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Question

A condenser of capacity C1 is charged to a potential V0. The electrostatic energy stored in it is U0. It is connected to another uncharged condenser of capacity C2 in parallel. The energy dissipated in the process is :

A
C2C1+C2U0
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B
C1C1+C2U0
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C
(C1C2C1+C2)U0
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D
C1C22(C1+C2)U0
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Solution

The correct option is A C2C1+C2U0
Initial energy, Ui=U0=12C1V20
Initial charge of the system is Qi=C1V0.
After connecting another capacitor the final charge Qf=(C1+C2)Vc where Vc= common potential after connecting.
As total charge is conserved , Qi=QfC1V0=(C1+C2)Vc
Vc=C1V0C1+C2
Final energy , Uf=12(C1+C2)V2c=12(C1+C2)(C1V0C1+C2)2=C1U0C1+C2
Energy dissipation =UiUf=U0C1U0C1+C2=C2U0C1+C2

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