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, $2 t e^{-t}=e^{-t} t^{2}$
$\Rightarrow t=2 sec$.
