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Energy Stored in an Inductor

The current f...

Question

The current flowing in a coil of inductance $L = 2 m H$ varies as $i = t^{2} e^{- t}$ . The time in which emf induced in the coil will be zero is:

A

2s

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B

1s

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C

4s

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D

3s

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Solution

The correct option is C 2s
$ϵ = L \frac{d i}{d t}$
$0 = 2 \times 10^{- 3} \times [2 t e^{- t} - t^{2} e^{- t}]$
$2 t e^{- t} = t^{2} e^{- t}$
$t = 2 s$

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