Electrostatics 5 Question 33

35. 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 charged 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

(1995,2M)

(a) zero

(b) 32CV2

(c) 256CV2

(d) 92CV2

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Answer:

Correct Answer: 35. (b)

Solution:

  1. The diagramatic representation of given problem is shown in figure.

The net charge shared between the two capacitors is

Q=Q2Q1=4CVCV=3CV

The two capacitors will have the same potential, say V.

The net capacitance of the parallel combination of the two capacitors will be

C=C1+C2=C+2C=3C

The potential difference across the capacitors will be

V=QC=3CV3C=V

The electrostatic energy of the capacitors will be

U=12CV2=12(3C)V2=32CV2



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