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In the circuit shown, the internal resistance of the cell is negligible. The steady state current in the $2 ~\Omega$ resistor is

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Verified Answer
The correct answer is:
$0.9 \mathrm{~A}$
$2 \Omega$ and $3 \Omega$ resistors are in parallel, so their equivalent resistance,
$$
R_{\text {eq }}=\frac{2 \times 3}{2+3}=\frac{6}{5}=1.2 \Omega
$$
As capacitor blocks DC at steady state, so the resistor $4 \Omega$ is ineffective.
The $R_{\text {eq }}$ and $28 \Omega$ are in series, so total resistance of circuit,
$$
R_{T}=1.2+2.8=4 \Omega
$$
Current in circuit, $I=\frac{V}{R_{T}}=\frac{6}{4}=15 \mathrm{~A}$
Potential across the combination of $2 \Omega$ and $3 \Omega$ resistors $\quad V^{\prime}=15 \times 1.2=1.8 \mathrm{~V}$
$\therefore$ The steady state current in $2 \Omega$ resistor is
$$
I^{\prime}=\frac{V^{\prime}}{2}=\frac{1.8}{2}=0.9 \mathrm{~A}
$$
$$
R_{\text {eq }}=\frac{2 \times 3}{2+3}=\frac{6}{5}=1.2 \Omega
$$
As capacitor blocks DC at steady state, so the resistor $4 \Omega$ is ineffective.
The $R_{\text {eq }}$ and $28 \Omega$ are in series, so total resistance of circuit,
$$
R_{T}=1.2+2.8=4 \Omega
$$
Current in circuit, $I=\frac{V}{R_{T}}=\frac{6}{4}=15 \mathrm{~A}$
Potential across the combination of $2 \Omega$ and $3 \Omega$ resistors $\quad V^{\prime}=15 \times 1.2=1.8 \mathrm{~V}$
$\therefore$ The steady state current in $2 \Omega$ resistor is
$$
I^{\prime}=\frac{V^{\prime}}{2}=\frac{1.8}{2}=0.9 \mathrm{~A}
$$
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