Electromagnetic Induction — DPP 3

20 NEET questions from Electromagnetic Induction, with answers and explanations. Attempt it as a timed test to get scoring, accuracy breakdown and mistake tracking.

Attempt this test free 20 questions · 30 minutes · +80 marks
1
A semicircle loop PQ of radius 'R' is moved with velocity 'v' in transverse magnetic field as shown in figure. The value of induced emf. between the ends of loop is :-
Electromagnetic Induction – NEET-20281
  1. A $\operatorname { Bv } ( \pi \mathrm { r } )$, end ' P ' at high potential
  2. B 2 BRv , end P at high potential
  3. C 2 BRv , end Q at high potential
  4. D $\mathrm { B } \frac { \pi \mathrm { R } ^ { 2 } } { 2 } \mathrm { v }$, end P at high potential
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Correct answer: C

2
A solenoid of 10 henry inductance and 2 ohm resistance, is connected to a 10 volt battery. In how much time the magnetic energy will reach to 1/4th of the maximum value?
  1. A 3.5 sec
  2. B 2.5 sec
  3. C 5.5 sec
  4. D 7.5 sec
Show answer & explanation

Correct answer: A

Electromagnetic Induction – NEET-20191
3
Two coaxial solenoids are made by winding thin Cu wire over a pipe of cross-sectional area A = 10 cm$^{2}$ and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is :-
  1. A $2.4 \pi \times 10 ^ { - 5 } \mathrm { H }$
  2. B $4.8 \pi \times 10 ^ { - 4 } \mathrm { H }$
  3. C $4.8 \pi \times 10 ^ { - 5 } \mathrm { H }$
  4. D $2.4 \pi \times 10 ^ { - 4 } \mathrm { H }$
Show answer & explanation

Correct answer: D

$\mathrm{M}=\frac{\mu_{0} \mathrm{~N}_{1} \mathrm{~N}_{2} \mathrm{~A}}{\ell}$
4
The ratio of the secondary to the primary turns in a transformer is 3 : 2 and the output power is P. Neglecting all power losses, the input power must be :-
  1. A $\frac { P } { 2 }$
  2. B P
  3. C $\frac { 2 P } { 3 }$
  4. D $\frac { 3 P } { 2 }$
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Correct answer: B

5
The mutual inductance of two coils when magnetic flux changes by $2 \times 10 ^ { - 2 } \mathrm {~Wb}$ and current changes by 0.01 A is :-
  1. A 2 H
  2. B 3 H
  3. C 4 H
  4. D 8 H
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Correct answer: A

$\phi=\mathrm{MI} \Rightarrow \frac{\mathrm{d} \phi}{\mathrm{dt}}=\mathrm{M} \frac{\mathrm{dI}}{\mathrm{dt}} \Rightarrow \mathrm{M}=\frac{\mathrm{d} \phi}{\mathrm{dI}}=\frac{2 \times 10^{-2}}{0.01}=2 \mathrm{H}$
6
A coil of 40 henry inductance is connected in series with a resistance of 8 ohm and the combination is joined to the terminals of a 2 volt battery. The time constant of the circuit is :-
  1. A $\frac { 1 } { 5 } \mathrm { sec }$
  2. B 40 sec
  3. C 20 sec
  4. D 5 sec
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Correct answer: D

$\lambda=\frac{L}{R}=\frac{40}{8}=5$ second
7
A coil of inductance 300 mH and resistance 2 Ω is connected to a source of voltage 2 V. The current reaches half of its steady-state value in:-
  1. A 0.3 s
  2. B 0.15 s
  3. C 0.1 s
  4. D 0.05 s
Show answer & explanation

Correct answer: C

Current becomes half of its peak value in half the lifetime
$\mathrm{T}=\frac{\mathrm{L}}{\mathrm{R}} \times 0.693=\frac{300 \times 10^{-3}}{2} \times 0.693=0.1 \mathrm{sec}$.
8
A conducting rod of 1 m length rotating with a frequency of 50 rev/sec. about its one of end inside the uniform magnetic field of 6.28 mT. The value of induced emf between end of rod is:
  1. A 1 V
  2. B 2 V
  3. C 0.5 V
  4. D 0.25 V
Show answer & explanation

Correct answer: A

$\begin{aligned} e & =\frac{1}{2} B \omega \ell^{2}=\frac{1}{2} B(2 \pi f) \ell^{2} \\ & =\frac{1}{2}\left(6.28 \times 10^{-3}\right)(2 \times 3.14 \times 50)(1)^{2}=1 V\end{aligned}$
9
Two coil have a mutual inductance 0.005 H. The current changes in first coil according to equation $\mathrm { I } = \mathrm { I } _ { 0 } \sin \omega \mathrm { t }$, where $\mathrm { I } _ { 0 } = 2 \mathrm {~A}$ and $\omega = 100 \pi \mathrm { rad } / \mathrm { s }$. The maximum value of induced emf in second coil is
  1. A $4 \pi \mathrm {~V}$
  2. B $3 \pi \mathrm {~V}$
  3. C $2 \pi \mathrm {~V}$
  4. D $\pi \mathrm { V }$
Show answer

Correct answer: D

10
In order to avoid eddy currents in the core of a transformer :-
  1. A The number of turns in the secondary coil is made considerably large
  2. B A laminated core is used
  3. C A step down transformer is used
  4. D A high voltage alternating weak current is used
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Correct answer: B

11
Two co-axial solenoids shown in figure. If key of primary suddenly opened then direction of instantaneous induced current in resistance 'R' which connected in secondary:
Electromagnetic Induction – NEET-20236
  1. A L to N
  2. B N to L
  3. C Alternating
  4. D Zero
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Correct answer: A

12
Faraday law represents :-
  1. A relation between I and B
  2. B relation between magnetic force and magnetic field
  3. C relation between e.m.f and rate of change of flux
  4. D none of these
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Correct answer: C

13
The inductance of a solenoid is 5 H and its resistance is 5 Ω. If it is connected to a 10 volt battery then time taken by the current to reach $9 / 10 ^ { \text {th } }$ of its maximum will be :-
  1. A 4.0 s
  2. B 2.3 s
  3. C 1.4 s
  4. D 1.2 s
Show answer & explanation

Correct answer: B

Electromagnetic Induction – NEET-20216
14
Mutual inductance of two coils depends on their self inductance $\mathrm { L } _ { 1 }$ and $\mathrm { L } _ { 2 }$ as :-
  1. A $\mathrm { M } _ { 12 } = \mathrm { L } _ { 1 } / \mathrm { L } _ { 2 }$
  2. B $\mathrm { M } _ { 12 } = \mathrm { L } _ { 2 } / \mathrm { L } _ { 1 }$
  3. C $\mathrm { M } _ { 12 } = \sqrt { \mathrm { L } _ { 1 } \mathrm {~L} _ { 2 } }$
  4. D $\mathrm { M } _ { 12 } = \sqrt { \mathrm { L } _ { 1 } / \mathrm { L } _ { 2 } }$
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Correct answer: C

$\begin{array}{l}\mathrm{M}=\mathrm{K} \sqrt{\mathrm{L}_{1} \mathrm{~L}_{2}} \text { here }(\mathrm{K}=1) \\ \text { so } \mathrm{M}=\sqrt{\mathrm{L}_{1} \mathrm{~L}_{2}}\end{array}$
15
The energy density in magnetic field B is proportional to :-
  1. A $\frac { 1 } { B }$
  2. B $\frac { 1 } { \mathrm {~B} ^ { 2 } }$
  3. C B
  4. D $\mathrm { B } ^ { 2 }$
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Correct answer: D

16
In figure (a) and figure (b) two air–cored solenoids P and Q have been shown. They are placed near each other. In figure (a), when I P, the current in P, changes at the rate of 5 As$^{–1}$, an emf of 2 mV is induced in Q. The current in P is then switched off, and a current changing at 2 As$^{–1}$ is fed through Q as shown in the diagram. What emf will be induced in P?
Electromagnetic Induction – NEET-20249
  1. A $8 \times 10^{-4} \mathrm{~V}$
  2. B $2 \times 10^{-8} \mathrm{~V}$
  3. C $5 \times 10^{-3} \mathrm{~V}$
  4. D $8 \times 10^{-2} \mathrm{~V}$
Show answer & explanation

Correct answer: A

In both cases (a) & (b), M is constant
For (a) $\varepsilon_{2}=\mathrm{M} \frac{\mathrm{dI}_{1}}{\mathrm{dt}}$
$\mathrm{M}=\frac{\varepsilon_{2}}{\left(\mathrm{dI}_{1} / \mathrm{dt}\right)}=\frac{2 \times 10^{-3}}{5}=4 \times 10^{-4} \mathrm{H}$
For (b) $e_{1}=M \frac{d I_{2}}{d t}=4 \times 10^{-4} \times 2=8 \times 10^{-4} V$
17
The flux linked with a coil at any instant 't' is given by $\phi = 10 t ^ { 2 } - 50 t + 250$. The induced emf at t = 3 s is :-
  1. A 190 V
  2. B -190 V
  3. C -10 V
  4. D 10 V
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Correct answer: C

$e=-\frac{d \phi}{d t}=-\frac{d}{d t}\left(10 t^{2}-50 t+250\right)=-(20 t-50)$
Put t = 3 sec
e = –(20 × 3 – 50) = –10 V
18
A semi-circular loop of radius R is placed in a uniform magnetic field as shown. It is pulled with a constant velocity. The induced emf in the loop is :
Electromagnetic Induction – NEET-20284
  1. A $B v ( \pi R ) \cos \theta$
  2. B $\mathrm { Bv } ( \mathrm { pR } ) \sin \theta$
  3. C $\operatorname { Bv } ( 2 R ) \cos \theta$
  4. D $\operatorname { Bv } ( 2 \mathrm { R } ) \sin \theta$
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Correct answer: D

Effective length of the loop = 2R
perpendicular component of velocity to effective length v sin θ
$\begin{array}{l}\mathrm{e}=\mathrm{B}|(\vec{\ell} \times \overrightarrow{\mathrm{v}})| \\ \mathrm{e}=\mathrm{B} 2 \mathrm{R} \mathrm{v} \sin \theta\end{array}$
19
If the input voltage of a transformer is 2500 volts and output current is 80 ampere. The ratio of number of turns in the primary coil to that in secondary coil is 20 : 1. If efficiency of transformer is 100%, then the voltage in secondary coil is :
  1. A $\frac { 2500 } { 20 }$ volt
  2. B $2500 \times 20$ volt
  3. C $\frac { 2500 } { 80 \times 20 }$ volt
  4. D $\frac { 2500 \times 20 } { 80 }$ volt
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Correct answer: A

$\begin{array}{l}\frac{V_{S}}{V_{P}}=\frac{N_{S}}{N_{P}}=\frac{1}{20} \Rightarrow V_{s}=\frac{1}{20} \times V_{P} \\ V_{s}=\frac{2500}{20} \text { volt }\end{array}$
20
A circular loop of radius r is placed in a region where magnetic field increases with respect to time as B(t) = at then induced emf in coil :-
  1. A $\pi r ^ { 2 } a$
  2. B $3 \pi r ^ { 2 } a$
  3. C $2 \pi r ^ { 2 } a$
  4. D $4 \pi r ^ { 2 } a$
Show answer

Correct answer: A

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