Electromagnetic Induction - Result Question 26

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

[2001]

(a) $4 s$

(b) $3 s$

(c) $2 s$

(d) $1 s$

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Answer:

Correct Answer: 26. (c)

Solution:

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

$E=-L \frac{d i}{d t}=-L[-t^{2} e^{-t}+2 t e^{-t}]$

when $E=0$,

$-e^{-t} t^{2}+2 t e^{-t}=0$

or, $2 t e^{-t}=e^{-t} t^{2}$

$\Rightarrow t=2 sec$.