Question 424: Electrostats & Capacitance

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)

Accepted Answer

$${U_i} = {1 \over 2}c{v^2}$$
$$ = {1 \over 2} 	imes 14 	imes {(12)^2}$$ pJ
= 1008 pJ
$${U_f} = {{{Q^2}} \over {2kC}}$$
$$ = {{{{(14 	imes 12)}^2}} \over {2 	imes 7 	imes 14}}$$
= 144 pJ
oscillating energy = U
i
$$-$$ U
f
= 1008 $$-$$ 144
= 864 pJ

Electrostats & Capacitance

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