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(C) After a long time,an inductor in a $DC$ circuit behaves as a short circuit (a wire with zero resistance).In the given circuit,there are three para

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(C) After a long time,an inductor in a $DC$ circuit behaves as a short circuit (a wire with zero resistance).In the given circuit,there are three parallel branches:$1$. The top branch contains an inductor $L$ and a resistor $R$. Since the inductor acts as a short circuit,the effective resistance of this branch is $R = 12\,\Omega$.$2$. The middle branch contains only a resistor $R = 12\,\Omega$.$3$. The bottom branch contains a resistor $R$ and an inductor $L$. Similarly,the effective resistance of this branch is $R = 12\,\Omega$.Since all three branches are in parallel and each has an effective resistance of $12\,\Omega$,the equivalent resistance $R_{eq}$ of the circuit is:$\frac{1}{R_{eq}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} = \frac{3}{R}$$R_{eq} = \frac{R}{3} = \frac{12\,\Omega}{3} = 4\,\Omega$The current $I$ through the battery is given by Ohm's law:$I = \frac{V}{R_{eq}} = \frac{12\,V}{4\,\Omega} = 3\,A$.

Three identical resistors with resistance $R = 12\,\Omega$ and two identical inductors with self-inductance $L = 5\,mH$ are connected to an ideal battery with an emf of $12\,V$ as shown in the figure. The current through the battery long after the switch has been closed will be $......A$.

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