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The current in a 90 mH inductor changes with time as $i = 1.0 t^{2} - 6.0 t,$ where $i$ is in amperes and $t$ is in seconds

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the magnitude of the induced emf at $t = 4.0 s$ is $180 m V$

the emf zero at time $t = 3.0 s$

the magnitude of the induced emf at $t = 4.0 s$ is $360 m V$

the emf zero at time $t = 4.0 s$

answer is A, B.

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Detailed Solution

$| ε | = L \frac{d i}{d t} = | (90 \times 10^{- 3}) \frac{d}{d t} | (1.0 t^{2} - 6.0 t)$

$= (90) | 2.0 t - 6.0 |, ε$ is in millivolts $(m V)$ and $t$ in seconds at $t = 4.0 s, ε = 180 m V$

If $ε = (90) (2 t - 6) = 0$

Hence $t = 3.0 s$

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