First slide

Capacitance

Question

A capacitor is charged to store an energy U. The charging battery is disconnected. An identical capacitor is now connected to the first capacitor in parallel. The energy in each of the capacitor is

Easy

A

U/4
B

U/2
C

U
D

3U/2

Solution

Initial energy E₁ is given by
$E_{1} = \frac{1}{2} {CV}^{2} = U$
The total final energy E₂ is given by
$E_{2} = \frac{1}{2} (C + C) {(\frac{CV}{C + C})}^{2} = \frac{1}{4} {CV}^{2}$
or $E_{2} = \frac{U}{2}$
This energy is shared by both capacitors. Therefore, the energy of each capacitor is U/4.

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