The figure shows a capacitor of capacitance $C$ connected to a battery via a switch, having a total charge $Q$ on it, in steady-state. When the switch $S$ is turned from position $A$ to position $B$ , the energy dissipated in the circuit is

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Q 0 = C ε Q 1 C = Q 2 3 C Q 1 + Q 2 = Q 0 ⇒ Q 1 = Q 0 4 ; Q 2 = 3 Q 0 4 Energy dissipated, E = 1 2 Q 0 2 C - 1 2 Q 1 2 C - 1 2 Q 2 2 3 C = 1 2 C Q 0 2 - Q 0 2 16 - 9 Q 0 2 3 × 16 = Q 0 2 32 C 16 - 1 - 3 = 3 8 Q 0 2 C

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