A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by $\mathrm{V}=3 t$ volt. (where $t$ is in second). If the voltage is applied when $t=0$, the energy stored in the coil after 4 s is \_\_\_\_ J.

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Electromagnetic Induction

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by

V = 3 t

volt. (where

t

is in second). If the voltage is applied when

t = 0

, the energy stored in the coil after 4 s is ____ J.

Answer: 144

Solution

The coil has no resistance, so the whole applied voltage appears across its inductance:

3 t = L \frac{d i}{d t} = 2 \frac{d i}{d t} \Rightarrow d i = \frac{3 t}{2} d t

Integrating from the switch-on instant, where the current is zero,

i = \frac{3 t ^{2}}{4}

t = 4

s this gives

i = \frac{3 ( 16 )}{4} = 12

A, so the energy stored in the coil is

U = \frac{1}{2} L i^{2} = \frac{1}{2} (2) (12)^{2} = 144 J

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Integer answer

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