Electromagnetic Induction | Physics JEE Main questions with Solutions

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Topic Question Set

Q 1 :

In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of 8 A/s. At an instant when R is 12 $Ω$ , the value of the current in the circuit will be ________ A. [2025]

0%

(3)

$ε - \frac{L d I}{d t} - I R = 0$

$12 - 3 \times (- 8) - I \times 12 = 0$

$\Rightarrow I = 3 A$

Q 2 :

Three identical resistors with resistance $R = 12 Ω$ and two identical inductors with self inductance L = 5 mH are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be ________ A. [2023]

0%

(3)

After long time an inductor behaves as a resistance-less path. So current through cell

$I = \frac{12}{R / 3} = 3 A {∵ R = 12 Ω}$

Q 3 :

As per the given figure, if $\frac{d I}{d t} = - 1 A/s$ then the value of $V_{A B}$ at this instant will be _______ V. [2023]

0%

(30)

$\frac{d I}{d t} = - I \frac{A}{\sec}$

$V_{A} - I R - L \frac{d I}{d t} - 12 = V_{B}$

$V_{A} - 2 \times 12 - 6 (- 1) - 12 = V_{B}$

$V_{A} - V_{B} = 36 - 6 = 30 V$

Q 4 :

In the given figure, an inductor and a resistor are connected in series with a battery of emf E volt. $\frac{E^{a}}{2 b} J/s$ represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of $\frac{b}{a}$ will be _________. [2023]

0%

(25)

$E = \frac{1}{2} L I^{2}$

$Rate of energy storing = \frac{d E}{d t} = L I \frac{d I}{d t}$

$Now we know for an R - L circuit$

$I = \frac{E}{R} (1 - e^{- \frac{R}{L} t})$

$So \frac{d I}{d t} = \frac{E}{L} e^{- t \frac{t R}{L}}$

$\frac{d E}{d t} = \frac{E^{2}}{R} (1 - e^{- t \frac{t R}{L}}) (e^{- t \frac{R}{L}})$

$Time at which rate of power storing will be maximum, t = \frac{L}{R \ln 2}$

$So \frac{d E}{d t} = \frac{E^{2}}{R} (1 - \frac{1}{2}) \times \frac{1}{2}$

$\Rightarrow \frac{E^{2}}{4 R} = \frac{E^{2}}{100} = \frac{E^{2}}{2 \times 50}$

$a = 2, b = 50$

$So \frac{b}{a} = 25$

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