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Question

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?
 
  1. ϵ0A4dV2
  2. ϵ0AdV2
  3. ϵ0A2dV2
  4. 2ϵ0AdV2


Solution

The correct option is C ϵ0A2dV2
U1=12Q2c      (1)
U2=12Q2c1=12Q2c2=Q2c    (2)
W=U2U1,=12Q2c[21]
=12C2V2c=12CV2=12ϵ0AdV2

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