An inductor L= 50 mH carrying an initial current $I_{0}$ = 2.5 amp is connected at t = 0 across a non linear resistor . The voltage across resistor is related to current as $V = 10 I^{2}$ . How long after (in ms) current through inductor becomes 1.25 amp.

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answer is 2.

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Detailed Solution

$\begin{array}{l} G i v e n - L \frac{d I}{d t} = 10 I^{2} \\ - \int_{2.5}^{1.25} L \frac{d I}{I^{2}} = 10 \int_{0}^{t} d t \\ \Rightarrow t = 2 ms \end{array}$

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