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Q.

The capacities of two conductors are  C1 and C2  and their respective potentials are V1  and V2 . If they are connected by a thin wire, then the loss of energy will be given by

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a

C1C2V1+V22C1+C2

b

C1C2V1−V22C1+C2

c

C1C2V1−V222C1+C2

d

C1+C2V1−V2C1+C2

answer is C.

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Detailed Solution

Initial energy  Ui=12C1V12+12C2V22, final energy Uf=12C1+C2V2   (Where V=C1V1+C2V2C1+C2) Hence energy loss  ΔU=Ui−Uf  = 12C1V12+12C2V22  - C1+C22C1V1+C2V2C1+C22 =C1C22C1+C2V1−V22
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The capacities of two conductors are  C1 and C2  and their respective potentials are V1  and V2 . If they are connected by a thin wire, then the loss of energy will be given by