A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V . Another capacitor of capacitance 2 C is similarly charge to a potential difference 2

Question

A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V . Another capacitor of capacitance 2 C is similarly charge to a potential difference 2 V . The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is

TestHub · Accepted Answer

From the figure. The net charge shared between the capacitors $Q^{'} = Q_{2} - Q_{2} = 4 C V - C V = 3 C V$
The two capacitors will have some potential, say $V^{'}$ . The net capacitance of the parallel combination of the two capacitors $C^{'} = C_{1} + C_{2} = C + 2 C + 3 C$ The potential of the capacitors $V^{'} = \frac{Q ^{'}}{C ^{'}} = \frac{3 CV}{3 C} = V$ The electrostatic energy of the capacitors $E^{'} = \frac{1}{2} C^{'} V^{'2} = \frac{1}{2} (3 C) V^{2} = \frac{3}{2} CV^{2}$

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JEE Main 2027 (Class 12)