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)

Question

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)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

U i =(1/2) × 14 × 12 × 12 pJ (∵ U =(1/2) CV 2) =1008 pJ U f =(1008/7) pJ =144 pJ (∵ C m = kC 0) Mechanical energy =Δ U =1008-144 =864 pJ

Ui​=21​×14×12×12pJ(∵U=21​CV2) =1008pJ Uf​=71008​pJ=144pJ(∵Cm​=kC0​) Mechanical energy =ΔU =1008−144 =864pJ

$U_{i} = \frac{1}{2} \times 14 \times 12 \times 12 p J (∵ U = \frac{1}{2} C V^{2})$
$= 1008 p J$
$U_{f} = \frac{1008}{7} p J = 144 p J (∵ C_{m} = k C_{0})$
Mechanical energy $= Δ U$
$= 1008 - 144$
$= 864 p J$