A solenoid has self inductance of $5 mH$ and the current through it is given by $i = 10 t^{2} - 20 t$ where $t$ is time in second. At what instant of time, the induced emf will be zero?

1 s

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2 s

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3 s

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4 s

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Solution

The correct option is A $1 s$
Given :

Self inductance, $L = 5 mH = 5 \times 10^{- 3} H$

Current, $i = 10 t^{2} - 20 t$

$\Rightarrow \frac{d i}{d t} = 20 t - 20 . . . (1)$

Also, induced emf,

$E = - L \frac{d i}{d t}$

Induced emf will be zero when $\frac{d i}{d t} = 0$

From $(1)$ ,

$20 t - 20 = 0 \Rightarrow t = 1 s$

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