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Q.

A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V=12 V between its plates. The charging battery is now disconnected and a porcelain plate with k=7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of _______ pJ. (Assume no friction)

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answer is 864.

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Detailed Solution

Initial energy stored in the capacitor,
$U_{i} = \frac{1}{2} \times 14 \times 12 \times 12 pJ = 1008 pJ$
After inserting porcelain plate, k=7
$\begin{array}{l} U_{f} = \frac{1}{2} \frac{{CV}^{2}}{k} = 144 pJ \\ △ U = U_{i} - U_{f} = 1008 - 144 \\ = 864 pJ \end{array}$
Constant M.E. with which plate oscillates back and forth

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