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Question

Two identical capacitors have the same capacitance C. One of them is charged to potential V1 and the other to V2. The negative ends of the capacitors are connected together . When the positive ends are also connected, the decrease in energy of the combine system is

A
C4(V21V22)
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B
C4(V21+V22)
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C
C4(V1V2)2
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D
C4(V1+V2)2
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Solution

The correct option is C C4(V1V2)2
Initial energy of the combined system
U1=12CV21+12CV21=C2(V21+V22)
On joining the two condensers in parallel, common potential.
V=CV1+CV2C+C=V1+V22
Final energy of the combined system
U2=12(C+C)(V1+V22)2
Decrease in energy
ΔU=U1U2=12C(V21+V22)12(2C)(V1+V22)2
=C2[2(V21+V22)(V1+V2)2]=C4[2V21+2V22V21V222V1+V2]=C4(V1V2)2

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