In the circuit shown in Figure- the cell is ideal with emf 15 V- Each resistance is of 3 - - The potential difference across the capacitor in steady state is

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Question

In the circuit shown in Figure, the cell is ideal with emf 15 V. Each resistance is of $3 Ω$ . The potential difference across the capacitor in steady state is

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9 V

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12 V

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15 V

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Solution

The correct option is C 12 V
In the steady state, no current flow through C. So no current will pass through rightmost resistor. The current flow is shown in figure.
By apply Kirchhoff's law
for loop ABEFGA: $15 = 3 i_{1} + 3 (i_{1} + i_{2}) \Rightarrow 2 i_{1} + i_{2} = 5 . . . (1)$ and
for loop ABCDEFGA: $15 = R i_{2} + R i_{2} + R (i_{1} + i_{2}) \Rightarrow i_{1} + 3 i_{2} = 5 . . . (2)$
From (1) and (2), $i_{1} + 3 (5 - 2 i_{1}) = 5$
or $5 i_{1} = 10 \Rightarrow i_{1} = 2 A$ and $i_{2} = 5 - 2 (2) = 1 A$
Potential across C $= V_{D F} = V_{D E} + V_{E F}$
or $V_{C} = R i_{2} + R (i_{1} + I_{2}) = 3 (1) + 3 (2 + 1) = 12 V$

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In the circuit shown in Figure, the cell is ideal with emf 15 V. Each resistance is of 3Ω . The potential difference across the capacitor in steady state is

In the circuit shown in Figure, the cell is ideal with emf 15 V. Each resistance is of $3 Ω$ . The potential difference across the capacitor in steady state is