8) Consider a capacitor of value C O charged by a battery with a voltage differe

Question

8) Consider a capacitor of value CO charged by a battery with a voltage difference VO. A dielectric with a dielectric constant of K is introduced between the plates of the capacitor. Calculate the ratio of final energy (with dielectric) to the initial energy (no dielectric) for the following two scenerios:
i) the capacitor remains connected to the battery.
ii) the capacitor is disconnected from the battery before the insertion of the dielectric.

Comment on why these energy ratios are different for the two scenerios.

Explanation / Answer

1) before insertion

Energy = 0.5 x C x V2

after insertion

Energy = 0.5 x K x C X V2

therefore

ration of final and initial energy = K ( answer)

2)

In this case as capacitor is disconnected from battery charge is conserved

initial energy E = Q2/2C

after insertion

Final energy E = Q2/2KC

ratio of final energy and initial energy = 1/K ( answer )

any doubts u can comment below

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