A parallel plate capacitor whose capacitance C is 14pF is charged...

A parallel plate capacitor whose capacitance $C$ is $14pF$ is charged by a battery to a potential difference $V = 12V$ 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)

Correct answer

Step-by-step solution

${U}_{i} = \dfrac{1}{2} \times 14 \times 12 \times 12pJ\left(∵ U = \dfrac{1}{2}C{V}^{2}\right)$

$= 1008pJ$

${U}_{f} = \dfrac{1008}{7}pJ = 144pJ\left(∵ {C}_{m} = k{C}_{0}\right)$

Mechanical energy $= \DeltaU$

$= 1008 - 144$

$= 864pJ$

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