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Question

(C) In a $DC$ circuit at steady state,the inductor acts as a simple wire with zero resistance (ideal inductor) or just a conductor with its inherent r

Vedclass · Accepted Answer

$\frac{4 E}{R}$

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(C) In a $DC$ circuit at steady state,the inductor acts as a simple wire with zero resistance (ideal inductor) or just a conductor with its inherent resistance $R$.Since the coil is broken into two identical parts,the resistance of each part becomes $R' = \frac{R}{2}$.When these two parts are connected in parallel,the equivalent resistance $R_{eq}$ is given by $\frac{1}{R_{eq}} = \frac{1}{R'} + \frac{1}{R'} = \frac{2}{R'} = \frac{2}{R/2} = \frac{4}{R}$.Thus,$R_{eq} = \frac{R}{4}$.The current $I$ through the battery is given by Ohm's law: $I = \frac{E}{R_{eq}} = \frac{E}{R/4} = \frac{4 E}{R}$.

An inductor coil wound uniformly has self-inductance $L$ and resistance $R$. The coil is broken into two identical parts. The two parts are then connected in parallel across a battery of $E$ volt of negligible internal resistance. The current through the battery at steady state is

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