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 charged 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

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 charged 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, zero, 25 6 CV 2, 9 2 CV 2, 3 2 CV 2

MARKS App · Accepted Answer

The diagramatic representation of given problem is shown in the figure. The net charge shared between the two capacitors is, Q ' = Q 2 - Q 1 = 4 CV - CV = 3 CV The two capacitors will have the same potential, say V ' . The net capacitance of the parallel combination of the two capacitors will be, C ' = C 1 + C 2 = C + 2 C = 3 C The potential difference across the capacitors will be, V ' = Q ' C ' = 3 CV 3 C = V The electrostatic energy of the capacitors will be, U ' = 1 2 C ' V ' 2 = 1 2 3 C V 2 = 3 2 CV 2

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