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

Options

A. `(epsilon_(0)AV_(0)^(2))/(3d)`
B. `(epsilon_(0)AV_(0)^(2))/(2d)`
C. `(epsilon_(0)AV_(0)^(2))/(4d)`
D. `(epsilon_(0)AV_(0)^(2))/(d)`

Answer

D

Explanation

`C = (epsilon_(0)A)/(d)` and charge `Q = CV_(0)`
When spacing is made (3d), `C. = (epsilon_(0)A)/(3d) = (C )/(3)`
As battery is disconnected, charge Q is constant `:.` Workdone = Final energy - Initial energy
`= (Q^(2))/(2C.) - (Q^(2))/(2C)`
`= (Q^(2) xx 3)/(2C) - (Q^(2))/(2C) = (2 xx Q^(2))/(2C) = ((CV_(0))^(2))/(C ) = CV_(0)^(2) = (epsilon_(0)AV_(0)^(2))/(d)`