Two spherical conductors each of capacity `C` are charged to potetnial `V` and `-V`. These are then conneted by means of a fine wire. The loss of energy will be

Options

A. `(1)/(2)CV^(2)`
B. zero
C. `CV^(2)`
D. `2CV^(2)`

Answer

C

Explanation

When two charged spheres of capacities `C_(1) and C_(2)` are joined together the loss is energy
`DeltaU=U_(i)-U_(f)=(1)/(2)(C_(1)C_(2))/((C_(1)+C_(2)))(V_(1)-V_(2))^(2)`
In this case, `C_(1)=C_(2)`
`therefore Delta U=(1)/(2)(CxxC)/(2C)[V-(-V)]`
`=(1)/(2)xx(1)/(2)Cxx4V^(2)=CV^(2)`