CBSE Class 12 Physics Electromagnetic Induction And Alternating Current Worksheet Set B

Important Questions for NCERT Class 12 Physics Electromagnetic Induction

Question. A rectangular coil of 20 turns and area of cross-section 25 sq. cm has a resistance of 100 W. If a magnetic field which is perpendicular to the plane of coil changes at a rate of 1000 tesla per second, the current in the coil is    
(a) 1 A
(b) 50 A
(c) 0.5 A
(d) 5 A 
Answer   C

Question. A conducting square frame of side ‘a’ and a long straight wire carrying current I are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity ‘V’. The emf induced in the frame will be proportional to    
(a) 1/(2x + a)²
(b) 1/(2x − a)(2x + a)
(c) 1/x²
(d) 1/(2x − a)²
Answer   B

Question. If N is the number of turns in a coil, the value of self inductance varies as   
(a) N 0
(b) N
(c) N 2
(d) N–2 
Answer   C

Question. A magnetic field of 2 × 10–2 T acts at right angles to a coil of area 100 cm2, with 50 turns. The average e.m.f. induced in the coil is 0.1 V, when it is removed from the field in t sec. The value of t is    
(a) 10 s
(b) 0.1 s
(c) 0.01 s
(d) 1 s
Answer   B

Question. An electron moves on a straight line path XY as shown. The abcd is a coil adjacent to the path of electron. What will be the direction of current, if any, induced in the coil?
(a) The current will reverse its direction as the electron goes past the coil    
(b) No current induced
(c) abcd
(d) adcb 
Answer   A

Question. Two coils of self inductance 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other.
The mutual inductance between these coils is    
(a) 16 mH
(b) 10 mH
(c) 6 mH
(d) 4 mH 
Answer   D

Question. A metal ring is held horizontally and bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet is    
(a) more than g
(b) equal to g
(c) less than g
(d) either(a) or (c) 
Answer   C

Question. Faraday’s laws are consequence of conservation of    
(a) energy
(b) energy and magnetic field
(c) charge
(d) magnetic field
 Answer   A

Question. A conducting rod AB moves parallel to X-axis in a uniform magnetic field, pointing in the positive X-direction. The end A of the rod gets    
(a) positively charged
(b) negatively charged
(c) neutral
(d) first positively charged and then negatively charged
 Answer   A

Important Questions for NCERT Class 12 Physics Alternating Induction

Question. In an a.c. circuit the e.m.f. (e) and the current (i) at any instant are given respectively by e = E0sinwt , i = I0sin(wt – f)
The average power in the circuit over one cycle of a.c. is
(a) E0I0 /2 cosΦ
(b) E0I0
(c) E0I0/2
(d) E0I0 /2 sinΦ 
Answer   A

Question. A coil of inductive reactance 31 W has a resistance of 8 W. It is placed in series with a condenser of capacitative reactance 25 W. The combination is connected to an a.c. source of 110 V. The power factor of the circuit is
(a) 0.33
(b) 0.56
(c) 0.64
(d) 0.80
Answer   D

Question. The mutual inductance of a pair of coils, each of N turns, is M henry. If a current of I ampere in one of the coils is brought to zero in t second, the emf induced per turn in the other coil, in volt, will be A
(a) MI /t
(b) NMI/t
(c) MN /It
(d) MI/Nt
Answer  A

Question. For a series LCR circuit, the power loss at resonance is
(a)  V2 /[ωL - 1/ωC]
(b) I² Lω
(c) I²R
(d)  V²/ Cω
Answer   C

Question. In an a.c. circuit with phase voltage V and current I, the power dissipated is
(a) V.I
(b) depends on phase angle between V and I
(c) 1/2 ×V.I
(d) 1/√2 ×V.I
Answer   B

Question. A step down transformer is connected to 2400 volts line and 80 amperes of current is found to flow in output load. The ratio of the turns in primary and secondary coil is 20 : 1. If transformer efficiency is 100%, then the current flowing in the primary coil will be 
(a) 1600 amp
(b) 20 amp
(c) 4 amp
(d) 1.5 amp
Answer  C

Question. An series L-C-R circuit is connected to a source of A.C. current. At resonance, the phase difference between the applied voltage and the current in the circuit, is 
(a) p
(b) zero
(c) p/4
(d) p/2
Answer  B

Question. A bar magnet is being moved towards a stationary coil (i) rapidly (ii) slowly:
a. larger in case (i)
b. smaller in case (ii)
c. equal in both cases
d. cannot say
Answer : A, B

Question. In which of the following cases with a bar magnet and the solenoid, an induced emf is generated?
a. when magnet is withdrawn from the solenoid
b. when magnet is inserted into the solenoid
c. when solenoid is moved towards or away from the magnet
d. when both the solenoid and magnet are moved in the same direction with the same speed
Answer : A, B, C

Question. Eddy currents produced in a conductor are responsible for:
a. damping
b. heating
c. sparking
d. loss of energy
Answer : A, B, D

Question. Two solenoids have identical geometrical constructions put one is made of thick wire and the other of thin wire.
Which of the following quantities are different for the two solenoids?
a. self inductance
b. rate of joule heating if the same current goes through them
c. magnetic field energy if the same current goes through them
d. time constant if one solenoid is connected to one battery and the other is connected to another battery
Answer : B, D

Question. Two different coils have self-inductances L₁ = 8mH, L₂ = 2mH. The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same constant rate. At a certain instant of time, the power given to the two coils is the same. At that time the current, the induced voltage and the energy stored in the first coil are i₁, V₁ and W₁ respectively. Corresponding values for the second coil at the same instant are i₁, V₂ and W₂ respectively. Then
a. i₁/i₂ = 1/4
b. i₁/i₂ = 4
c. W₂/W₁ = 4
d. V₂/V₁ = 1/4
Answer : A, C, D

Question. Which of the following is/are equal to Henry?
a. Volt second/ampere
b. Volt (second)² /coulomb
c. Volt² second/coulomb
d. Joule (second)² / (coulomb)²
Answer : A, B, D

Question. If R, C and L be the resistance, capacitance and inductance in a circuit in which a.c. of frequency f is set up then which of the following has the dimensions of R?
a. f C
b. f L
c. 1/fC
d. L/f
Answer : B, C

Question. A series R-C circuit is connected to AC voltage source. Consider two cases; a. when C is without a dielectric medium and b. when C is filled with dielectric of constant 4. The current R I through the resistor and voltage C V across the capacitor are compared in the two cases. Which of the following is/are true?

Answer : B, C

Question. A bar magnet is moved along the axis of a copper ring placed far away from the magnet. Looking from the side of the magnet, an anticlockwise current is found to be induced in the ring. Which of the following may be true?
a. The south-pole faces the ring and the magnet moves towards it
b. The north-pole faces the ring and the magnet moves towards it
c. The south-pole faces the ring and the magnet moves away from it
d. The north-pole faces the ring and the magnet moves away from it
Answer : B, C

Question. If R, C and L denote the resistance, capacitance and inductance, which of the following will have the dimensions of frequency?
a. RL⁻¹
b. R⁻¹ C⁻¹
c. L^−1/2 C^−1/2
d. RCL
Answer : A, B, C

Comprehension Based

Paragraph-I

The capacitor of capacitance C can be charged (with the help of a resistance R) by a voltage source V, by closing switch S₁ while keeping switch S₂ open. The capacitor can be connected in series with an inductor L by closing switch S₂ and opening S₁.

Question. Initially, the capacitor was uncharged. Now, switch S₁ is closed and S₂ is kept open. If time constant of this circuit is τ, then
a. after time interval τ, charge on the capacitor is CV/2
b. after time interval 2τ , charge on the capacitor is CV(−e⁻²)
c. the work done by the voltage source will be half of the heat dissipated when the capacitor is fully charged
d. after time interval 2τ , charge on the capacitor is CV(−e⁻²)
Answer : B

Question. After the capacitor gets fully charged, S₁ is opened and S₂ is closed so that the inductor is connected in series with the capacitor. Then,
a. at t = 0, energy stored in the circuit is purely in the form of magnetic energy
b. at any time t > 0, current in the circuit is in the same direction
c. at t > 0, there is no exchange of energy between the inductor and capacitor
d. at any time t > 0, maximum instantaneous current in the circuit may be V √C/L
Answer : D

Question. If the total charges stored in the LC circuit is 0 Q , then for t ≥ 0

Answer : C

Paragraph – II

A point charge Q is moving in a circular orbit of radius R in the x-y plane with an angular velocityω. This can be considered as equivalent to a loop carrying a steady current . Qω / 2π A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The applications of the magnetic field induces an emf in the orbit.
The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with proportionality constantγ.

Question. The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is:
a. BR/4
b. −BR/2
c. BR
d. 2BR
Answer : C

Question. The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is:
a. γ (BQR²/2)
b. - γ (BQR²/2)
c. γ (BQR²/2)
d. γ BQR²
Answer : B

Paragraph –III

A thermal power plant produces electric power of 600 kW at 4000 V, which is to be transported to a place 20 km away from the power plant for consumer’ usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation is much smaller. In this method, a step -up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumer’s end a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with a power factor unity. All the current and voltages mentioned are rms values.

Question. If the direct transmission method with a cable of resistance 1 0.4 km) − is used, the power dissipation (in %) during transmission is:
a. 20
b. 30
c. 40
d. 50
Answer : B

Question. In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is 1 : 10. If the power to the consumers has to be supplied at 200V, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is:
a. 200 : 1
b. 150 : 1
c. 100 : 1
d. 50 : 1
Answer : A

Paragraph –IV

A point charge Q is moving in a circular orbit of radius R in the x-y plane with an angular velocity ω. This can be considered as equivalent to a loop carrying a steady current .Qω/2π. A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The applications of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant γ
.
Question. The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is:
a. BR/4
b. −BR/2
c. BR
d. 2BR
Answer : B

Question. The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is:
a. −γ BQR²
b. −γ(BQR²/2)
c. γ(BQR²/2)
d. γ BQR²
Answer : B

Integer

Question. The sum and difference of self inductance of two coils are 13 mH and 5 mH respectively. What is the maximum value of mutual inductance of the two coils?
Answer : 6

Question. A transformer working on 220 V a.c. line gives an output current of 4 A at 55 V. What is the primary current?
Assume that there is no loss of energy.
Answer : 1

Question. The magnetic flux of φ (in weber) in a closed circuit of resistance 3 ohm varies with time t (in second) according to the equation φ = 2t² −10t + 3. What will be the magnetic of induced current at t = 0.25 s ?
Answer : 3

Question. An a.c. generator gives an output voltage of E = 170sin 56⋅52t.What is the frequency of alternating voltage produced?
Answer : 9

Question. A condenser of capacitance 0.144pH is used in a transmitter to transmit at wavelength λ. If inductance of 2 1/π mH is used for resonance, what is the value of λ?
Answer : 7

Question. In the series RLC circuit as shown in Fig., what would be the ammeter reading?

Answer : 2

Question. An a.c. source of frequency 1000 Hz is connected to a coil of 200/π mH and negligible resistance. If effective current through the coil is 7.5 mA, what is the voltage across the coil?
Answer : 3

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