A current $i_{0}$ is flowing through an $L - R$ circuit of time constant $t_{0}$ . The source of the current is switched off at time $t = 0$ . Let $r$ be the value of $(- d i / d t)$ at time $t = 0$ . Assuming this rate to be constant, the current will reduce to zero in a time interval of:

t_{0}

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e t_{0}

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t_{0} / e

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⎧ ⎪ ⎪ ⎪ ⎩ 1 - \frac{1}{e} ⎫ ⎪ ⎪ ⎪ ⎭ t_{0}

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Solution

The correct option is B $t_{0}$
$i = i_{0} e^{- t / t_{0}}$
$(- \frac{d i}{d t}) = \frac{i_{0}}{t_{0}} e^{- t / t_{0}}$
$(- \frac{d i}{d t}) = \frac{i_{0}}{t_{0}} = r$
$∴$ The desired time as $\frac{i_{0}}{r}$ or $t_{0}$

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