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Question

Two identical parallel plate capacitors A and B are connected to battery of V volts with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant K. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.

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Solution

Energy stored before introduction of dielectric,
UiA=UUiB=UUi=U+U=2U
After introduction of dielectric,
UfA=KU
UfB=UK
Uf=KU+UK=U(K+1K)
Ratio =UiUf=2UU(K+1K)=2KK2+1

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