A current i₀ is flowing through an L-R circuit of time constant t₀. The source of the current is switched off at time t = 0. Let r be the value of (- di/dt) at time t = 0.Assuming this rate to be constant, the current will reduce to zero in a time interval of

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$\frac{t_{0}}{e}$

et₀

$(1 - \frac{1}{e}) t_{0}$

t₀

answer is A.

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Detailed Solution

$i = i_{0} e^{- t / t_{0}}$

$(- \frac{d i}{d t}) = \frac{i_{0}}{t_{0}} e^{- t / t_{0}}$

$(- \frac{d i}{d t}) = \frac{i_{0}}{t_{0}} = r$ (at t = 0)

$∴ T h e d e s i r e d t i m e i s \frac{i_{0}}{r} o r t_{0}$

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