltmeter

6.In the given circuit, with steady current, calculate the potential drop across the capacitor in terms of V.

38

MIND MAP

39

Question For the answer of the following questions choose the correct alternative from among the given ones.

(1) Two wires of equal lengths, equal diameters and having resistivity’s ρ1 and ρ2 are connected in series.The equivalent resistivity of the combination is....

(Ans –B)

2. Figure, shows a network of eight resistors numbered 1 To 8, each equal to 2Ω , connected to a 3V battery of negligible internal resistance

The current I in the circuit is.... (A) 0.25A (B) 0.5A (C) 0.75A (D) 1.0 A

(Ans_D) 3.Seven resistors, each of resistance 5Ω, are connected as shown in fig, The equivalent resistance between points A and B is.... (A) 1Ω (B) 7Ω (C) 35Ω (D) 49Ω

Ans B

4.In the circuit shown in fig, the effective resistance between A and B

40

is.... (A) R/2 (B) R (C) 2 R (D) 4R

Ans A 5.In the circuit shown, the heat produced in the 5 ohm resistor due to current flowing through it, is 10 calories per second. Then the heat generated in the 4 ohm resistor is:

(A) 1 calorie per sec (B) 2 calorie per sec (C) 4 calorie per sec (D) 3 calorie per sec

6.In the potentiometer circuit shown in fig, the internal resistance of the 6V battery is 1Ωand the length of the wire is 100 cm. when AD=60 cm, the galvanometer shows no deflection. The emf of cell c is (the resistance of wire AB is 2Ω ) (A) 0.7 V (B) 0.8 V

(C) 0.9 V (D) 1.0V

7. Calculate net resistance beween A and B

41

(A) 2 r (B) 3 r (C) r /2 (D) r

8.What is the p.d between the terminals A and B? (A) 12 V (B) 24 V (C) 36 V (D) 48V

9. what is the potential aross the points A and B? (A) 0.9 V (B) 1.1 V (C) 1.3 V (D) 0.7 V

10.The drift velocity of free electrons through a conducting wire of radius r, carrying current I, is if the same current is passed through a conductor of radius 2r what will be the drift velocity? (A) Vd/4 (B) Vd (C) 2Vd (D) 24Vd 11. Two electirc bulbs whose resistances are in the ratio of 1:2 are connected in parallel to a constant voltage source the power dissipated in them have the ratio. (A) 1:2 (B) 1:1 (C) 2:1 (D)1:4

42

Assertion and reason type question:

Assertion and reason are given in follwing questions each question has four options one of them is correct select it. (a) Both assertion and reason are true and the reason is correct ercplanation of the assertion. (b) Both assertion and reason are true, but reason is not correct explanation of the assertion. (c) Assertion is true, but the reason is false. (d) Both, assertion and reason are false.

13.Assertion: There is no current in the metals in the absence of electric field. Reason: Motion of free electrons is random. (A) a (B) b (C) c (D) d 14.Assertion: the drift velocity of electrons in a metallic wire will decrease, if the tempreature of the wire is increased Reason: On increasing temperature, conductivity of metallic wire decreases. (A) a (B) b (C) c (D) d 15.Assertion: A potentiometer of longer length is used for acaurate measurement. Reason: The potential gardient for a potentiometer of longer length with a given source of e.m.f become small. (A) a (B) b (C) c (D) d 16. Assertion: The 200w bulbs glow with more brightness than 100w bulbs. Reason: A 100w bulb has more resistance than a 200w bulb. (A) a (B) b (C) c (D) d

43

CHAPTER-4

MAGNETIC EFFECTS OF CURRENT

SYNOPSIS

1. Magnetic effect of current means that a current flowing in a wire produces a magnetic field

around it.

2. The magnetic force (Fm) on a charge ‘q’ moving with velocity ‘v’ in a magnetic field B is given

both in magnitude and direction by F=q(v x B). The direction of F is perpendicular to the plane

containing v and B ( according to right hand thumb rule)

3. The force acting on a point charge q moving in the presence of both electric and magnetic field

is given by F=q[E+(ν x B)] and is known as Lorentz force.

4. The force acting on a conductor of length L carrying current I and placed inside a magnetic field of strength B is given by F= I(Lx B). Direction of force can be found out using Fleming’s left hand rule.

5. Motion of a charge in (a) Perpendicular magnetic field F=q(v x B),F=qvBSin 900=q v B (circular path) (b) Parallel or antiparallel field F=qvBSin0 (or) qvBSin1800=0 (Straight-line path) (c ) If 0<θ<90, the path is helix

vcosθ is responsible for linear motion, v sinθ is responsible for circular motion Hence trajectory is a helical path.

6. Cyclotron is a particle accelerator and is used to accelerate the positive ions. Under the action of the magnetic field, the positive ions move along the spiral path and gain energy as they cross the alternating electric field again and again.

7. Cyclotron frequency or magnetic resonance frequency ν=qB/2πm, T=2πm/Bq; ω=Bq/m

Maximum velocity and maximum kinetic energy of charged particle: Vm=Bqrm/m Em=B2q2rm

2 / 2m 8. According to Biot- Savart law, the strength of magnetic field dB due to a small current element

Idl carrying a current I at a distance r from the element is given by: dB =μ0IdlSinθ/4πr2 , where θ is the angle between dl and r

μ0=4π x 10-7 Tm/A

9. Applications of Biot-Savart law : Magnetic field at a centre of a current carrying circular coil B= μ0I/2a Magnetic field at a point on the axis of current carrying coil. B= μ0Nia2/2(a2+x2)3/2 (N=no. of turns in the coil)

44

10. Ampere’s circuital law

It states that the line integral of magnetic field around any closed path in vacuum/air is μ0 times the total current threading the closed path. ∫ B. dl= μ0 I

11. Applications i) Magnetic field due to straight infinitely long current carrying straight conductor. B= μ0 I/2πr ii) Magnetic field due to a straight solenoid carrying current

B= μ0n I n= no. of turns per unit length

iii) Magnetic field due to toroidal solenoid carrying current. B= μ0N I / 2πr N= Total no. of turns.

12. Force per unit length between parallel infinitely long current carrying straight conductors. F/l= μ0 I1 I2/2πd (a) If currents are in same direction the wires will attract each other. (b) If currents are in opposite directions they will repel each other. (c) 1 Ampere – One ampere is that current, which when flowing through each of the two parallel

straight conductors of infinite length and placed in free space at a distance of 1m from each other, produces between them a force of 2x10-7 N/m of their length.

13. When an electric current flows in a closed loop of wire, placed in a uniform magnetic field, the magnetic forces produces torque which tends to rotate the loop so that the area of the loop is perpendicular to the direction of the magnetic field. The torque is given by τ = NIBA Sinθ, where θ is the angle between the coil and the direction of the magnetic field, τ=MXB, Where M=NIA.

14. An arrangement of two unlike poles of equal strength and separated by a small distance is

called a magnetic dipole. The SI unit of magnetic pole strength is Am. The product of pole

strength of the either magnetic pole and magnetic length of the magnetic dipole is called its

magnetic dipole moment. It is expressed as M= m (2l), where m is the pole strength of the

magnetic dipole. SI unit of magnetic dipole moment is Am2.

15. Current loop as a magnetic dipole, its magnetic moment is given by M= evr/2

16. Moving coil galvanometer is a device used to detect small current flowing in an electric circuit.

It is based on the principle that when a current carrying coil placed in a magnetic field, it

experiences a torque.

45

17. A moving coil galvanometer can be converted into an ammeter by introducing a shunt

resistance of small value in parallel. It can be converted into voltmeter by introducing a

resistance of large value in series.

(i) Conversion of galvanometer into ammeter A small resistance S is connected in parallel to the galvanometer coil

S=IgG/( I - I g) ; RA=GS/(G+S)

(ii) Conversion of galvanometer into a voltmeter. A high resistance R is connected in series with the galvanometer coil.

R=( V/Ig) –G ; Rv=G+R

18. I αθ and I = K θ where K= NAB / C, where C is the torsional constant of the spring and is equal

to restoring torque per unit twist.

19. Current sensitivity, I s= θ / I=NBA/K

20. voltage sensitivity, Vs= θ /V=NBA/KR

46

CHAPTER-5

MAGNETISM

SYNOPSIS

1. The hypothetical lines which tells us about the strength of magnetic field in a particular region

such as near a bar magnet are called magnetic field lines.

2. Properties of magnetic field lines are : (i) They form closed continuous curves, (ii) the tangent

to the field lines gives the direction of magnetic field at that point, (iii) no two filed lines can

intersect each other, (iv) the lines of force contract longitudinally and dilate laterally, (v)

crowding of field lines represent stronger magnetic field and vice versa.

3. Magnetic field due to bar magnet is B= μ02m/ 4πr3.

4. Potential energy of the bar magnet is U=-M.B, where M is the magnetic moment and B is the

strength of the magnetic field.

5. The number of magnetic field lines that passes through a surface normally is called magnetic

flux.

6. The quantities magnetic declination, magnetic inclination and horizontal component of Earth’s

magnetic field completely determine the Earth’s magnetic field at a given place and are called

magnetic elements. (i) Magnetic declination θ is the angle between the geographic meridian

and the magnetic meridian, (ii) Magnetic inclination δ (or dip) is the angle between the

direction of the intensity of the Earth’s magnetic field and the horizontal, (iii) Horizontal

component of Earth’s magnetic field BH is the component of the Earth’s total magnetic field

along the horizontal.

7. Neutral point is that point where the magnetic field due to a bar magnet is completely

cancelled by the component of the Earth’s magnetic field.

8. The net magnetic moment per unit volume of the material is known as the magnetization M of

the material. It is a vector quantity and its SI unit is A/m.

9. Magnetic Induction is defined as the number of magnetic field lines inside the material crossing

per unit area normally through the magnetic material. B= μ0 (H+M), where H is the magnetic

47

intensity and is equal to the extent to which a material can be magnetized by a magnetic field.

SI unit of magnetic induction is tesla (T).

10. Magnetic susceptibility (𝜒)of a material is defined as the ratio of the intensity of magnetization

(M) and strength of the magnetizing field. 𝜒 =𝑀

𝐻. Magnetic susceptibility has no units. It can be

proved that µr = 1+χ, where µr is known as relative magnetic permeability.

11. The magnetic permeability (µ) of a material is defined as the ratio of the magnetic induction of

the material to the strength of magnetizing field. SI unit of magnetic permeability is Tm/A.

12. If µ0 is the absolute permeability of free space, then the relative permeability of a medium is

given by µr = µ/µ0.

13. Curie temperature is the temperature for a ferromagnetic substance above which, it behaves

as a paramagnetic substance. Curie’s law states that the magnetic susceptibility of a

paramagnetic substance varies inversely with its absolute temperature. It is expressed

as𝜒 𝛼 1/𝑇.

14. Properties of magnetic substances:

DIAMAGNETIC PARAMAGNETIC FERROMAGNETIC

1. Diamagnetic substances are those substances which are feebly repelled by a magnet.

Egg. Antimony, Bismuth, Copper, Gold, Silver, Quartz, Mercury, Alcohol, water, Hydrogen, Air, Argon, etc.

Paramagnetic substances are those substances which are feebly attracted by a magnet.

Egg. Aluminium, Chromium, Alkali and Alkaline earth metals, Platinum, Oxygen, etc.

Ferromagnetic substances are those substances which are strongly attracted by a magnet.

Egg. Iron, Cobalt, Nickel, etc.

2. When placed in magnetic field, the lines of force tend to avoid the substance.

The lines of force prefer to pass through the substance rather than air.

The lines of force tend to crowd into the specimen.

3. When placed in non-uniform magnetic field, it moves from stronger to weaker field (feeble repulsion).

When placed in non-uniform magnetic field, it moves from weaker to stronger field (feeble attraction).

When placed in non-uniform magnetic field, it moves from weaker to stronger field (strong attraction).

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4. When a diamagnetic rod is freely suspended in a uniform magnetic field, it aligns itself in a direction perpendicular to the field.

When a paramagnetic rod is freely suspended in a uniform magnetic field, it aligns itself in a direction parallel to the field.

When a paramagnetic rod is freely suspended in a uniform magnetic field, it aligns itself in a direction parallel to the field very quickly.

5. If diamagnetic liquid taken in a watch glass is placed in uniform magnetic field, it collects away from the centre when the magnetic poles are closer and collects at the centre when the magnetic poles are farther.

If paramagnetic liquid taken in a watch glass is placed in uniform magnetic field, it collects at the centre when the magnetic poles are closer and collects away from the centre when the magnetic poles are farther.

If ferromagnetic liquid taken in a watch glass is placed in uniform magnetic field, it collects at the centre when the magnetic poles are closer and collects away from the centre when the magnetic poles are farther.

6. Induced Dipole Moment (M) is a small –vet value.

Induced Dipole Moment (M) is a small + vet value.

Induced Dipole Moment (M) is a large + vet value.

7. Intensity of Magnetisation (I) has a small – vet value.

Intensity of Magnetisation (I) has a small + vet value.

Intensity of Magnetisation (I) has a large + vet value.

8. Intensity of Magnetisation (I) has a small – vet value.

Intensity of Magnetisation (I) has a small + vet value.

Intensity of Magnetisation (I) has a large + vet value.

9. Magnetic permeability μ is always less than unity.

Magnetic permeability μ is more than unity.

Magnetic permeability μ is large i.e. much more than unity.

10. Magnetic susceptibility cm has a small – vet value.

Magnetic susceptibility cm has a small + vet value.

Magnetic susceptibility cm has a large + vet value.

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11. They do not obey Curie’s Law. I.e. their properties do not change with temperature.

They obey Curie’s Law. They lose their magnetic properties with rise in temperature.

They obey Curie’s Law. At a certain temperature called Curie Point, they lose ferromagnetic properties and behave like paramagnetic substances.

CONCEPT BASED EXERCISE

VSA QUESTIONS:

1. How are the figure of merit and current sensitivity of galvanometer related with each other? (Reciprocal)

2. The force per unit length between two parallel long current carrying conductors is F. If the current in each conductor is tripled, what would be the value of the force per unit length between them? (9 times)

3. If the current is increased by 1% in a moving coil galvanometer, what will be percentage increase in deflection? (1%)

4. In a certain arrangement, a proton does not get deflected while passing through a magnetic field region. State the condition under which it is possible. (FB=FE)

5. What is the work done by the magnetic force on a charged particle moving perpendicular to the magnetic field? (zero)

6. An electron beam is moving vertically upwards. If it passes through a magnetic field directed from South to North in a horizontal plane, in what direction will the beam be deflected? (Towards west)

7. Show graphically the variation of magnetic field due to a straight conductor of uniform cross-section of radius ‘a’ and carrying steady currently as a function of distance r (a >r) from the axis of the conductor.

8. What is the principle of a moving coil galvanometer? 9. Which one of the two an ammeter or millimetre, has a higher resistance and why? 10. What will be (I) Pole strength (ii) Magnetic moment of each of new piece of bar magnet if the magnet is cut into two equal pieces: (a) normal to its length? (b) Along its length? 11. Where on the Earth surface is the value of angle of dip maximum? 12. A magnetic needle, free to rotate in a vertical plane, orients itself vertically at a certain place on the earth. What are the values of (I) horizontal components of Earth’s magnetic field, (ii) angle of dip at this place? 13. Mention two characteristics of a material for making permanent magnet.

14. How does the magnetic induction of a paramagnetic material vary with temperature? 15...The permeability of a magnetic material is 0.9983. Name the type of magnetic material it represents.

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16...An iron bar magnet is heated to 10000C and then cooled in a magnetic field free space. Will it retain its magnetism? 17...What is the net magnetic moment of an atom of a diamagnetic material? 18...What is the angle of dip at a place where vertical and horizontal component of earth’s field are equal? 19...Two similar bars, made from two different materials P and Q are placed one by one in a non-uniform magnetic field. It is observed that (a) the bar P tends to move from the weak to the strong field region. (b) The bar Q tends to move from the strong to the weak field region. What is the nature of the magnetic materials used for making these two bars? 20. (I) How is an electromagnet different form a permanent magnet? (ii) Write two properties of a material which make it suitable for making electromagnets.

NUMERICALS: LEVEL -1

Q. 1. The vertical component of Earth's magnetic field at a place is times the horizontal component. What is the value of angle of dip at this place? Q. 2. A short bar magnet placed with its axis at 30o to a uniform magnetic field of 0.2 T experiences a torque of 0.06 Nm. (I) Calculate the magnetic moment of the magnet. (ii) Find out what orientation of the magnet corresponds to its stable equilibrium in the magnetic field. Q. 3. A solenoid has a core of a material with relative permeability 400. The winding of the solenoid are insulated from the core and carry a current of 2 A. If the number of turns is 1000 per meter, calculate (I) H, (ii) M and (iii) B. Q. 4. In the Bohr model of hydrogen atom, an electron revolves around the nucleus in a circular orbit of radius 5.11 x 10-11 m at a frequency of 6.8 x 1015 Hz. What is the magnetic field at the Centre of the orbit? Q. 5. Two long parallel wires carrying currents 8 A and 5 A in the same direction are separated by a distance of 4 cm. Estimate the force on 10 cm length of one wire due to the other wire. Q. 6. A solenoid of 500 turns per meter is carrying a current of 3 A. Its core is made of iron of relative permeability 5000. Determine the magnitudes of magnetic intensity and magnetic field inside the core Q.7. A long straight wire carries a current of 35 A. What is the magnitude of magnetic field at a point 20 cm from the wire? Q. 8. A circular coil of wire consisting of 100 turns, each of radius 8 cm carries a current of 0.4 A. What is the magnitude of magnetic field at its centre? Q. 9. A closely wound solenoid 80 cm long has 5 layers of winding of 400 turns each. If the current carried is 8 A, estimate the magnetic field inside the solenoid near its centre. Q. 10. A galvanometer of coil resistance 50 Ω shows full scale deflection for a current of 5 mA. How can it be converted into a voltmeter of range 0 to 15 V?

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LEVEL -II Q. 1. Two identical magnetic dipoles of magnetic moment 1Am2 each are placed at a separation of 2 m with their axes perpendicular to each other. What is the resultant magnetic field at a point mid-way between the dipoles? Q. 2. A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60o and one of the field has a magnitude of 1.2 x 10-2 T. If the dipole comes to stable equilibrium at an angle of 15o with this field, what is the magnitude of the other field? Q. 3. The wire shown below carries a current I. Determine magnetic field at the centre. Radius of circular section is R.

Q. 4. To increase the current sensitivity of a moving coil galvanometer by 50%, its resistance is increased so that the new resistance becomes twice its initial resistance. By what factor does its voltage sensitivity change? Q. 5. A voltmeter V of resistance 400Ω is used to measure the potential difference across a 100 Ω resistor as shown. What will be the reading of the voltmeter? Also find the potential difference across the resistor before the voltmeter is connected.

Q.6. A compass needle of magnetic moment 60 Am2pointing geographical north at a place where the horizontal component of earth’s magnetic field is 40 µWeb/m2, experiences a torque of 1.2x10-3 Nm. What is the declination of the place? Q. 7. A straight wire carrying a currant of 12 A is bent into a semi-circular arc of radius 2 cm as shown below. What is the magnitude and direction of magnetic field at the centre of the arc? Would the answer change if it bent in the opposite way as shown in another figure?

Q.8. A straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is suspended in mid-air by a uniform horizontal magnetic field. What is the magnitude of the field?

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Q. 9. Two magnets of magnetic moments M and are joined to form a cross. The combination is suspended in a uniform magnetic field B. The magnetic moment M now makes an angle θ with the field direction. Find the value of θ.

Q. 10. The following figure shows the variation of intensity of magnetization versus the applied magnetic field intensity for two magnetic materials A and B. (I) identify the materials. (ii) For the material B, plot the variation of intensity of magnetization versus temperature.

ENRICHMENT EXERCISES 1. A voltmeter reads 8V at full scale deflection and is graded according to its resistance per volt at full scale deflection as 5000 ΩV–1. How will you convert it into a voltmeter that reads 20V at full scale deflection? Will it still be graded as 5000 ΩV–1? Will you prefer this voltmeter to one that is graded as 2000 ΩV–1? [7.5 × 104Ω] 2.An electron travels on a circular path of radius 10m in a magnetic field of 2 × 10–3 T. Calculate the speed of electron. What is the potential difference through which it must be accelerated to acquire this speed? [Speed = 3.56 × 109 m/s; V = 3.56 × 107 volts] 3. What is the radius of the path of an electron (mass 9 x 10–31 kg and charge 1.6 x 10–19 C) moving at a speed of 3 x 107 m/s in a magnetic field of 6 x 10–4 T perpendicular to it? What is its frequency? Calculate its energy in Kev. (1 eV = 1.6 x 10–19 J). 4.An electron moving with Kinetic Energy 25 Kev moves perpendicular to a uniform magnetic field of 0.2 Mt Calculate the time period of rotation of electron in the magnetic field. 5.A Galvanometer of resistance 3663 ohm gives full scale deflection for a certain current Ig.Calculate the value of the resistance of the shunt which when joined to the galvanometer coil will result in 1/34 of the total current passing through the galvanometer. Also find the total resistance of the Galvanometer and shunt. [111Ω, 107.7Ω]

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6.A long straight conductor PQ , carrying a current of 60 A, is fixed horizontally. Another long conductor XY is kept parallel to PQ at a distance of 4 mm, in air. Conductor XY is free to move and carries a current ‘I’ . Calculate the magnitude and direction of current ‘I’ for which the magnetic repulsion just balances the weight of the conductor XY. 7.Calculate the torque acting on a magnet of length 20 cm and pole strength 2 x 10 -5 Am, placed in the earth’s magnetic field of flux density 2 x 10 -5 T, when (a) magnet is parallel to the field (b) magnet is perpendicular to the field 8.A galvanometer can be converted into a voltmeter to measure upto (i) ‘V’ volts by connecting a resistance R1 in series with the coil, (ii) V/2 volts by connecting R2 in series with its coil. Find the resistance R in terms of R1 and R2 required to convert it into a voltmeter that can read upto 2V volts. 9.An alpha particle and a proton are released from the centre of the cyclotron and made to accelerate (i) Can both be accelerated at the same cyclotron frequency? Justify your answer. (ii) When they are accelerated in turn, which of the two will have higher velocity at the exit slit of the dees? 10.A multirange voltmeter can be constructed by using a galvanometer circuit as shown. We want to construct a voltmeter that can measure 2V, 20V and 200V using a galvanometer of resistance 10Ω and that produces maximum deflection for current of 1 mA. Find R1, R2 and R3 that have to be used.(R1=1990 Ω, R2=18 KΩ, R3=180 KΩ)

11.A rectangular loop of sides 25 cm and 10 cm carrying current of 15A is placed with its longer side parallel to a long straight conductor 2.0 cm apart carrying a current of 25A. What is the new force on the loop? Ans : 7.82 x 10–4 N towards the conductor 12.Two identical circular loops P and Q carrying equal currents are placed such that their geometrical axis are perpendicular to each other as shown in figure. And the direction of current appear’s anticlockwise as seen from point O which is equidistant from loop P and Q. Find the magnitude and direction of the net magnetic field produced at the point O.

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13.A magnetic dipole of magnetic moment M is kept in a magnetic field B. What is the minimum and maximum potential energy? Also give the most stable position and most unstable position of magnetic dipole. 14.A proton, alpha particle and deuteron are moving in circular paths with same kinetic energies in the same magnetic fields. Find the ratio of their radii and time periods. Draw their path. 15.A coil of N turns and radius R carries a current I. It is unwound and rewound to make another coil of radius R/2, current remaining the same. Calculate the ratio of the magnetic moment of the new coil and original coil. 16. A ship is to reach a place 15° south of west. In what direction should it be steered if declination at the place is 18° west? [Ans. : 87° west of North] 17.A particle of mass m and charge q moves at right angles to a uniform magnetic field. Plot a graph showing the variation of the radius of the circular path described by it with the increase in its kinetic energy, where, other factors remain constant. 18.Each of eight conductors in figure carries 2A of current into or out of page. Two path are indicated

for the line integral What is the value of the integral for the path (a) and (b).

19.At a place horizontal component of the earths magnetic field is B and angle of dip at the place is 60°. What is the value of horizontal componentof the earth’s magnetic field. (i) at Equator; (ii) at a place where dip angle is 30° 20.A current loop is placed in a uniform magnetic field in the following orientations (1) and (2). Calculate the magnetic moment in each case

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21. Obtain an expression for the magnetic moment of an electron, moving with speed ‘v’ in a circular orbit of radius ‘r’. How does this magnetic moment change when (i) the frequency of revolution is doubled, (ii) the orbital radius is halved?

22. An iron rod of volume 10-4 m3 and relative permeability 1000 is placed inside a long solenoid wound with 5 turns/cm. If a current of 0.5A is passed through the solenoid, find the magnetic moment of the rod.

23.A magnetising field of 1600 A/m produces a magnetic flux of 2.4 x 10 -5Wb in a bar of iron of cross section 0.2 cm2. Calculate permeability and susceptibility of the bar

56

1.Two straight long conductors AOB and COD are perpendicular to each other and carry currents I1and I2. The magnitude of the mag. field at a point "P" at a distance "a" from the point "O" in a direction perpendicular to the plane ABCD is

2.A length L of wire carries a steady current 1. It is bent first to form a coil of 1 turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same current is.................

(a) A quater of its first value (b) Un changed(c) Four times of its first value (d) A half of its first value

3.If a long hollow copper pipe carries a direct current, the magnetic field associated with the current will be ................ (a) Only inside the pipe (b) Only outside the pipe (c) Neither inside nor outside the pipe (d) Both inside and outside the pipe 4.If the strength of the magnetic field produced at 10 cm away from a infinilely long straight

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conductor is 10-5 tesla. The value of the current flowing in the conductor will be...............Ampere.

(a) 5 (b) 10 (c) 500 (d) 1000

5.The direction of mag. field lines close to a straight conductor carrying current will be ............... (a) Along the length of the conductor (b) Radially outward (c) Circular in a plane perpendicular to the conductor (d) Helical 6.Due to 10 Amp of current flowing in a circular coil of 10 cm radius, the mag. field produced at its centre is πx10-3 Tesla. The number of turns in the coil will be (a) 5000 (b) 100 (c) 50 (d) 25 7.A conducting rod of 1 meter length and 1 kg mass is suspended by two vertical wires through itsends. An external magnetic field of 2 Tesla is applied normal to the rod. Now the current to bepassed through the rod so as to make the tension in the wires zero is [take g = 10 ms-2] (a) 0.5 Amp (b) 15 Amp (c) 5 Amp (d) 1.5 Amp 8.A long solenoid has 200 turns per cm and carries a current of 2.5 Amp. The mag. field at its centre is ...................... tesla.

9.When the current flowing in a circular coil is doubled and the number of turns of the coil in it is halved, the magnetic field at its centre will become (a) Four times (b) Same (c) Half (d) Double 9. A current I, carrying wire AB is placed near an another long wire CD carrying current I2 As shown in Fig. If free to move, wire AB will have (a) rotational motion only (b) translational motion only (c) rotational as well as translational motion (d) neither rotational nor translational motion

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10. The deflection in a Galvanometer falls from 50 division to 20 when 12Ω shunt is applied. The Galvanometer resistance is ............................. (a) 18Ω (b) 36Ω (c) 24Ω (d) 30Ω 11 The coercivity of a bar magnet is 100 A/m. It is to be demagnetised by placing it inside a solenoid of length 100 cm and number of turns 50. The current flowing through the solenoid will be (a) 4 A (b) 2 A (c) 1 A (d) Zero 12. Assertion: We cannot think of magnetic field configuration with three poles. Reason: A bar magnet does exert a torque on itself due to its own field. 13. Assertion: If a compass needle be kept at magnetic north pole of the earth, the compass needle may Stay in any direction. Reason: Dip needle will stay vertical at the North Pole. 14. Assertion: Dia-magnetic materials can exhibit magnetism. Reason: Dia-magnetic materials have permanent magnetic dipole moment. 15. Assertion: A paramagnetic sample displays greater magnetisation when it is cooled. Reason: The magnetisation does not depend on temperature

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CHAPTER-6 ELECTROMAGNETIC INDUCTION

SYNOPSIS

1. The phenomenon of generation of current or emf by changing the magnetic field is known as

electromagnetic Induction (EMI). The emf developed in the conductor by the process of

electromagnetic induction is known as induced emf. If the conductor is in the form of closed loop

then the current flowing in the conductor is called induced current.

2. The total number of magnetic field lines crossing any surface held in a magnetic field B is known as magnetic flux. ΦB = B.A = BAcosθ, where θ is the angle between B and Area vector A. Also ΦB=

∮ 𝐵. 𝑑𝐴, Magnetic flux is a scalar quantity and its SI unit is weber (Wb)

3. According to Faraday’s first law of electromagnetic induction, an emf is induced in a closed loop

when the flux linked with the closed loop changes.

4. According to the second law of electromagnetic Induction, the rate of change of magnetic flux

is directly proportional to the induced emf, ε= −𝑑∅𝐵

𝑑𝑡. The induced emf in the loop due to

changing flux always opposes the change in magnetic flux.

5. According to Lenz law, the direction of induced current or the polarity of the induced e.m.f is such that it tends to oppose the change in magnetic flux that produces it. (The negative sign in Faraday’s law indicates this fact.) Lenz law obeys the principle of energy conservation.

6. When a metal rod of length l is placed normal to a uniform magnetic field B and moved with a

velocity v perpendicular to the field, the induced e.m.f is called motional e.m.f produced across the ends of the rod which is given byε = Blv.

7. The currents induced in bulk pieces of conductors when the magnetic flux linked with the

conductor changes are known as eddy currents.

8. When a current in a coil changes it induces a back e.m.f in the same coil. The self inducede.m.f is

given by ε = −𝑳𝒅𝑰

𝒅𝒕where L is the self-inductance of the coil. It is a measure of inertia of the coil

against the change of current through it. Its S.I unit is henry (H). 9. A changing current in a coil can induce an e.m.f in a nearby coil. This relation,

ε = −𝑴𝟏𝟐𝒅𝒊𝟐

𝒅𝒕, shows that Mutual inductance of coil 1 with respect to coil 2 (M12) is due to change

of current in coil 2. (M12 = M21).

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10. The self-inductance of a long solenoid is given by L = µ0n2Al where A is the area of cross-section of the solenoid, l is its length and n is the number of turns per unit length.

11. The mutual inductance of two co-axial coils is given by M12 = M21 = µ0 n1n2Al where n1& n2 are the number of turns per unit length of coils 1 & 2. A is the area of cross-section and l is the length of the solenoids.

12. Energy stored in an inductor in the form of magnetic field is 2

max

1

2BU Li and

Magnetic energy density 0

2

2B

BU

13. A transformer is a device for increasing or decreasing ac voltage. Transformer works on the principle of mutual induction. In actual transmission of power energy loss takes place due to the following reasons: copper loss, flux leakage, iron loss, hysteresis loss.

For a transformer, ps s

p p s

iE NK

E N i (Transformation ratio)

In an ideal transformer, εPIP = εSIS. i.e If NS>NP; εS>εP& IS<IP – step up. If NP>NS;εP>εS& IP<IS – step down.

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CHAPTER-7

ALTERNATING CURRENT

SYNOPSIS

1. In an A.C. generator, mechanical energy is converted to electrical energy by virtue of electromagnetic induction. It is based on the principle of electromagnetic induction i.e. whenever the magnetic flux linked with a coil changes, an emf is induced in the coil. The direction of induced emf is determined by Fleming’s right hand rule.

Φ = NBACosωt, Change in flux induces e.m.f in the coil which is given by ε= -dΦ/dt = NBAωSinωt, 𝜀= ε0Sinωt Current induced in the coil I = ε/R = ε0Sinωt/R = I0Sinωt.

2. An alternating voltage ε=ε0Sinωt, applied to a resistor R drives a current I = I0Sinωt in the resistor, I0 = ε0 /R where ε0& I0 are the peak values of voltage and current. (also represented by Vm&Im)

3. The root mean square value of a.c. may be defined as that value of steady current which would generate the same amount of heat in a given resistance in a given time as is done by the a.c. when passed through the same resistance during the same time. Irms = I0/√2 = 0.707i0 , Similarly, vrms = v0/√2 = 0.707v0.

4. For an a.c. ε = ε0 Sin ωt applied to a resistor, current and voltage are in phase. 5. In case of an a.c. circuit having pure inductance current lags behind e.m.f by a phase angle 90°.

ε = ε0 Sin ωt and i = i0 Sin (ωt-π/2) I0 = ε0/XL; XL = ωL is called inductive reactance 6. In case of an a.c. circuit having pure capacitance, current leads e.m.f by a phase angle of 90°. ε =

ε0Sinωt and I= I0Sin(ωt+π/2) where I0 = ε0/XC and XC = 1/ωC is called capacitive reactance

7. In case of an a.c. circuit having R, L and C, the total or effective

resistance of the circuit is called impedance (Z).

Z = ε0 / I0 = 2

LC

2 )X-(X +R tanΦ = c LX X

R

where φ is the phase difference

between current and voltage. ε = ε0Sinωt, I= I0Sin(ωt+Φ)

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8.The condition in which the impedance of series LCR circuit is minimum and therefore maximum current flows through the circuit is known as resonance. The frequency of oscillation of the circuit at resonance is known as resonant frequency 𝜔𝑟, i.e. if XC = XL, so that Z = R and resonant frequency

𝜔𝑟 =1

√𝐿𝐶 𝑎𝑛𝑑 𝜗𝑅 =

1

2𝜋√𝐿𝐶

9.Average power loss over a complete cycle in an LCR circuit is

P = εrmsIrmsCosΦ

* In a purely resistive circuit Φ = 0; P = VRMSIRMS.

* In a purely inductive circuit Φ = Π/2; P = 0.

* In a purely capacitive circuit Φ = Π/2; P = 0.

10. When the resistance of an LCR circuit is very low, a large current flows and the angular frequency is close to the resonant frequency. Such an LCR series circuit is said to be more selective and sharper. 11. Q factor of series resonant circuit is defined as the ratio of voltage developed across the inductance or capacitance at resonance to the applied voltage across ‘R’,

Q=𝜔𝑟𝐿

𝑅 𝑜𝑟

1

𝜔𝑟𝐶𝑅 also 𝑄 =

𝜔𝑟

2∆𝜔 where 2∆𝜔 is bandwidth.

12.A circuit containing an inductor L and a capacitor C (initially charged) with no a.c. source and no resistors exhibits free oscillations of energy between the capacitor and inductor. The charge q satisfies the equation :

2

2

10

d qq

LCdt

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CONCEPT BASED EXERCISE

VSA QUESTIONS( 1 Mark)

1. Why core of a transformer is laminated?(Ans.To reduce loss due to eddy currents) 2. The divisions marked on the scale of an a.c. ammeter are not equally spaced. Why? ( Ans. A.C.

ammeter works on the principle of heating effect ) 3. In an a.c. circuit, instantaneous voltage and current are V = 200 sin 300 t volt and i = 8 cos 300t

ampere respectively. What is the average power dissipated in the circuit?(Ans. Zero) 4. Why do we prefer carbon brushes than copper in an a.c. generator? 5. What is the Significance of Q-factor in a series LCR resonant circuit? 6. How does an inductor behave in a DC circuit after the current reaches to steady state? Justify. 7. An ac source of rms voltage V is put across a series combination of an inductor L, capacitor C

and a resistor R. If VL, VC and VR are the rms voltage across L, C and R respectively then why is V ≠ VL + VC + VR? Write correct relation among VL, VC and VR.(Ans. r.m.s voltages are added vectorially and not algebraically. V = (VR

2 +(VL -VC)2)1/2)

8. Why a 220 V AC is considered to be more dangerous than 220 V DC? 9. The instantaneous value of e.m.f is given by ε= 300sin 314t. What is the peak value and rms

value of emf? 10.What are eddy currents? How are these minimized? Mention two applications of eddy currents. 11.What is the direction of induced currents in metal rings 1 and 2 seen from the top when current I in the wire is increasing steadily?

12 In which of the following cases will the mutual inductance be (i) minimum (ii) maximum?

13.A coil A is connected to an A.C. ammeter and another coil B to A source of alternating e.m.f. What will be the reading in ammeter if a copper plate is introduced between the coils as shown.

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NUMERICALS

LEVEL -I

1. What is the self-inductance of a coil in which magnetic flux of 40mWb is produced when 2A current flow through it? 2. If the self inductance of an air core inductor increases from 0.01mH. to 100mH on introducing an iron core into it. What is relative permeability of the core used? 3. What is the power dissipated in an a.c circuit in which voltage and current are given by V=230 sin(ωt + 𝜋/2) and I=10 sinωt ? 4. When a lamp is connected to an a.c. supply it light with the same brightness as when connected to a 12V d.c battery. What is the peak value of alternating voltage?

5.What is the average value of the emf for the shaded part of graph?

6.An inductor of inductance 100mH is connected in series with a resistance, a variable capacitance and an AC source of frequency 2 kHz. What should be the value of the capacitance so that maximum current may be drawn into the circuit? (Ans.6x10-8 F)

7.A capacitor, a resistor and 4 /π2 henry inductor are connected in series to an a.c. source of 50 Hz. Calculate capacitance of capacitor if the current is in phase with voltage. (25 μF.)

8.A power transmission line feeds input power at 2400 V to a step down ideal transformer having 4000 turns in its primary. What should be number of turns in its secondary to get power output at 240V? (400) 9. A circular coil of radius 8 cm and 20 turns rotates about its vertical diameter with an angular speed of 50/s in a uniform horizontal magnetic field of magnitude 3 x 10-2 T. Find the max. and average value of the emf induced in the coil. 10.The instantaneous current from an a.c. source is I = 5 sin (314 t) ampere. What are the average and rms values of the current? 11. An inductor L, a capacitor 20 𝜇F ac source of frequency 50 Hz. If the current is in phase with voltage, calculate the Inductance L.

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LEVEL II

Q1. A conductor of length 1.0 m falls freely under gravity from a height of 10 m so that it cuts the lines of force of the horizontal component of earth’s magnetic field of 3x10-5 Wbm-2. Find the emf induced in the conductor. Q2. A 0.4 m long straight conductor is moved in a magnetic field of induction 0.9 Wbm-2 with velocity of 7 ms-1. Calculate the maximum emf induced in the conductor. Q3. A metal disc of radius 200 cm is rotated at a constant angular speed of 60 rads-1 in a plane at right angles to an external field of magnetic induction 0.05 Wbm-2 .Find the emf induced between the centre and a point on the rim. Q4. Find the maximum value of current when an inductance of one Henry is connected to an a.c. source of 200 volts, 50 Hz.

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Q5. What is the inductive reactance of a coil if current through it is 800 mA and the voltage across it is 40 V? Q6. A transformer has 300 primary turns and 2400 secondary turns .If the primary supply voltage is 230 V, what is the secondary voltage? Q7. A transformer of 100% efficiency has 500 turns in the primary and 10,000 turns in the secondary coil. If the primary is connected to 220 V supply, what is the voltage across the secondary coil? Q8. A capacitor in series with a resistance of 30 ohm is connected to a.c. mains. The reactance of the capacitor is 40 ohm. Calculate the phase difference between the current and the supply voltage. Q9. Determine the impedance of a series LCR-circuit if the reactance of C and L are 250 ohm and 220 ohm respectively and R is 40 ohm. Q10. A series circuit with L=0.12 H, C=0.48 mF and R=25 ohm is connected to a 220 V variable frequency power supply. At what frequency is the circuit current maximum?

LEVEL III 1. A bulb of resistance 10Ω, connected to an inductor of inductance L, is in series with an ac source marked 100V, 50Hz. If the phase angle between the voltage and current is radian, calculate the value of L. 2. Figure shows how the reactance of an inductor varies with frequency. (a) Calculate the value of inductance of the inductor using the information given in the graph. (b) If this inductor is connected in series to a resistor of 8 ohm, find what would be the impedance at 300 Hz. 3. In a series RC circuit, R = 30 Ω, C = 0.25 μ F, V = 100 V and ω = 10,000 radian per second. Find the current in the circuit and calculate the voltage across the resistor and the capacitor. Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox. 4. When an alternating voltage of 220V is applied across a device X, a current of 0.5A flows through the circuit and in phase with the applied voltage. When the same voltage is applied across another device Y, the same current again flows through the circuit but it leads the applied voltage by π/2 radians. (i) Name the devices X and Y, (ii) Calculate the current flowing in the circuit when the same voltage is applied across the series combination of X and Y. 5.In the series LCR circuit, suppose R = 300 Ω, L = 60 mH, C = 0.5 μ F. An ac source of emf 50 V, angular frequency 10,000 rad/s is connected across the combination. Find the reactance XL, and XC, the impedance Z, the current amplitude I, the phase angle φ, and the voltage amplitude across each circuit element. 6. In a series RC circuit with an AC source, R = 300 Ω, C = 25 µF, e0 = 50 V and γ = 50Hz, find the peak current and the average power dissipated in the circuit.

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7. An inductor 200 mH, capacitor 500 μ F, resistor 10 Ω are connected in series with a 100 V, variable frequency ac source. Calculate the (i) frequency at which the power factor of the circuit is unity; (ii) current amplitude at this frequency; (iii) Q-factor.

50 Hz ac source. If the current in the circuit is 0.49 A, find the (i) voltage across the resistor and capacitor (ii) value of inductance required so that voltage and current are in phase. 9. A resistor of 200 Ω and a capacitor of 15 μ F are connected in series to a 220 V, 50 Hz ac source. (a) Calculate the current in the circuit; (b) calculate the voltage (rms) across the resistor and the capacitor. Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox. 10. A town is situated 15 km away from a power plant generating power at 440V, requires 800 kW of electric power at 220V. The resistance of the two wire line carrying power is 0.5 ohm per km. The town gets power from the line through a 4000-220V step down transformer at a substation in the town. (i) Find the line power losses in the form of heat. (ii) How much power must the plant supply, assuming there is negligible power loss due to leakage? (iii) Characterize the step up transformer at the plant. 11. An ac generator consists of a coil of 50 turns and area 2.5 m2 rotating at an angular speed of 60 rad/s in a uniform magnetic field B = 0.3 T between two fixed pole pieces. The resistance of the circuit including that of the coil is 500 Ω. Determine the Calculate (i) maximum current drawn from the generator. (ii) maximum power dissipation in the coil. (iii) What will be orientation of the coil with respect to the magnetic field to have (a) maximum, (b) zero magnetic flux? (iv) Would the generator work if the coil was stationary and instead the pole pieces rotated together with the same speed as above? 12. A circular coil having 20 turns, each of radius 8 cm, is rotating about its vertical diameter with an angular speed of 50 radian/s in a uniform horizontal magnetic field of magnitude 30 mT. Obtain the maximum average and rms value of the emf induced in the coil. If the coil forms a closed loop of resistance 10 Ω, how much power is dissipated as heat in it? 13.An athlete peddles a stationary tricycle whose pedals are attached to a coil having 100 turns each of area 0.1m2. The coil, lying in the X-Y plane, is rotated, in this plane, at the rate of 50 rpm, about the Y-axis, in a region where a uniform magnetic field, = (0.01) tesla, is present. Find the (i) ma B = 0.01 kˆ .Find the (i) maximum emf (ii) average e.m.f generated in the coil over one complete revolution

69

ENRICHMENT EXERCISES

1. An A.C source of voltage V= VmSinωt is connected one-by-one to three circuit elements X, Y and Z. It is observed that the current flowing in them (i) is in phase with applied voltage for X (ii) Lags applied voltage in phase by π /2 for elements Y. (iii) Leads the applied voltage in phase by π /2 for element Z. Identify the three circuit elements. (Resistor,inductor,Capacitor)

2. An ac generator consists of a coil of 50 turns and an area of 2.5m2 rotating at an angular speed of 60 rad/s in a uniform magnetic field of B= 0.3T between two fixed pole pieces. The resistance of the circuit including that of the coil is 500Ώ (i) What is the maximum current drawn from the generator? (ii)What is the flux through the coil when current is zero? (iii)What is the flux when current is maximum? (solution(i) 4.5 A (ii) 37.5 Wb (iii) 0 )

3. A rectangular conducting loop of length I and breadth b enters a uniform magnetic field B as shown below.. The loop is moving at constant speed v and at t = 0 it just enters the field B. Sketch the following graphs for the time interval t = 0 to t 3l /v (i) Magnetic flux – time (ii) Induced emf – time (iii) Power – time. Resistance of the loop is R.

4. Show that in the free oscillation of an LC circuit, the sum of energies stored in the capacitor and the inductor is constant with time.

5. Twelve wires of equal lengths are connected in the form of a skeleton of a cube, which is moving with a velocity v in the direction of magnetic field B. Find the emfin each arm of the cube. (Ans. Zero)

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6.Circuit shown here uses an airfield parallel plate capacitor. A mica sheet is now introduced between the plates of capacitor. Explain with reason the effect on brightness of the bulb B. (

Ans.(increases) 7.An alternating voltage of frequency f is applied across a series LCR circuit. Let frbe the resonance frequency for the circuit. Will the current in the circuit lag, lead or remain in phase with the applied voltage when (i) f >fr(ii) f <fr? Explain your answer in each case.(Ans.(i) lag (ii) lead) 8.How does mutual inductance of a pair of coils kept coaxially at a distance in air change when (i) the distance between the coils is increased? (ii) an iron rod is kept between them?(Ans .(i) decreases (ii) decreases) 9.In a series L–R circuit, XL = R and power factor of the circuit is P1. When capacitor with capacitance C such that XL = XC is put in series, the power factor becomes P2. Find P1/P2. 10.Current versus frequency (I – ) graphs for two different series L–C–R circuits have been shown in adjoining diagram. R1 and R2 are resistances of the two circuits. Which one is greater–R1 or R2?

11. A bar magnet is falling with some acceleration ‘a’ along the vertical axis of a coil as shown in fig. What will be the acceleration of the magnet(whether a > g or a < g or a = g) if (a) coil ends are not connected to each other? (b) coil ends are connected to each other?

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12.In the figure shown, coils P and Q are identical and moving apart with same velocity V. Induced currents in the coils are I1 and I2. Find I1/I2.

13.A bar magnet M is dropped so that is falls vertically through the coil C. Thegraph obtained for voltage produced across the coil Vs time is shown in figure (i) Explain the shape of the graph (ii) Why is the negative peak longer than the positive peak?

Q-14Which of the following curves may represent the reactance of a series LCcombination

72

MIND MAPS

73

MCQ For the answer of the following questions choose the correct alternative from among the given ones.

1. A coil having area 2m2 is placed in a magnetic field which changes from 1 wb /m2 to 4 wb/m2 in an interval of 2 second. The emf induced in the coil of single turn is.... (a) 4 v (b) 3 v (c) 1.5 v (d) 2 v

2.Two different loops are concentric & lie in the same plane. The current in outer loop is clockwise & increasing with time. The induced current in the inner loop then, is..........

(a) clockwise (b) zero (c) counter clockwise (d) direction depends on the ratio of loop radii 3.A bar magnet is moving along the common axis of two coils A &B towards A. current is induced in

(a) Only A (b) Only B (c) both A& B in same direction (d) both A & B in opposite direction 4.An electron moves along the line AB,which lies in the same plane as a circular loop of conducting wires as shown in figure. What will be the direction of current induced if any, in the loop

(a) No current will be induced (b) The current will be clockwise (c) The current will be anticlockwise (d) The current will change direction as the electron passes by

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5.Consider the situation shown in the figure. The wire AB is sliding on the fixed rails with a constant velocity v . If the wire AB replaced by semi-circular wire the magnitude of the induced current will.

(a) Increases (b) decreased (c) Remain same (d) depending on whether the semicircle bulge is towards the resistance or away from it 6.The self-inductance of a straight conductor is... (a) zero (b) very large (c) very small (d) infinity 7. Two coils of self-inductances 2 mH & 8 mH are placed so close together that the effective flux in one coil is completely half with the other.The mutual inductance between these coils is.......

(a) 4 mH (b) 6 mH (c) 2 mH (d) 16 mH

8. In circular coil. when no. of turns is doubled & resistance becomes half of the initial then inductance becomes....

(a) 4 times (b) 2 times (c) 8 times (d) No change

9.When the switch S turned off.

(a) Both B1 and B2 die out promptly (b) Both B1 and B2 die out with some delay

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(c) B1 dies out promptly but B2 with some delay (d) B2 dies out promptly but B1 with some delay

10.A coil of inductance 300 mH and resistance 2 Ωis connected to a source of voltage 2V. The current reaches half of its steady state value in......... (a) 0.15 sec (b) 0.3 sec (c) 0.05 sec (d) 0.1sec 11. If rotational velocity of a dynamo armature is doubled, then induced emf will become... What is increased in step down transformer?

(a) Half (b) Two times (c) Four times (d) unchanged

12.The instantaneous voltage through a device of impedance 20Ω is ε = 80sin100π t . The effective value of the current is, (a) 3A (b) 2.828 A (c) 1.732 A (d) 4A 13. A choke coil has. (a) High inductance and low resistance (b) Low inductance and high resistance (c) High inductance and high resistance (d) Low inductance and low resistance 14. A resistor and a capacitor are connected in series with an ac source. If the potential drop across the capacitor is 5 V and that across resistor is 12 V, the applied voltage is, (a) 13 V (b) 17 V (c) 5 V (d) 12 V

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CHAPTER-8

ELECTROMAGNETIC WAVES

SYNOPSIS

1. The current which comes into play in the region in which the electric field and the electric flux are

changing with time is known as displacement current. 𝑰𝑫 = 𝜺𝟎 ∫𝒅∅𝑬

𝒅𝒕

2. Conduction current and displacement current together have the property of continuity. 3. The four fundamental equations of electromagnetism called as Maxwell’s equations are:

Gauss’s Law in Electrostatics

∮ . 𝑑𝑆=𝑄

𝜀0

Gauss’s Law in Magnetism

∮ . 𝑑𝑆=0 Faraday’s -Lenz law of electromagnetic induction. ∮ 𝐸.𝑑𝑙 = − 𝑑𝜙B/𝑑𝑡

Modified Ampere’s circuital Law ∮𝐵.𝑑𝑙 = 𝜇0 ( I + 𝜀0𝑑𝜙𝐸𝑑𝑡 )

Concept of displacement current Displacement current is that current which appears in a region in which the electric field (and hence electric flux) is changing with time. Note- We have ID = 𝜀0𝑑𝜙𝐸𝑑𝑡 = 𝜀0 𝑑/𝑑𝑡 (EA) = 𝜀0 𝑑𝑑𝑡 (𝑞𝜀0𝐴 A) = 𝑑𝑞𝑑𝑡 = I

4. The wave in which there is sinusoidal variation of electric and magnetic field at right angles to each

other as well as right angles to the direction of wave propagation. Accelerated charge acts as a source of electromagnetic waves.

5. EM wave is a transverse wave because of which it undergoes polarization effect. 6. Electric vectors are only responsible for optical effects of EM waves.

7. The amplitude of electric & magnetic fields are related by 𝐸

𝐵= 𝑐

8. Oscillating or accelerating charged particle produces EM waves.

9. Velocity of EM waves in free space:𝑐 =1

√𝜇0𝜀0

3x108 m/s

10. EM waves also carry energy, momentum and information. 11. EM waves in x- direction are represented by the following equations

13. Electromagnetic spectrum, its production, detection and uses in general:

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Type Wave length Range Frequency Range

Production Detection Uses

Radio

>0.1m 109 to 105Hz

Rapid acceleration / deceleration of electrons in aerials

Receiver’s aerials

Radio, TV Communication

Microwave

0.1mm 1011 to109 Hz

Klystron valve or magnetron valve

Pointcontact diodes

Radar, TV communication

Infrared

1mm to 700nm 1011 to1014 Hz

Vibration of atom or molecules

Thermopiles, Bolometer Infrared Photographic Film

Green House effect, looking through haze, fog and mist, Ariel mapping.

Light

700nm to 400nm 8x1014 Hz

Electron in an atom during transition

Eye, Photocell, Photographic Film

Photography, Illuminations, Emit & reflect by the objects.

Ultraviolet

400nm to 1nm 5x1014 to 8x1014

Inner shell electron in atom moving from one energy level to a lower energy level

Photocell & photographic film

Preservation of food items, Detection of invisible writing, finger print in forensic laboratory. Determination of Structure of molecules & atoms.

X-rays

1nm to 10-3nm 1016 to 1021 Hz

X-ray tube or inner shell Electrons

Photographic film, Geiger tube, ionization chamber.

Study of crystal structure & atom, fracture of bones.

Gamma ray

<10-3nm

1018 to 1022 Hz

Radioactive decay

of the nucleus

Photographic

film, Geiger

tube, ionization

chamber

Nuclear reaction &

structure of atoms &

Nuclei.

To destroy cancer

cells.

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CONCEPT BASED EXERCISE

VSA

1. What is the phase difference between electric and magnetic field vectors in an em wave? 2. Arrange the following em waves in descending order of wavelengths: γ ray, microwaves UV

radiations. 3. Which physical quantity is the same for microwaves of wavelength 1 mm and UV radiations of

1600 A° in vacuum? 4. What is the source of energy associated with propagating EM waves? 5. Name the part of the electromagnetic spectrum of wavelength 10–2 m and mention its one

application. 6. Write the expression for the displacement current? 7. The charging current for capacitor is 0.5 A. What is the displacement current across its plate? 8. Write an expression for the speed of e.m. waves in free space. 9. For an electromagnetic wave, write the relationship between amplitude of electric and

magnetic fields in free space. 10. What was the range of wavelength of em waves produced by Professor J.C.Bose?

LEVEL -I Represent EM waves propagating along the x-axis. In which electric and magnetic fields are along y-axis and z-axis respectively.

1. Show by giving example, how EM waves carry energy and momentum? 2. How are microwaves produced? Why is it necessary in microwave ovens to select the

frequency of microwave to match the resonant frequency of water molecules? 3. Welders use special types of glasses while working. Explain. 4.Conduction current and displacement currents are individually discontinuous, but their sum is continuous. Comment 4. What is displacement current? Why was this concept introduced? 5. Give one uses of each of the following:a. Microwave b. Infra-red wave c. Ultra violet radiation

d. Gamma rays 6. Identify the following electromagnetic radiation as per the wavelength given below. Write one

application of each. a. 1mm b. 10-3nm 7. Identify the following electromagnetic radiation as per the wavelength given below. Write one

application of each. (a)10-12m (b)10-4m (c)10-6m 8.Name the electromagnetic radiation having the wavelength range from 1mm to 700nm. Give its two important applications.

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LEVEL -II

1. The charging current for a capacitor is 0.2A. What is the displacement Current? (0.2 A) 2. An EM wave has amplitude of electric field E0 and amplitude of magnetic field is B0 the

electric field at some instant become 3/4E0.What will be magnetic field at this instant? (Wave is travelling in vacuum). ( Ans .3/4B0 )

3. Show that the average energy density of the electric field E equals the average energy density of the magnetic fields B?

4. An EM wave is travelling in vacuum. Amplitude of the electric field vector is 5 × 104 V/m. Calculate amplitude of magnetic field vector.(1.66 x 10 -4 T )

5. The amplitude of the magnetic field vector of an electromagnetic wave travelling in vacuum is 2.4mT. Frequency of the wave is 16 MHz Find: (i) Amplitude of electric field vector and (ii) Wavelength of the wave.(7.2x105V/m; 18.7 m)

6. An EM wave travelling through a medium has electric field vector. Ey= 4 × 105cos (3.14×108t – 1.57 x) N/C. Here x is in m and t in s. Then find: (i) Wavelength (ii) Frequency (iii) Direction of propagation (iv) Speed of wave (v) Refractive index of medium (vi) Amplitude of magnetic field vector.(Ans (i) 4 m(ii)0.5x108Hz (iii)+ve direction of x- axis (iv) 2x108 m/s(v)1.5(vi)1.33x10-3 T)

7. Suppose the electric field amplitude of an em wave is E0 = 120 NC–1 and that its frequency is ν = 50.0 MHz (a) Determine B0, ω, k and λ, (b) Find expressions for E and B.(Ans (a) 40 x10-

8;3.14x106 rad/s ;1.04 m-1;6 m(b) E= 120 Sin(3.14x106 t -1.04 x) V/m; B = 4x 10 -5Sin((3.14x106 t -1.04 x) T)

ENRICHMENT EXERCISES

1. When an ideal capacitor is charged by a dc battery, no current flows. However, when an ac source is used, the current flows continuously. How does one explain this, based on the concept of displacement current? 2. How are EM waves produced by oscillating charges? Why is it not possible to produce EM waves in the visible region with modern electronic circuits in the laboratory? What is the method of production of X-rays?

80

MIND MAPS

81

MCQ

For the answer of the following questions choose the correct alternative from among the given ones. (1) Who produced the electromagnetic waves first ?

(A) Marconi (B) Maxwell (C) J.C. Bose (D) Hertz

2. A plane electromagnetic wave is incident on a material surface. The wave delivers momentum P and energy E

3. According to Maxwell, a changing electric field produces (A) emf (B) Electric current (C) magnetic field (D) radiation pressure 4. An electromagnetic wave going through vaccum is described by E= E0 sin(kx- ω t).Which of the following is independent of the wavelength?

(A) ω (B) k/ ω (C) k ω (D) k

5.Which of the following have zero average value in a plane electromagnetic wave? (A) Electric energy (B) Magnetic energy (C) Electric field (D) None of these.

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6.Astronomers have found that electromagnetic waves of wavelength 21cm are continuously reaching the Earth’s surface . Calculate the frequency of this radiation. (A) 14.28 GHz (B) 1.428 kHz (C) 1.428 MHz (D) 1.428 GHz 7.Speed of electromagnetic wave is the same (A) for all wavelengths (B) in all media (C) for all intensities (D) for all frequencies 8 .The maximum electric field in a plane electromagnetic wave is 1 900NC-1 . The wave is going in the x direction and the electric field is in the y direction. The maximum magnetic field in the wave is ____________T

9.Electromagnetic waves are produced by

(A) a static charge (B) a moving charge (C) an accelerating charge (D) chargeless particles

(10) Maxwells equations are derived from the laws of___________ (A) electricity (B) magnetism (C) both electricity and magnetism (D) mechanics (11) Which of the following electromagnetic waves has the longest wavelength? (A) Radio waves (B) Infrared radiations(C) x rays (D) visible rays (12) Which of the following electromagnetic waves has the highest frequency? (A) radio waves (B) micro waves (C) r rays (D) x rays (13) Which of the following electromagnetic waves is used in telecommunication? (A) radio waves (B) visible radiations (C) ultraviolet rays (D) micro waves (14) The velocity of light in vaccum can be changed by changing____ (A) frequency (B)wavelength (C)amplitude (D) none of these (15)According to Maxwell, a changing electric field produces_____ (A) emf (B) radiation pressure (C) electric current (D) magnetic field

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CHAPTER-9

WAVE OPTICS

SYNOPSIS

1. Partciles of light which are equidistant from the light source and vibrate in same phase constitute a

wavefront.

2. For a point source of light we obtain a spherical wavefront, for a linear source of light we get a

cylindrical wavefront, and for a point source located very far away we get a plane wavefront.

3. According to Huygen’s principle, each and every point on the given wavefront, called primary

wavefront acts as a source of new disturbances, called “secondary wavelets” that travel in all

directions with the velocity of light in that medium. A surface touching thses secondary wavelets

tangentially in the forward direction at any instant gives a new wavefront at that instant, which is

known as the secondary wavefront.

4. According to the superposition principle, when two or more waves travelling through a medium

superpose on each other, a new wave is formed in which the resultant displacement at any instant

is equal to the vector sum of the displacements due to the individual waves at that instant. Y=

y1+y2+y3+…

5. Sources of light which emit continuous light waves having same wavelength, same frequency and in

the same phase or having a constant phase difference are known as coherent sources of light.

6. Two independent sources of light cannot be coherent. The coherent sources of light can be obtained

from a single source of light by reflection, refraction etc.

7. The redistribution of light energy on account of superposition of light waves from two coherent

sources of light is known as interference of light.

8. For constructive interference at a point, the phase difference between two waves reaching at that

point should be zero or an even integral multiple of 2π or path difference between the two waves

reaching the point should be zero or integral multiple of wavelength λ.

9. For destructive interference at a point, the phase difference between the two waves reaching the

point should be odd integral multiple of π or path difference between the two waves reaching the

point should be an odd integral multiple of half wavelength λ/2.

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10. The position of nth bright fringe from the centre of screen:xn= 𝑛𝐷𝜆

𝑑

11. The position of nth dark fringe from the centre of screen is xn= (2𝑛−1)𝐷λ

2𝑑

12. Fringe width is the separation between two successive bright or dark fringes and is given by β=Dλ/d.

In Young’s double slit interference, dark fringes are situated in between bright fringes and vice versa.

All the bright and dark fringes are of equal width.

13. When we use white light instead of monochromatic source of light then the interference fringes will

be coloured and the central maximum will be white in colour.

14. Ratio of intensity of maxima and minima of an interference pattern : If a1 and a2 are the amplitudes

of two interfering waves, then the ratio between the intensities at maxima and minima will be I max/I

min= (a1+a2)2/(a1-a2)2.

15. If Young’s double slit apparatus is immersed in a liquid of refractive index µ, the wavelength of light

decreases to λ/µ and the fringe width reduced to β’=Dλ/dµ = β/µ.

16. Conditions for sustained interference: the two sources should be coherent, amplitudes of the

interfering waves should be equal, the two sources should be narrow, sources should be

monochromatic etc.

17. Intensity distribution curve for interference:

18. The phenomenon of bending of light around the corners of an obstacle placed in its path, on account

of which it penetrates into the region of geometrical shadow of the obstacle, is known as diffraction

of light.

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When source of light is monochromatic, the diffraction pattern consists of alternate dark and

bright bands of unequal widths. When we use white light, diffraction pattern is coloured.

Central maximum is white and the other bands are coloured.

In a single slit diffraction experiment,

For nth minimum: dsinθn = nλ n=1, 2, 3..

For nth secondary maxima: dsinθn= (2n+1) λ/2 n=1, 2, 3

Width of secondary maximum, β=Dλ/d

Width of central maximum, β0=2β=2λD/d

Intensity distribution curve for diffraction

19. The power or ability of an optical instrument to produce distinctly separate images of two closely

spaced objects is known as resolving power of the optical instrument.

20. Resolving power of a microscope is given by the relation: R.P= 1/d= 2µsinθ/1.22λ

21. Resolving power of a telescope is given by the relation: R.P= 1/θ= D/1.22λ.

22. The phenomenon of restricting the vibrations of light in a single plane is known as polarisation of

light. If the polarizer and analyzer are rotated with same angular velocity in the same direction, no

change in the intensity of transmitted light is observed.

23. A polaroid consists of long chain molecules aligned in a particular direction. The electric vectors

(associating with the propagating light wave) along the direction of the aligned molecules get

absorbed. Thus, if an unpolarised light wave is incident on such a polaroid then the light wave will get

linearly polarized with the electric vector oscillating along a direction perpendicular to the aligned

molecules, this direction is known as pass-axisofthepolaroid.

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24. According to Malus law, when a beam of plane polarized light is incident on the analyzer, the

intensity of transmitted light from the analyzer is directly proportional to the square of the cosine of

the angle θ between the planes of transmission of the polarizer and analyzer.

I=I0cos2θ

25. According to Brewster’s law, when unpolarised light is incident at polarizing angle on the interface

separating air from a medium of refractive index µ, the reflected light is fully polarized. µ= tan ip.

87

CONCEPT BASED EXERCISE

VSA QUESTIONS (1 Mark) 1. Light falls from glass to air. Find the angle of incidence for which the angle of deviation is 90°. 2. For the same angle of the incidence the angle of refraction in three media A, B and C are 15°,

25° and 35° respectively. In which medium would the velocity of light be minimum? 3. How does focal length of lens change when red light incident on it is replaced by violet light? 4. Why does violet colour deviate more than red in prism? 5. What is the phase difference between two points on a cylindrical wave front? 6. Show that maximum intensity in interference pattern is four times the intensity due to each slit

if amplitude of light emerging from slits is same. 7. How is a wave front different from a ray? Draw the geometrical shape of the wave fronts when.

(i) light diverges from a point source, (ii) light emerges out of convex lens when a point source is placed at its focus.

8. What two main changes in diffraction pattern of single slit will you observe when the monochromatic source of light is replaced by a source of white light?

9. What is the shape of the wave front on earth for sunlight? 10. Why is the diffraction of sound waves more evident in daily experience than that of light wave? 11. How can we differentiate between polarized and unpolarised light.

LEVEL – I 1. An object is placed at the principal focus of a concave lens of focal length f. Where will its image be formed? 2. A prism of angle 60° gives a minimum deviation of 30°. What is the refractive index of the material of the prism? 3. An equi-convex lens has refractive index 1.5. Write its focal length in terms of radius of curvature R. 4. Estimate the distance for which ray optics is good approximation for an aperture of 4mm and wavelength 400nm. 5. What is Brewster’s angle for air to glass transition? Refractive index of glass = 1.5. 6. In Young’s double slit experiment the slits are separated by 0.28mm and the screen is placed 1.4m away. The distance of 4th bright fringe is measured to be 1.2cm. Determine the wavelength of light used in this experiment. 7. An astronomical telescope uses two lenses of powers 10D and 1D. What is its magnifying power in normal adjustment? 8. Light of wavelength 500nm falls, from a distant source, on a slit 0.5mm wide. Find the distance between the two dark bands, on either side of the central bright band of the diffraction pattern observed, on a screen placed 2m from the slits. 9. An illuminated object and a screen are placed 90cm apart. Determine the focal length and nature of the lens required to produce a clear image on the screen, twice the size of the object. 10. The near vision of an average person is 25cm. To view an object with an angular magnification of 11. What should be the power of the microscope?

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LEVEL – II 1. A mirror is turned through 15°. Through what angle will the reflected ray turn? 2. Velocity of light in a liquid is 1.5 x 10 8 m/s and in air, it is 3 x 10 8 m/s. If a ray of light passes from liquid into the air, calculate the value of critical angle. 3. Why does a convex lens of glass of refractive index 1.5 behave as a diverging lens when immersed in carbon disulphide of refractive index 1.65? 4. In Young’s double slit experiment, light waves of wavelength 5.4 x 10 -7 m and 6.85 x 10 -8 m are used in turn keeping the same geometry. Compare the fringe width in the two cases. 5. If the two slits in Young’s experiment have width ratio 1:4, deduce the ratio of intensity at maxima and minima in the interference pattern. 6.Figure shows a cross-section of a ‘light pipe’ made of a glass fibre of refractive index 1.68. The outer covering of the pipe is made of a material of refractive index 1.44. What is the range of the angles of incident rays with the axis of the pipe for which total reflections inside the pipe take place as shown. (3)

7.Three identical Polaroid sheets P1, P2 and P3 are oriented so that the (pass) axis of P2 and P3 are at angles of 60° and 90° respectively, with respect to the pass axis of P1. A monochromatic source, S, of intensity Io , is kept in front of the Polaroid sheet P1. Find the intensity of this light, as observed by observers O1 , O2 and O3 , positioned as shown below

. 8.Light of wavelength λ1 propagates from medium 1 incident at angle θ1. The angle inside medium 2 is θ2 . What is its wavelength in medium 2?

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9. A few coloured fringes, around a central white region, are observed on the screen when the source of monochromatic light is replaced by white light in Young’s double slit experiment. Give reason. 10. Light from two sources has intensity ratio 1:9 and is monochromatic. The light is made to superpose. What will be the resultant intensity obtained if the sources are (i) incoherent & (ii) coherent?

ENRICHMENT EXCERCISE 1. Show that a concave lens always produces a virtual image, irrespective of the position of the

object. 2. Calculate the critical angle for glass air surface, if a ray falling on the surface from air, suffers a

deviation of 150 when the angle of incidence is 400. 3. Three rays of light red (R) green (G) and blue (B) are incident on the surface of a right angled

prism as shown in figure. The refractive indices for the material of the prism for red green and blue are 1.39, 1.43 and 1.47 respectively. Trace the path of the rays through the prism. How will the situation change if the rays were falling normally on one of the faces of an equilateral prism?

.

4. How does the ‘resolving power’ of an astronomical telescope get affected on (i) Increasing the aperture of the objective lens? (ii) Increasing the wavelength of the light used

5.Complete the ray diagram in the following figure where, n1, is refractive index of medium and n2 is refractive index of material of lens.

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6.Using the data given below, state which two of the given lenses will be preferred to construct a (i) telescope (ii) Microscope. Also indicate which is to be used as objective and as eyepiece in each case.

1. The critical angle of incidence in a glass slab placed in air is 450. What will be the critical angle when it is immersed in water of refractive index 1.33?

2. A convex lens of focal length 0.2m and made of glass of refractive index 1.5 is immersed in water of refractive index 1.33. Find the change in focal length of the lens.

3. A compound microscope uses an objective lens of focal length 4cm and eye lens of focal length 10cm. An object is placed at 6cm from the objective lens. (a) Calculate the magnifying power of the compound microscope, if the final image is formed at the near point. (ii) Calculate the length of the compound microscope also.

4. A telescope objective has a focal length of 100cm. when the final image is formed at the least distance of distinct vision, the distance between the lenses is 105cm. Calculate the focal length of the eyepiece and the magnifying power of the telescope.

5. The magnifying power of an astronomical telescope in the normal adjustment position is 100. The distance between the objective and the eyepiece is 101 cm. Calculate the focal lengths of the objective and of the eye-piece.

6. Complete the path of light with correct value of angle of emergence.

7. If the angle between the pass axis of polarizer and the analyser is 450, write the ratio of

intensities of original light and the transmitted light after passing through the analyser.

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8. In Young’s double-slit experiment a monochromatic light of wavelength λ, is used. The intensity of light at a point on the screen where path difference is λ is estimated as K units. What is the intensity of light at a point where path difference is λ /3?

9. Why does the intensity of the secondary maximum become less as compared to the central maximum in diffraction pattern?

10. What is meant by coherent sources of light? Can two identical and independent sodium lamps act as coherent sources? Give reason for your answer.

11. How does the resolving power of a compound microscope change, when (i) refractive index of the medium between the object and objective lens increases, and (ii) wavelength of the radiation used is increased?

12. Two narrow slits are illuminated by a single monochromatic source. Name the pattern obtained on the screen. One of the slits is now completely covered. What is the name of the pattern now obtained on the screen? Draw intensity pattern obtained in the two cases. Also write two differences between the patterns obtained in the above two cases.

13. How is the width of central maxima affected on increasing the (i) Wavelength of light used (ii) width of the slit? What happens to the width of the central maxima if the whole apparatus is immersed in water and why?

14. Give an example of interference of light in everyday life. In Young’s double slit experiment, the two slits are 0.03 cm apart and the screen is 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.

15. Draw a graph showing the variation of intensity versus the position on the screen in Young’s experiment when (a) both the slits are opened and (b) one of the slit is closed. What is the effect on the interference pattern in Young’s double slit experiment when: (i) Screen is moved closer to the plane of slits? (ii)Separation between two slits is increased. Explain your answer in each case. .

16. In young’s experiment, the width of the fringes obtained with light of wavelength 6000Å is 2mm. Calculate the fringe width if the entire apparatus is immersed in a liquid medium of refractive index 1.33

17. In young’s double slit experiment, two slits are separated by 3mm distance and illuminated by light of wavelength 480nm. The screen is 2m from the plane of the slits. Calculate the separation between the 8th bright fringe and the 3rd dark fringe observed with respect to the central bright fringe.

18. Two coherent sources have intensities in the ratio 25:16. Find the ratio of the intensities of maxima to minima, after the interference of light occurs.

19. Determine the angular separation between central maximum and first order maximum of the diffraction pattern due to a single slit of width 0.25nm when light of wavelength 5890Å incident on it normally.

20. A beam of light consisting of two wavelengths,650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment.(a)Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm.(b)What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?

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21. . In Young’s double slit experiment, using light of wavelength 400 nm, interference fringes of width ‘X’ are obtained. The wavelength of light is increased to 600 nm and the separation between the slits is halved. In order to maintain same fringe with, by what distance the screen is to be moved? Find the ration of the distance of the screen in the above two cases.

22. Two Sources of Intensity I and 4I are used in an interference experiment. Find the intensity at points where the waves from two sources superimpose with a phase difference (i) zero (ii) π/2 (iii) π.

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MCQ Questions

1.The velocity of light is maximum in a medium of________________. (A) diamond (B) water (C) glass (D) vaccum 2. A light of wavelength 320 nm enters in a medium of refractive index 1.6 from the air of refractive index1.0 The new wavelength of light in the medium will be____________nm. (A) 520 (B) 400 (C) 320 (D) 220 3. "Bhautik" runs towards a plane mirror with a speed of 20 ms–1 , what is the speed of his image ?

(A) 45 ms–1 (B) 20 ms–1 (C) 15 ms–1 (D) 7.5 ms–1

4.A convex lens is made up of three diffrent materials as shown in figure, for point object placed on its axis, the no. of imges formed are__________. (A) 4 (B) 2 (C) 3 (D) 1

5.If thin prism of 5degree gives a deviation of 2degree then the refractive index of material of prism is_________. (A) 1.4 (B) 1.5 (C) 1.6 (D) 1.0 (6). It is difficult to see through the fog because _________________ (A) light is scattered by the droplets in the fog. (B) fog absorbs light. (C) refractive index of fog is infinity. (D) light suffers total internal refection.

7.Read the following questions and choose if________________.

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(A) both assertion and reason are true and the reason is correct explanation of the assertion. (B) both assertion and reason are true but reason do not explain the assertion. (C) Assertion is true but the reason are false. (D) both assertion and reason are false. (1) Assertion : Focal length of a lens for red colour is smaller than its focal length for violet colour Reason : is because nr is greater than nV (A) B (B) A (C) C (D) D

8.In which of the following cases a man will not see image greater than himself. (A) convex mirror (B) concave mirror (C) plane mirror (D) none of these 9. A glass slab n =1.5 cm of thickness 9 cm is placed over a written paper what is the Shift in the latter ? (A) 6 cm (B) 3 cm (C) 2 cm (D) 0 cm 10.A concave mirror of focal length 20 cm forms an virtual image having twice the linear dimensions of the object, the position of the object will be ___________cm

(A) 7.5 (B) –10 (C) 10 (D) –7.5

11.A double convex lens made of glass of refractive index 1.6 has radius of curvature 15 cm each. The focal length of this lens when immersed in a fluid of refractive index 1.63 is____________.

(A) –40.75 (B) –407.5 (C) –125 (D) 12.5 12.A prism of glass is shown in figure A, ray incident normally on one face is totally reflected. If θ is equal to 45 , the index of refraction of glass is_____________.

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13.The magnifying power of objective of a compound microscope is 5.0 If the magnifying power of microscope is 30, then magnifying power of eye–piece will be_________.

(A) 3 (B) 6 (C) 9 (D) 12

14.The effective focal length of the lens combination shown in the curved surface of the plano convex lenses are 12 cm each and refractive index of the material of the lens is 1.5. the refractive index of liquid is________. (A) 1.33 (B) 1.42 (C) 1.53 (D) 1.60

15.The distance between the first and sixth minima in the diffraction pattern of a single slit, it is 0.5 mm.The screen is 0.5 m away from the Slit. If the wavelength of light is 5000 A0 , then the width of the slit will be_______________mm

(A) 5 (B) 2.5 (C) 1.25 (D) 1.0 16. ____________change in the polarization phenomena of light ? (A) intensity (B) wavelength (C) phase (D) frequency

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CHAPTER-11

DUAL NATURE OF MATTER AND RADIATION

SYNOPSIS

1. A certain minimum amount of energy is required for an electron to be pulled out from the

surface of a metal. This minimum energy is called the work function of that metal. Unit of work

function is eV.

1eV is the kinetic energy gained by an electron when it is accelerated through a potential

difference of 1 volt.

2. When light of suitable frequency illuminates the metal surface, electrons are emitted. This

process of ejection of electrons using light is known as photoelectric emission.

The number of photoelectrons emitted per second is directly proportional to the

intensity of incident radiation.

The minimum frequency of the incident light below which photoelectrons are not

ejected from the metal surface is known as threshold frequency ν0.

The minimum negative potential given to the metal plate with respect to the collector

at which the photoelectrons become zero is known as stopping potential or cut off

potential.

The stopping potential Vo depends on i) The frequency of incident light and ii) the nature of emitter material. For a given frequency of incident light, the stopping potential is independent of its intensity. eVo =(1/2)mv2= Kmax

The maximum kinetic energy of the ejected electrons is independent of the intensity of

incident radiation but depends upon the frequency of the incident radiation.

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3. EINSTEIN’S PHOTO ELECTRIC EQUATION: ENERGY QUANTUM OF RADIATION

Light is composed of discrete packets of energy called quanta or photons.

The energy carried by each photon is E = hν, where ν is the frequency and momentum p= h/λ. The energy of the photon depends on the frequency γ of the incident light and not on its intensity.

Photo electric emission from the metal surface occurs due to absorption of a photon by an electron

Einstein’s photo electric equation: Kmax = hν – φ0 or eV0 = hν - φ0.

4. PARTICLE NATURE OF LIGHT: THE PHOTON

Radiation has dual nature: wave and particle. The wave nature is revealed in phenomenon like interference, diffraction and polarization. The particle nature is revealed by the phenomenon photo electric effect.

By symmetry, matter also should have dual nature: wave and particle. The waves associated with the moving material particle are called matter waves or De Broglie waves.

The De Broglie wave length (λ) associated with the moving particle is related to its moment p as: λ =h/p = h/mv

De Broglie wavelength of an electron accelerated through a potential V. Consider an electron with mass ‘m’ and charge ‘e’ accelerated from rest through a potential V.

KE = eV

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K = 1/2mv2 = p2/2m

P2 = 2mK

P = √2mK = √2meV

λ = h/ √2meV

Substituting numerical values of h, m and e

.

5. PHOTOELECRTIC EFFECT COULD NOT BE EXPLAINED ON THE BASIS OF WAVE THEORY.

CONCEPT BASED EXERCISE

VSA Questions (1 MARK)

1. What is the rest mass of photon? 2. Name the phenomenon which shows quantum nature of electromagnetic radiation. 3. .What is the de-Broglie wavelength of a neutron at absolute temperature T K ?

4.The work function of the following metal is given Na = 2.75 eV, K = 2.3eV, Mo = 4.14 eV, Ni = 5.15 eV which of these metal will not give a photoelectric emission for radiation of wave length 3300 Ao from a laser source placed at 1m away from the metal. What happens if the laser is brought nearer and placed 50 cm away. 5.Which of the following radiations is more effective for electron emission from the surface of sodium?(i) Microwave(ii) Infrared(iii) Ultraviolet. 6.Name any two phenomena which show the particle nature of radiation. 7.The photoelectric cut off voltage in a certain photoelectric experiment is 1.5V. What is the max kinetic energy of photoelectrons emitted? 8.What is the de-Broglie wavelength of a 3 kg object moving with a speed of 2m/s? 9.Work functions of Caesium and lead are 2.14 eV and 4.25 eV respectively. Which of the two has a higher threshold wavelength? 10.Do all the photons have same dynamic mass? If not, why? 11. Why photoelectrons ejected from a metal surface have different kinetic energies although the frequency of incident photons are same? 12. If the frequency of incident light in photoelectric experiment is doubled then does the stopping potential become double or more than double, justify?

λ = (1.227/√𝑉) nm

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NUMERICALS

Level-I:- Numerical direct formula based (1 mark, 2 mark)

1. If the maximum kinetic energy of electrons emitted by a photocell is 4ev.What is the Stopping potential? 2. What is the energy associated in joules with a photon of wavelength 4000A0? 3. The photoelectric cut-off voltage in a certain experiment is 1.5V.What is the maximum Kinetic energy? 4. Calculate the work function of a metal in eV.If its threshold wavelength is 6800A0? 5. What is the momentum of a photon of energy 120 MeV? 6. What is the de-Broglie wavelength (in A0) associated with an electron accelerated through a Potential of 100V? 7.Calculate the ratio of de-Broglie wavelength associated with a deuteron moving with velocity 2V and an alpha particle moving with velocity V? 8. The work function of cesium metal is 2.14eV.When light of frequency 6 X 1014 Hz is incident on the metal surface, photoemission of electrons occurs. What is the (a) Maximum kinetic energy of the emitted electron and (b) Stopping potential of the emitted photoelectron? 9.In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is found to be 4.12 X 10-15Vs.Calculate the value of Planck’s constant. 80 10.The threshold frequency for a certain metal is 3.3 X1014Hz is incident on the metal; Predicts the cut-off voltage for photoelectric emission.

LEVEL-I 1.An electron and an alpha particle have same kinetic energy. Which of these particles has the shortest de- Broglie wavelength? 2.The de Broglie wavelength of an electron is 1 A0. Find the velocity of the electron. 3.Determine the accelerating potential required for an electron to have a de-Broglie wavelength of 1 Å 4.An electron, an alpha particle and a proton have the same kinetic energy, which one of these particles has (i) the shortest and (ii) the largest, de, Broglie wavelength? 5.In an experiment on photo electric emission , following observations were made; ( i ) wave length of incident light = 1.98 x 10-7m ( ii ) stopping potential = 2.5 V. Find ( a ) kinetic energy of photo electrons with maximum speed ( b ) work function & ( c ) threshold frequency 6. Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser. The power emitted is 9.42 mW. (a) Find the energy and momentum of each photon in the light beam, (b) How many photons per second, on the average, arrive at a target irradiated by this beam? (Assume the beam to have uniform cross-section which is less than the target area), and

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(c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon? 7. 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. 8. The threshold frequency for a certain metal is 3.3 × 1014 Hz. If light of frequency 8.2 × 1014 Hz is incident on the metal, predict the cutoff voltage for the photoelectric emission. 9. The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm? 10. Light of wavelength 488 nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is 0.38 V. Find the work function of the material from which the emitter is made.

LEVEL -3 LEVEL-III:- 10 numericals challenging/difficulty level ( 1 mark, 2 marks, 3marks) 1. A radio transmitter operates at a frequency of 880 KHz and a power of 1KW.Find the Number of photons emitted per second. 2 A blue lamp mainly emits light of wavelength 4500 A0. The lamp is rated at 150 W and 8% of the energy is emitted as visible light. How many photons are emitted by the lamp per second? 3 Calculate the de-broglie wavelength of a proton of a momentum 2.55 X 10-22 Kgms-1 ? 4The work function of Cesium is 2.14 eV.Find (a) the threshold frequency for Cesium, and (b) the wavelength of the incident light if the photocurrent is brought to zero by a stopping potential of 0.60eV? 5 If the photoelectrons are to be emitted from a potassium surface with a speed of 6 X 106 ms-1.What frequency of radiation must be used? (Threshold frequency for potassium is 4.22 X 1014 Hz, h= 6.6 X10-34 Js and me = 9.1 X 10-31 kg ) 6.A sheet of silver is illuminated by monochromatic ultraviolet light of wavelength = 1810 A0. What is the maximum energy of the emitted electron? Threshold wavelength of of silver is 2640 A0.

7.By how much would be stopping potential for a given photosensitive surface go up if the frequency of the incident radiation were to be increased from 4 X1015 Hz to 8 X 1015? Given h= 6.6 X10-34 Js, e = 1.6 X 10-19 C and c = 3 X 108 ms-1? 8.The photosensitive threshold wavelength for a metal is 10000 A0.When light of wavelength 5461 A0 is incident on it, the retarding potential in Millikan’s experiment is 1.02 Calculate the value of Planck’s constant? 9.When light of wavelength 400 nm is incident on the cathode of a photocell, the stopping recorded is 6V.If the wave of the incident light is increased to 600nm.Calculate the new stopping potential? 10 The two identical photocathodes receive light of frequencies f1 and f2.If the velocity of the photoelectron (of mass m) coming out are respectively v1 and v2 , then show that 𝑣12 - 𝑣22 = 2ℎ/𝑚 (f1-f2).

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ENRICHMENT EXERCISE

1.In a photoelectric effect experiment, the graph between the stopping potential V and frequency of the incident radiation on two different metals P and Q are shown in Fig. (i) Which of the two metals has greater value of work function? (ii) Find maximum K.E. of electron emitted by light of frequency ᴠ = 8 × 1014 Hz for metal P.

2.Find the ratio of de-Broglie wavelengths associated with two electrons ‘A’ and ‘B’ which are accelerated through 8V and 64 volts respectively. 3.If kinetic energy of thermal neutron is 3/ 2kT then show that de-Broglie wavelength of waves

associated with a thermal neutron of mass m at temperature T kelvin is h/√(3mkT )where k is boltzmann constant. 4.X-rays of wave length λ fall on a photo sensitive surface emitting electrons. Assuming that the work function of the surface can be neglected, prove that the de-Broglie wavelength of electrons emitted will be

5.A metal surface illuminated by 8.5 × 1014 Hz light emits electrons whose maximum energy is 0.52 eV the same surface is illuminated by 12.0 × 1014 Hz light emits elections whose maximum energy is 1.97eV. From these data find work function of the surface and value of Planck’s constant. 5.How does the value of work function influence the kinetic energy of electrons liberated during photoelectric emission? 6.Red light, however bright, cannot cause emission of electrons from a clean zinc surface. But, even weak ultraviolet radiations can do so. Why? 7An electron and a proton have same kinetic energy. Which of the two has a greater wavelength? Explain. 8.Draw the variation of maximum kinetic energy of emitted electrons with frequency of the incident radiation on a photosensitive surface. On the graph drawn, what do the following indicate: (i) slope of the graph & (ii) intercept on the energy axis.

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9.Draw the graph showing the variation of photoelectric current with anode potential of a photocell for (i) the same frequency but different intensities I3>I2>I1 of incident radiation and (ii) the same intensity but different frequencies ν1>ν2>ν3 of incident radiation 10 .A particle of mass M at rest decays into two particles of masses m1 and m2 having velocities V1 and

V2 respectively. Find the ratio of de-broglie Wavelengths of the two particles.

11.A proton is accelerated through a potential difference V. Find the percentage increase or decrease in

its De- Broglie wavelength if potential difference is increased by 21%.

12.For what Kinetic energy of a neutron will the associated de Broglie wavelength be 5.6 × 10–10m?

MIND MAP(Source: Internet)

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MCQ QUESTIONS For the answer of the following questions choose the correct alternative from among the given ones. 1.When electric bulb having 100 W efficiency emits photon having wavelength 410 mm every second, numbers of photons will be......

2.Work function of a body is 4.0 eV. For emission of photoelectron from body, maximum wavelength of light = .......... (A) 540 nm (B) 400 nm (C) 310 nm (D) 220 nm 3. A body of mass 200 g moves at the speed of 5 m/hr. So de-Broglie wavelength related to it is of the

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order

6. According to Einstein's photoelectric equation, graph of kinetic energy of emitted photo electrons from metal versus frequency of incident radiation is linear. Its slope............. (A) depends on type of metal used (B) depends on intensity of radiation (C) depends on both metal used and intensity of radiation. (D) is same for all metals and free from intensity of radiation. 7. Photocell cell is enlightened by small bright source 1 m away. If the same light source is placed0.5 m away, number of electrons emitted by cathode will be............

(A) increases twice (B) decreases twice (C) increases 4 times (D) decreases 4 times

8.Energy corresponding to threshold frequency of metal is 6.2 eV. If stopping potential corresponding to radiation incident on surface is 5V, incident radiation will be in the.....region.

(A) X-ray (B) Ultraviolet (C) infrared (D) Visible

9.If intensity of incident light is increased,.........of photo electrons will increase. (A) number (B) Frequency (C) energy (D) wavelength 10. A photon having energy 5.5 eV is incident on metal surface and emits photo electrons having maximum kinetic energy 0.4 eV. Then stopping potential of this electron is.................. (A) 5.5 eV (B) 5.1 eV (C) 5.9 eV (D) 4.0 eV

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CHAPTER- 12 & 13

ATOMS & NUCLEI

SYNOPSIS

Thomson’s model of atom- Every atom consists of fuels charged sphere in which electrons are embedded like seeds in water melon.

Its drawbacks: couldn’t explain large angle scattering & the origin of spectral series.

Rutherford’s model of atom- i) Every atom consists of a tiny central core, called the atomic nucleus, in which the entire positive charge and almost entire mass of the atom are concentrated. ii) The size of nucleus is of the order of 10-15m , which is very small as compared to the size of the atom which is of the order of 10-10m. iii)The atomic nucleus is surrounded by certain number of electrons. As atom on the whole is electrically neutral, the total negative charge of electrons surrounding the nucleus is equal to total positive charge on the nucleus. iv)These electrons revolve around the nucleus in various circular orbits as do the planets around the aun. The centripetal force required by electron for revolution is provided by the electrostatic force of attraction between the electrons and the nucleus.

Limitations: couldn’t explain the stability of the nucleus & the emission of line spectra of fixed frequencies.

Distance of closest approach of the alpha particle in the α particle scattering experiment

r0 = 2kZe2 1/2mv2

Impact parameter of the alpha particle (It is the perpendicular distance between the initial velocity

b = kZe2cotθ/2 1/2mv2

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vector of the alpha-particle from a central line passing through the centre of nucleus when the alpha particle is far away from the nucleus)

Bohr’s model of atom

Limitations-applicable only for hydrogen like atoms & couldn’t explain the splitting of spectral lines. (not consider electro static force among the electrons)

Orbit radius of the electron around the nucleus

r = e2/4πЄ0mv2, v = 2πke2/nh, r = n2h2mke2

Energy of the electron in the nth orbit of hydrogen atom

En= -me4/8Є02n2h2 = -13.6/n2eV

E=-2.18*10-18 J / n2

Angular momentum of electron in any orbit is integral multiple of h/2π

L = mvr = nh/2π, n=1,2,3,…

• Wave number ν

1/λ = R(1/n12 – 1/n2

2) R=1.097 * 10+7m-1

Atomic Number (Z) No of protons in a nucleus

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Mass Number (A) Number of neutrons

No. of nucleons(protons + neutrons) in a nucleus A-Z

Nuclear radius R=R0 A1/3

Nuclear density ρ= 3m/4πR0

3

The density of nuclear matter is independent of the size of the nucleus.

Isotopes Same Z & different A Ex, 1H2,1H3,1h1, & C12,C14,C16

Isobars Same A & different Z [ 18Ar40,20Co40] & (1H3, 2H3)

Isotones Mass defect∆𝑚

Same no. of neutrons Mass of neutrons – 1H3, 2He4

Binding energy Eb E= ∆mc2 (∆m= mass of reactants – mass of products) 1 a.m.u.= 931.5 Mev

Radioactive decay law dN/dt=-λN -dN/dt= R is known as activity. Its unit isBq.

No: of nuclei remaining un-decayed at any instant of time

N =N0e-λt

OR

N=N0( ½)n , n = t/T1/2

Half-life (T1/2)

T1/2=0.693 Λ The half-life of a radionuclide is the time in which N has been reduced to half of its initial value.

Mean life (τ) τ= 1/λ The mean-life is the time at which N has been reduced to 1/e of its initial value.

3 types of radiations Alpha,beta,gamma

Nuclear fissio

Splitting of a heavy nucleus into lighter elements.This process is made use of in Nuclear reactor & Atom bomb Nuclear Reactor is based upon controlled

nuclear chain reaction. It consists of:

1) Nuclear fuel

2) modulator

3) control rods

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4) coolant

5) shielding

Nuclear fusion

Fusing of lighter nuclei to form a heavy nucleus.This process takes place in Stars & Hydrogen bomb. Controlled Thermonuclear Fusion

In a fusion reactor-

a) high particle density is required

b) high plasma temperature of 109K

c) a long confinement time is required

Radioactivity is the phenomenon in which nuclei of a given species transform by giving out α or

β or γ rays.

Α-rays are Helium nuclei, β-rays are electrons and γ-rays are electromagnetic radiation of

wavelength shorter than X-rays.

Alpha decay:

Q= (mx-mY-mHe)c2, the difference between the initial mass energy and final mas energy is called

Q-value of the process or disintegration energy. This energy is shared by the daughter nucleus

and the alpha p[article in the form of kinetic energy.

Beta decay:

In beta-decay either an electron or a positron is emitted by a nucleus along with a antineutrino

or neutrino respectively. The emitted particles share the disintegration energy. The electrons/

positrons emitted in beta decay have a continuous spectrum of energies from zero to a limit

Kmax.

(β decay)

(β+ decay)

Gamma dacay:

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Gamma decay usually follows and alpha or beta decay. A nucleus may left in an excited state

after alpha or beta emission. The excited nucleus goes to a lower state by emitting a gamma

photon. This shows that nuclei also have discrete energy levels that atoms have.

Binding Energy Curve

The nuclei with high BE/nucleon are very tightly bound i.e. a great amount of energy per

nucleon is required to break apart.

The BE per nucleon is practically constant for mass numbers 30<A<170. The curve has a

maximum value 8.75MeV for A=56.

The nuclei with lower BE/nucleon are on the left and right sides are less tightly bound and less

energy per nucleon would be required to break them apart.

Heavy nuclei undergo fission i.e. break into two lighter nuclei (with greater BE/nucleon). Energy

would be released in such process. For eg: Energy produced in Nuclear reactor

Lighter nuclei fuse together to form a heavy nucleus (with greater BE/nucleon). Energy would

be released in such process. For eg: occurs naturally in star

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CONCEPT BASED EXERCISES

VSA Questions (1Mark) 1. Name the series of hydrogen spectrum which has least wavelength. 2. An electron jumps from fourth to first orbit in an atom. How many spectral lines can be emitted

by the atom? 3. In Bohr’s atomic model, the potential energy is negative and has a magnitude greater than the

kinetic energy, what does this imply? 4. In the ground state of hydrogen atom orbital radius is 5.3 × 10–11 m. The atom is excited such

that atomic radius becomes 21.2 × 10–11 m. What is the principal quantum number of the excited state of atom? (n=2)

5. What is the ratio of nuclear densities of the two nuclei having mass numbers in the ratio 1: 4? 6. Why is the energy distribution of β-decay continuous? 7. Binding energies of neutron 2 1 H and -particle (2He4) are 1.25 MeV/nucleon and 7.2

MeV/nucleon respectively. Which nucleus is more stable? 8.Why does only a slow neutron (.03eV energy) cause the fission in the uranium nucleus and not the fast one? 9. Name the spectral series of hydrogen atom which lie in uv region. 10.The half life of a radioactive element A is same as the mean life time of another radioactive element B. Initially, both have same number of atoms.B decay faster than A. Why? 11.An -particle of kinetic energy ‘K’ is bombarded on a thin gold foil. The distance of the closet approach is ‘r’.What will be the distance of closest approach for an -particle of double the kinetic energy?

LEVEL –I 1.What is the ratio of the radii of orbits corresponding to first excited state and ground state in hydrogen atom? 2. What is the impact parameter for scattering of α- particle by1800? 3. Two nuclei have mass numbers in the ratio 1: 8. Find the ratio of their nuclear radii and nuclear densities. 4. What is the ground state energy of electron in case of 3Li 7 ? 5. Find the energy equivalent of 1amu in MeV. 6.Find first excitation energy and excitation potential of hydrogen atom. 7.Find ionisation energyand ionisation potential of hydrogen atom. 8. Tritium has half-life of 12.5 years against β decay. What fraction of the sample will remain undecayed after 25 years ? 9. What is the relation between decay constant and half-life of radioactiveelement? 10. Name the series of hydrogen spectrum which lies in visible part of the spectrum.

LEVEL –II 1. With the help of an example explain how the neutron to proton ratio changes during α – decay of nucleus.

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2. A radioactive isotope has half-life of 5 years after how much time is its activity reduces to 3.125% of its original activity? 97

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3. A heavy nucleus X of mass number 240 and binding energy per nucleon 7.6 MeV is split into two fragments Y and Z of mass numbers 110 and 130. The binding energy of nucleons in Y and Z is 8.5 MeV per nucleon. Calculate the energy Q released per fission in MeV. 4. The ground state energy of hydrogen atom is -13.6eV.What is the K.E& P.E of the electron in this state? 5. Select the pairs of isotopes & isotones from the following: i. 6C13 ii. 7N14 iii. 15P30 iv. 15P31 6 .At a given instant there are 25% un-decayed radioactive nuclei in a sample. After 10 seconds the number of un-decayed nuclei reduces to 12.5 %.calculate the i) mean life of the nuclei ii) the time in which the number of the un-decayed nuclei will further reduce to 6.25 % of the reduced number. 7. A radioactive nucleus ‘A’ decays as given below:

If the mass number & atomic number of A1 are 180 & 73 respectively, find the mass number & atomic number of A &A2 8. For an electron in the second orbit of hydrogen atom , what is the moment of linear momentum as per the Bohr’s model? 9. An alpha particle of energy 5 MeV is scattered through 1800 at a target ofuranium nucleus. What is the order of the distance of the closest approach? 10. By what factor must the mass number change for the nuclear radius to become twice?

LEVEL II

1.The total energy of an electron in the first excited state of the hydrogen atom is about –3.4 eV. What is (a) the kinetic energy, (b) the potential energy of the electron? (c) Which of the answers above would change if the choice of the zero of potential energy in changed to (i) + 0.5 eV (ii) –0.5 eV 2.Write two characteristic features of nuclear forces which distinguish them from Coulomb force. 3Using the graph of Potential energy of a pair of nucleons v/s separation between them, explain why (i) force is strongly repulsive for separation between nucleons less than ro, (ii) attractive for r> ro. 4.State Bohr’s postulate for the ‘permitted orbits’ for the electron in a Hydrogen atom. Use this postulate to prove that the circumference of the nth permitted orbit for the electron can contain exactly ‘n’ wavelengths of the de-broglie wavelength associated with the electron in that orbit.

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5.The wavelength of the second line of the Balmer series in H-atom is 1481Å. Calculate the wavelength of the first line. (6562Å) 6.Find the binding energy and binding energy per nucleon of nucleus 83B209. Given: mass of proton = 1.0078254 u. mass of neutron = 1.008665 u. Mass of 83Bi209 = 208.980388u. [1639.38 MeV and 7.84 MeV/Nucleon]. 7.Find the maximum energy that β-particle may have in the following decay :

8.The half-life of a radioactive substance s 50s. Calculate: (i) the decay constant, (ii) time taken for the sample to decay by 3/4th of the initial value. 9.The decay constant for a radionuclide, has a value of 1.386day-1. After how much time will a given sample of this radionuclide get reduced to only 6.25% of its present number?

ENRICHMENT EXERCISES

1.The activity R of an unknown radioactive nuclide is measured at hourly intervals. The results found

are tabulated as shown. (i)Plot the graph of R versus t and calculate half-life from the graph. (ii) Plot

the graph of ln(R/Ro) versus t and obtain the value of half-life from the graph. (λ = 1.05hours)

2.The atom 8O16 has 8 protons, 8 neutrons and 8 electrons while atom 4Be8 has 4 proton, 4 neutrons and 4 electrons, yet the ratio of their atomic masses is not exactly 2. Why? 3.What is the effect on neutron to proton ratio in a nucleus when – particle is emitted? Explain your answer with the help of a suitable nuclear reaction. 4.Why must heavy stable nucleus contain more neutrons than protons? 5.At a given instant, there are 25% undecayed radioactive nuclei in a sample.After 10 seconds, the number of undecayed nuclei reduces to 12.5%. Calculate the mean life of nuclei.

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6. Half life of certain radioactive nuclei is 3 days and its activity is 8 times the ‘safe limit’. After how much time will the activity of the radioactive sample reach the ‘safe limit’? 7. The energy levels of an atom are as shown below. a) Which of them will result in the transition of a photon of wavelength 275 nm? b) Which transition corresponds to the emission of radiation maximum wavelength

8.What is the power output of 𝑈92235 reactor if it takes 30 days to use up 2 kg of fuel and if each

fission gives 185 MeV of usable energy?

MIND MAPS

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MCQ

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For the answer of the following questions choose the correct alternative from the given ones.

(2)Read the following question and choose correct Answer form given below. (A) Both assertion and reason are true. Reason is the correct explanation of the Assertion (B) Both assertion and reason are true. Reason is not correct explanation of the assertion (C) Assertion is true but reason is false. (D) Both Assertion and Reason are false (i) Assertion :- In a radio-active disintegration, an election is emitted by nucleus. Reason :- electron are always Present in-side the nucleus. (ii) Assertion :- An election and Positon can annihilate each other creating Photon Reason:- Electron and Positon form a Particle and anti-Particle. (iii) Assertion:- An isolated radioactive atom may not decay at all what ever be its half time Reason:- Radioactive decay is a statistical Phenomenon. (iv) Assertion: - Fragment Produced in the fission of u235 are active Reason:- The fragments have abnormally high Proton to neutron ratio

(3) A radioative sample has no active atom at t=o, at the rate of disintegration at any time is R and the number of atom is N, then ratioR/N varies with time

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(7) Number of spectral lines in hydrogen atom is. (A) 6 (B) 8 (C) 15 (D) infinity

It the radius of a nucleus of mass number 3 is R. then the radius of a nucleus of mass number 81 is

(A) 27 R (B) 9 R (C) 3 R (D)

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10. which of the following series in the spectrum of hydrogen atom lies in the visible region of the electro magnetic spectrum? (A) Paschen (B) Lyman (C) Brakett (D) Balmer (11) If 13.6 eV energy is required to ionize the hydrogen atom the energy required to remove the electron form n=2 state is

(A) Zero (B) 10.2 eV (C) 6.8 eV (D) 3.4 eV

CHAPTER-14

ELECTRONIC DEVICES

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SYNOPSIS

1. Solids whose resistivity or conductivity is intermediate to that of conductors and insulators are

known as semiconductors.

2. The collection of closely spaced energy levels is known as energy band. (i) In metals, the

conduction band is either partially filled or overlaps the valence band (Eg ≅ 1𝑒𝑉) . (ii) In

insulators, the valence band is completely filled, the conduction band is empty and the forbidden

band is quite large (Eg>3eV), (iii) Insemiconductors, the valence band is completely filled,

conduction band is empty and the forbidden energy gap between the valence and conduction

band is less compared to insulators. (Eg<3eV).

Energy band diagrams:

3. At 0K, a semiconductor behaves as an insulator.

4. Distinction between Intrinsic and Extrinsic Semiconductor

Intrinsic Extrinsic

1 It is pure semiconducting material and no impurity atoms are added to it

1 It is prepared by doping a small quantity of impurity atoms to the pure semiconducting material.

2 Examples are crystalline forms of pure silicon and germanium.

2 Examples are silicon and germanium crystals with impurity atoms of arsenic, antimony, phosphorous etc. or indium, boron, aluminum etc.

3 The number of free electron in conduction band and the number of holes in valence band is exactly equal and very small indeed.

3 The number of free electrons and holes is never equal. There is excess of electrons in n-type semiconductors and excess of holes in p-type semiconductors.

4 Its electrical conductivity is low 4 Its electrical conductivity is high.

5 Its electrical conductivity is a function of temperature alone.

5 Its electrical conductivity depends upon the temperature as well as on the quantity of impurity atoms doped in the structure.

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Distinction between n-type and p-type semiconductors

n-type semiconductors p-type semiconductors

1 It is an extrinsic semiconductors which is obtained by doping the impurity atoms of Vth group of periodic table to the pure germanium or silicon semiconductor.

1 It is an intrinsic semiconductors which is obtained by doping the impurity atoms of III group of periodic table to the pure germanium or silicon semiconductor.

2 The impurity atoms added, provide extra electrons in the structure, and are called donor atoms.

2 The impurity atoms added, create vacancies of electrons (i.e. holes) in the structure and are called acceptor atoms.

3 The electrons are majority carriers and holes are minority carriers.

3 The holes are majority carriers and electrons are minority carriers.

4 The electron density (ne) is much greater than the hole density (nh)i.e. ne>>(nh)

4 The hole density (ne) is much greater than the electron density (nh)i.e. nh>> ne

5 The donor energy level is close to the conduction band and far away from valence band.

5 The acceptor energy level is close to valence band and is far away from the conduction band.

5. The process of addition of impurity atoms to an intrinsic semiconductor to increase its

conductivity is known as doping.

6. P-N junction diode

Two important processes occur during the formation of p-n junction diffusion and drift. The

motion of majority charge carriers give rise to diffusion current. Due to the space charge on n-

side junction and negative space charge region on p-side the electric field is set up and

potential barrier develops at the junction Due to electric field e- on p-side moves to n and holes

from n-side to p-side which is called drift current.

In equilibrium state, there is no current across p-n junction and potential barrier across p-n

junction has maximum value.

The width of the depletion region and magnitude of barrier potential depends on the nature of

semiconductor and doping concentration on two sides of p-n junction.

Forward Bias

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P-n junction is FB when p-type connected to the positive of battery and n-type connected to

negative battery. Potential barrier height is reduced and width of depletion layer decreases.

Resistance of p-n junction is low when forward biased.

Reverse Bias

P-n junction in RB p-type connected to the negative battery and n-type connected to positive.

The width of depletion region and potential barrier decreases. Resistance of p-n junction is high

to the flow of current.

7. Rectification: The process of converting ac into dc is called rectification. A junction diode

conducts when forward biased and does not conduct when reverse biased. The rectifier which

gives output for only half of the input wave is called half wave rectifier. The rectifier which gives

output for both half of the input wave is called full wave rectifier.

Half wave rectifier:

Full Wave rectifier:

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8. A junction diode designed to work in the reverse breakdown region is called Zener diode. The

voltage drop across it is independent of the current through it. So it can be used as a voltage

regulator.

I-V curve

9. Semiconductor devices in which charge carriers are generated when light of sufficient energy is

allowed to fall on the semiconductor material are known as optoelectronic devices. For eg, LED,

photodiode and solar cell.

LED PHOTODIODE SOLARCELL

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CONCEPT BASED EXERCISE VSA Questions (1 Mark)

1. Write the value of resistance offered by an ideal diode when (i) forward based (ii) reverse biased.

2. At what temperature does a semiconductor behave as an insulator? 3. What is the phase difference between input and output waveform in the common emitter

transistor amplifier? 4. Why LEDs are made of compound semiconductors? 5. Can the potential barrier across a p-n junction be measured by simply connecting a voltmeter

across the junction? 6. Sn, C, and Si, Ge are all group XIV elements. Yet, Sn is a conductor, C is an insulator while Si and

Ge are semiconductors. Why? 7. Name the p.n. junction diode which emits spontaneous radiation when forward biased. (LED) 8. How does the energy gap in a semiconductor vary, when doped, with a pentavalent

impurity?(decreases) 9. If the base region of the transistor is made large, as compared to a usual transistor, how does it

affect the (i) collector current and (ii) current gain of the transistor? 10. In the following diagram write which of the diode is forward biased and which is reverse

biased?

Forward biased Reverse biased No external baising,It generates emf when solar radiation falls on it.

Recombination of electrons and holes take place at the junction and emits e m radiations

Energy is supplied by light to take an electron from valence band to conduction band.

Generation of emf by solar cells is due to three basic process generation of e-h pair,separation and collection

It is used in Burglar alarm, remote control

It is used in photo detectors in communication

It is used in satellites ,space vechicles calculators.

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(Reverse biased) (Forward biased) 11. How does the energy gap in a semiconductor vary, when doped, with a pentavalent impurity? 12..In the given circuit, D is an ideal diode. What is the voltage across R. When the applied voltage V makes the diode. (a) Forward bias? (b) Reverse bias?

13.Which of the input and output circuits of a transistor has a higher resistance and why? 14.Why Si and GaAs are preferred materials for solar cell? 15. The ratio of the number of free electrons to holes ne/nh for two different materials A and B are 1 and < 1 respectively. Name the type of semiconductor to which A and B belong 16.Diode is a non linear device. Explain it with the help of a graph. 17 A n-type semiconductor has a large number of free electrons but still it is electrically neutral. Explain 18.Power gain of a transistor is high. Does it mean the power is generated by the transistor itself? Explain. 19.Why is n-type semiconductor neutral

NUMERICALS

1. Pure Si at 300 K has equal electron (ne) and hole (nh) concentration of 1.5 ×1016/m3. Doping by indium increases nh to 4.5 × 1022/m3. Calculate ne in the doped silicon.

2. If the current gain of a CE – Amplifier is 98 and collector current Ic = 4mA, determine the base current.

3. An LED is constructed from a p-n junction of a certain semiconducting material whose energy gap is 1.9eV. What is the wavelength of light emitted by this LED?

4. A transistor has a current gain of 30. If the collector resistance is 6kW and input resistance 1kCalculate the voltage gain.

5. A p-n junction is fabricated from a semiconductor with a band gap of 2.8 eV. Can it detect a wavelength of 600 nm? Justify your answer.

6. When the voltage drop across a p.n. Junction is increased from 0.65 v to 0.70, the charge in the diode current is 5 ma . What is the dynamic resistance of the diode ?

7. p – n – p transistor circuit, the collector is 10 ma , If 90 % of the reach the Collector, find emitter and base currents.

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8. The number of silicon atoms per m3 is 5 x 1022 atom per 33 of Anesenice and 5 x 1020 per m3 atoms of Indian. Calculate the number of electrons and holes . Given that Ni = 1.5 X 1016 per m3 . In the material N-type on P-Type?

9. Diode used in figure has a constant voltage drop at 0.5 V at all current and a maximum power rating of 100mw. What should be the value of resistance R, coneected in series for maximum current

10. On the figure shown, find out the current passing through RL and Zener diode

11.A common emitter transistor has current gain of 100. If emitter current is 8.08 m A, find the base

and collector current

12.In a common –emitter transistor amplifier, the input resistance is 200Ω , RL = 20KΩ. Find (i) voltage gain and (ii) Power gain . Given current gain B = 10. 13. In n p n transistor circuit, the collector current is 10 mA. If 95%of the electron emitted reach the collector, what is the base current ?

ENRICHMENT 1. Find the equivalent resistance of the network shown in figure between point A and B when the p-n junction diode is ideal and : (i) A is at higher potential (ii) B is at higher potential

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2.The diagram shows a piece of pure semiconductor S in series with avariable resistor R and a source of constant voltage V. Would you increase or decrease the value of R to keep the reading of ammeter A constant,when semiconductor S is heated? Give reason

3.Determine the current I for the network. (Barrier voltage for Si diode is 0.7volt).

4. The solar radiation spectrum shows that maximum solar intensity is near to energy h = 1.5 eV. Answer the following : (i) Why are Si and GaAs are preferred materials for solar cells. (ii) Why Cd S or CdSe (Eg ~ 2.4 eV) are not preferred. (iii)Why we do not use materials like PbS (Eg ~ 0.4 eV). 5. Determine V0, Idl and Id2 for the given network. Where D1 and D2 are madeof silicon.

6. Determine V0 and Id for the network

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MCQ For the answer of the following questions choose the correct alternative from among the given ones.

1.C, Si and Ge have same no. of valence electrons. C is an insulator because energy required to take one electron out from

(A) Si is more (B) C is more (C) Ge is more (D) C is less

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(2) Ionization energy of isolated phosphorous atoms 10 eV. Ionization energy of same atom in Si is nearly eV (Relative Permittivity of silicon = 12) (A) 0.1 (B) 0.2 (C) 0.3 (D) 0.4 (3) By adding impurity in intrinsic semiconductor P type semiconductor is made. charge of these P type semiconductor is

(A) trivalent, neutral (B) pentavalent, neutral (C) pentavalent, positive (D) trivalent, negative

(4) Strong overlapping of different atomic orbitals makes (A) Different energy level (B) energy band (C) Conductor (D) Insulators (5) We cannot make p-n junction diode by making P type semi-conductor join with N - type semi-conductor, because (A) Inter-atomic spacing becomes less than 1AO (B) P - type will repel N - type (C) There will be discontinuity for the flowing charge carriers (6) We can not make p-n junction diode by making P type semi-condutor join with N - type semi-conductor, because (A) Inter-atomic spacing becomes less than 1AO (B) P - type will repel N - type (C) There will be discontinuity for the flowing charge carriers (D) semi-conducting properties will be lost (7)For p-n junction, which statement is incorrect (A) Donor atoms are depleted of their holes in junction (B) No net charge exists far from junction (C) Barrier potential VB is generated

(D) Energy VB is to be surmounted before any charge can flow across junction

(8) The intrinsic semi-conductor has :

(A) a finite resistance which does not change with temperature

(B) infinite resistance which decreases with temperature (C) Finite resistance which decreases with temperature (D) Finite resistance which does not change with temperature (9) The behaviour of Ge as semi-conductor is due to width of : (A) Conduction band being large (B) Forbidden band being large (C) Conduction band being small

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(D) Forbidden band being small and 10. At 0 K temp, a N - type semi-conductor : (A) does not have any charge carriers (B) has few holes but no free electrons (C) few holes and few electrons (D) has equal number of holes and electrons (11) In Si-crystal, impurity donor atom have valency. (A) 2 (B) 3 (C) 4 (D) 5 12.A full wave rectifier is operating at 50Hz, 220V the fundamental frequency of ripple will be . (A) 50 Hz (B) 75 Hz (C) 110 Hz (D) 100 Hz (13) Reverse bias applied on a junction diode : (A) raises the potential barrier (B) increases majority charge carrier current (C) lowers the potential barrier (D) increases the temperature of junction

14.A sinusoidal voltage of peak value 200volts is connected to a diode and resistor R in the circuit shown.If diode is ideal, the r.m.s. voltage across R is…… volt

15.Assuming that the junction diode is ideal, the current through the diode is mA

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(A) 1 (B) 10 (C) 20 (D) 30

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SUBJECT TIPS

Read NCERT thoroughly

Understand the concepts before memorizing

Make your own notes for better comprehension

Revise regularly the difficult topics

Learn in the form of nmemonics wherever possible

Use mind maps in difficult concepts

Practice Circuit diagrams properly

Learn every topic with the help of a diagram along with the formula related

Do learn the SI units along with the physical quantities used in concepts.

Practice numericals simultaneously with the topic for better gripping of the concept

CBSE model answer key is available on the website for reference

BIBLIOGRAPHY

1. PHYSICS Textbook for class XII Part –I & II, NCERT

2. PHYSICS Reference book for class XII –by S.L.Arora

3. NCERT Exemplar problems class XII

4. Support Material 2017-18, Department of Education

5. Mind maps and diagrams : Google