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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 2C is similarly charge to a potential difference 2V. 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 :

A
Zero
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B
32CV2
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C
256CV2
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D
92CV2
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Solution

## The correct option is B 32CV2From the figure.The net charge shared between the two capacitorsQ′=Q2−Q2=4CV−CV=3CVThe two capacitors will have some potential, say V′.The net capacitance of the parallel combination of the two capacitorsC′=C1+C2=C+2C+3CThe potential of the capacitorsV′=Q′C′=3CV3C=VThe electrostatic energy of the capacitorsE′=12C′V′2=12(3C)V2=32CV2.

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