JEE PYQ: Electromagnetic Induction Question 4
Question 4 - 2021 (25 Feb Shift 1)
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.
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Answer: 144
Solution
$L\frac{di}{dt} = \varepsilon = 3t$. So $L \int di = 3\int t,dt$, giving $Li = \frac{3t^2}{2}$, hence $i = \frac{3t^2}{2L}$. Energy $E = \frac{1}{2}Li^2 = \frac{1}{2}L\left(\frac{3t^2}{2L}\right)^2 = \frac{9t^4}{8L}$. At $t = 4$: $E = \frac{9 \times 256}{8 \times 2} = 144$ J.
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