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Standard XII

Physics

Electric Potential at a Point in Space Due to a Point Charge Q

A capacitor o...

Question

A capacitor of capacitance $C_{0}$ is charged to a potential $V_{0}$ and is connected with another capacitor of capacitance C as shown. After closing the switch S, the common potential across the two capacitors becomes V. The capacitance C is given by

\frac{C_{0} (V_{0} - V)}{V_{0}}

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\frac{C_{0} (V - V_{0})}{V_{0}}

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\frac{C_{0} (V + V_{0})}{V}

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\frac{C_{0} (V_{0} - V)}{V}

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Solution

The correct option is D $\frac{C_{0} (V_{0} - V)}{V}$
The initial charge stored in the capacitor $C_{0}$ is $C_{0} V_{0}$ .
The final charge stored in capacitor $C_{0}$ when potential $V$ lies across it is $C_{0} V$ .
The final charged stored in capacitor $C$ is $C V$ .
Since the total charge must be conserved,
$C_{0} V_{0} = C_{0} V + C V$
$⟹ C = \frac{C_{0} (V_{0} - V)}{V}$

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A capacitor of capacitance C0 is charged to a potential V0 and is connected with another capacitor of capacitance C as shown. After closing the switch S, the common potential across the two capacitors becomes V. The capacitance C is given by

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