First slide

Capacitance

Question

Two condensers, one of capacity C and the other of capacity C/2, are connected to a V volt battery, as shown. The work done in charging fully both the condensers is

Easy

A

2CV²
B

$\frac{1}{4} {CV}^{2}$
C

$\frac{3}{4} {CV}^{2}$
D

$\frac{1}{2} {CV}^{2}$

Solution

Q = CV, In parallel, V = constant.
Net capacitance of circuit= $C + \frac{C}{2} = \frac{3 C}{2}$
Work done by the battery to fully charge both the capacitors = $\frac{1}{2} \times \frac{3 C}{2} \times V^{2} = \frac{3 C V^{2}}{4}$

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