A parellel plate capacitor with plate speration d is charged with a battery so that energy stored is U. If a plate of dielectric K and thickness d is placed betweeen the plates of capacitor and battery remains connected. The work by battery is?

Options:

  1. KU

  2. 2U(K - 1)

  3. U(K - 1)

  4. 2KU

1 Answer
Ananda Dasgupta
Mar 14, 2018

2U(K−1)

Explanation:

The energy stored in a capacitor is given by U=12CV2 where C is the capacitance and V is the potential.

When the dielectric is introduced, the capacitance increases by a factor of K, but since the battery is still connected, the potential V does not change.

So, the charge stored in the capacitor grows from CV to K×CV. The battery must pump in this extra charge (K−1)CV at the constant voltage V - and the work it must do for this is
(K−1)CV×V=(K−1)CV2=2(K−1)U

Note that this is twice the energy gained by the capacitor.

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