The plate separation in a parallel plate condenser and plate area is A. If it is charged to V volt battery is diconnected then the work done increasing the plate separation to 2d will be

Options

A. `(3)/(2) (epsi_(0)AV^(2))/(d)`
B. `(epsi_(0)AV^(2))/(d)`
C. `(2epsi_(0)AV^(2))/(d)`
D. `(epsi_(0)AV^(2))/(2d)`

Answer

D

Explanation

As battery is disconnected, charge remains the process. Work done= final potential energy- initial potentical energy
`=(Q^(2))/(2C.)- (Q^(2))/(2C^(@))`
`=(Q^(2))/(2) {(1)/(C.)- (1)/(C^(@))}`
whre, `Q= CV = (A epsi_(0)V)/(d) C^(@)= (A epsi_(0))/(d)`
`C.= (A epsi_(0))/(2d)`
Now, work done =`(epsi_(0)AV^(2))/(2d)`