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Mixed Combination of Cells

Two capacitor...

Question

Two capacitors $C_{1}$ and $C_{2} = 2 C_{1}$ are connected in a circuit with a switch between them as shown in the figure. Initially the switch is open and $C_{1}$ holds charge Q. The switch is closed. At steady state, the charge on each capacitor will be :

Q, 2Q

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\frac{Q}{3}, \frac{2 Q}{3}

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\frac{3 Q}{2}, 3 Q

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\frac{2 Q}{3}, \frac{4 Q}{3}

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Solution

The correct option is B $\frac{Q}{3}, \frac{2 Q}{3}$
In steady state, potential across $C_{1} =$ potential across $C_{2}$ .
i.e, $\frac{Q_{1}}{C_{1}} = \frac{Q_{2}}{C_{2}} = \frac{Q_{2}}{2 C_{1}} \Rightarrow Q_{2} = 2 Q_{1}$
Also total charge , $Q = Q_{1} + Q_{2} = Q_{1} + 2 Q_{1} = 3 Q_{1}$
$∴ Q_{1} = \frac{Q}{3}, Q_{2} = \frac{2 Q}{3}$

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