First slide

Time -Varying current in L-R circuit

Question

A current $I_{0}$ is flowing through on L – R circuit of time constant $t_{0}$ . The source of current is switched off at time t = 0. Let r be the value of $(- \frac{dI}{dt})$ at t = 0. Assuming this rate to be constant, the current will reduce to zero in a time interval of

Difficult

Solution

$I = I_{0} e^{- t / t_{o}} \Rightarrow (- \frac{dI}{dt}) = \frac{I_{0}}{t_{0}} e^{- t / t_{o}} . ∴ r = {(- \frac{dI}{dt})}_{t = 0} = \frac{I_{0}}{t_{0}}$
$∴ The desired time is \frac{I_{0}}{r} or t_{0}$

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