A parallel plate condenser with plate separation ‘d’ and plate are

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A parallel plate condenser with plate separation ‘d’ and plate area A is connected to a battery and charged to a potential V. Then the battery is disconnected and with insultated handles the plate separation is increased to 2d. Work done in the process will be?

Options:

A . ϵ0A4dV2

B . ϵ0AdV2

C . ϵ0A2dV2

D . 2ϵ0AdV2

Answer: Option C
:
C

U_{1} = \frac{1}{2} \frac{Q^{2}}{c} - - - - - - - (1)

U_{2} = \frac{1}{2} \frac{Q^{2}}{c_{1}} = \frac{1}{2} \frac{Q^{2}}{\frac{c}{2}} = \frac{Q^{2}}{c} - - - - - (2)

W = U_{2} - U_{1}, = \frac{1}{2} \frac{Q^{2}}{c} [2 - 1]

= \frac{1}{2} \frac{C^{2} V^{2}}{c} = \frac{1}{2} C V^{2} = \frac{1}{2} \frac{ϵ_{0} A}{d} V^{2}

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