An inductor stores u energy and I current is passed through it and dissipate energy at the rate of P.The time constant of the circuit,when this coil is connected across a battery of zero internal resistance?

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Answer is 2U/p

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Answer 1 · 2018-04-25T11:04:39

Energy stored in an inductor $L$ is given by

$U=1/2LI^2$
where $I$ is final value of the current.

Power dissipated $P$ in a resistor $R$ is given as

$P=I^2R$

Time constant of $LR$ circuit is given as

$tau = L/R$

Writing it in terms of $Land R$ , and noting that internal resistance of the battery is zero, we get

$tau=((2U)/I^2)/(P/I^2)$
$tau=(2U)/(P)$