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In an inductor of self-inductance $L = 2 m H,$ current changes with time according to relation $i = t^{2} e^{- t} .$ . At what time emf is zero?

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$4 s$

$3 s$

$2 s$

$1 s$

answer is C.

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Detailed Solution

$L = 2 mH, i = t^{2} e^{- t}$

$E = - L \frac{di}{dt} = - L [- t^{2} e^{- t} + 2 {te}^{- t}]$

When $E = 0,$

$\begin{array}{l} - e^{- t} t^{2} + 2 t e^{- t} = 0 \\ or, 2 t e^{- t} = e^{- t} t^{2} \\ \Rightarrow t = 2 \sec . \end{array}$

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