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JEE Main 2021 (25 Feb, Shift 1) · Self-Inductance & Energy

Self-Inductance & Energy question from JEE Main 2021 (25 Feb, Shift 1)

Q71JEE Main 2021 · 25 FEB · SHIFT 1Medium

Self-Inductance & Energy

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

Numerical answer type. Work it out, then open the answer.

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Answer: 144

With no resistance $V = L\dfrac{dI}{dt}$ , so $\dfrac{dI}{dt} = \dfrac{3t}{2}$ .
$I = \displaystyle\int_0^t \dfrac{3t}{2}\,dt = \dfrac{3t^2}{4}$ ; at $t = 4$ s, $I = 12$ A.
$U = \dfrac{1}{2}LI^2 = \dfrac{1}{2}\times 2 \times 144 = 144$ J
So the energy stored is $144$ J.

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