Question

A parallel plate capcitor has plate area `A` and separation `d`. It is charged to a potential difference `V_(0)`. The charging battery is disconnected and the plates are pulled apart to three times the initial separation. The work required to separate the plates is
A. `(3 epsilon_(0)AV_(0)^(2))/(d)`
B. `(epsilon_(0)AV_(0)^(2))/(2d)`
C. `(epsilon_(0)AV_(0)^(2))/(3d)`
D. `(epsilon_(0)AV_(0)^(2))/(d)`

Answer 1

Correct Answer - D
Work done `W = U_(f) - U_(i)`
`U_(i) = (1)/(2) CV_(0)^(2)` and `U_(f) = (1)/(2) ((C ))/(3). (3V_(0))^(2) = 3 xx (1)/(2) CV_(0)^(2)`
So `W = (epsilon_(0) AV_(0)^(2))/(d)`