In the circuit shown- the cell is ideal- with emf-15 v- Each resistance is of 3- The potential difference across the capacitor is

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Electrical Oscillations

In the circui...

Question

In the circuit shown, the cell is ideal, with $e m f = 15 v$ . Each resistance is of $3 Ω$ . The potential difference across the capacitor is

zero

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12V

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15V

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Solution

The correct option is C 12V
As a fully charged capacitor draws no current so no current flow through resistor on right. The current flow through remaining resistors as shown in figure.
Applying Kirchhoff's law
For loop ABEFGA: $R i_{1} + R (i_{1} + i_{2}) = 15$
$⟹ 2 i_{1} + i_{2} = \frac{15}{R} = \frac{15}{3} = 5 . . . . (1)$
For loop ABCDEFGA: $R i_{2} + R i_{2} + R (i_{1} + i_{2}) = 15$
$⟹ i_{1} + 3 i_{2} = \frac{15}{R} = \frac{15}{3} = 5 . . . . . (2)$
From (1) and (2):
$i_{1} + 3 (5 - 2 i_{1}) = 5 \Rightarrow 5 i_{1} = 10 \Rightarrow i_{1} = 2 A$
Putting, $i_{1} = 2$ in (1),
$\Rightarrow i_{2} = 5 - 2 (2) = 1 A$
Thus, Potential across capacitor is: $V_{c} = R i_{2} + R (i_{1} + i_{2}) = (3 \times 1) + 3 (2 + 1) = 3 + 9 = 12 V$

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