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A parallel plate capacitor has plate are...

A parallel plate capacitor 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

`(3epsilon_0AV_0^2)/(d)`

B

`(epsilon_0AV_0^2)/(d)`

C

`(epsilon_0AV_0^2)/(3d)`

D

`(epsilon_0AV_0^2)/(d)`

Text Solution

Verified by Experts

The correct Answer is:
D
`U_i=1/2CV^2=1/2(Aepsilon_0)/dV_0^2and Q=CV=(Aepsilon_0V_0)/d`
`U_f=Q^2/(2C)=(A^2epsilon_0^2V_0^2)/(2d^2(Aepsilon_0)/(3d))=(3Aepsilon_0V_0^(2))/(2d)`
`W=U_f-U_i(Aepsilon_0V_0^2)/d`
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