A parallel plate capacitor whose capacitance C is 14 , pF is char… - Vidyadip

MCQ

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 porcelin 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)

A
$872$
B
$972$
C
$784$
✓
$864$

✓

Answer

Correct option: D.

$864$

d
$U _{ i }=\frac{1}{2} \times 14 \times 12 \times 12 pJ \quad\left(\because U =\frac{1}{2} CV ^{2}\right)$

$=1008 pJ$

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

Mechanical energy $=\Delta U$

$=1008-144$

$=864 pJ$

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