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(C) The energy stored in an inductor is given by $U = \frac{1}{2} L I^2$,where $L$ is the inductance and $I$ is the current.From this,we can express t

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$\frac{2U}{P}$

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(C) The energy stored in an inductor is given by $U = \frac{1}{2} L I^2$,where $L$ is the inductance and $I$ is the current.From this,we can express the inductance as $L = \frac{2U}{I^2}$.The rate of energy dissipation (power loss) in the inductor due to its internal resistance $R$ is given by $P = I^2 R$.From this,we can express the resistance as $R = \frac{P}{I^2}$.The time constant $	au$ of an $LR$ circuit is defined as $	au = \frac{L}{R}$.Substituting the expressions for $L$ and $R$:$	au = \frac{2U / I^2}{P / I^2} = \frac{2U}{P}$.Therefore,the time constant is $\frac{2U}{P}$.

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

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