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A parallel plate capacitor of plate are ...

A parallel plate capacitor of plate are A and plate separation d is charged by a battery of voltage V. The battery is then disconnected. The work needed to pull the plates to a separation 2d is

A

`(Av^(2)epsilon_(0))/(d)`

B

`(2Av^(2)epsilon_(0))/(d)`

C

`(Av^(2)epsilon_(0))/(2d)`

D

`(3Av^(2)epsilon_(0))/(2d)`

Text Solution

Verified by Experts

The correct Answer is:
3
`Q=DeltaU=(Q^(2))/(2C_(r))-(Q^(2))/(2C_(i))`
`=(Q^(2))/(2)((1)/(C_(r))-(1)/(C_(i)))`
`=(Q^(2))/(2)((2d)/(epsilon_(0)A)-(d)/(epsilon_(0)A))`
`=(Q^(2))/(2).(d)/(epsilon_(0)A)`
`=(in_(0)AV^(2))/(2d)`
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