Two condensers one of capacity $\frac{C}{2}$ and other capacity $\mathrm{C}$ are connected to a battery of…
Two condensers one of capacity $\frac{C}{2}$ and other capacity $\mathrm{C}$ are connected to a battery of voltage $\mathrm{V}$ as shown. The work done in charging fully both the condensers is
$\frac{1}{2} \mathrm{CV}^2$
$\frac{3}{4} \mathrm{CV}^2$
$\frac{3}{2} \mathrm{CV}^2$
$2 \mathrm{CV}^2$
Solution
The two condensers are in parallel. Their equivalent capacitance is $\mathrm{C}_{\mathrm{e}}=\mathrm{C}+\frac{\mathrm{C}}{2}=\frac{3 \mathrm{C}}{2}$
The formula for work done is
$\begin{aligned}
& \mathrm{W}=\frac{1}{2} \mathrm{C}_{\mathrm{e}} \mathrm{V}^2 \\
& \mathrm{~W}=\frac{1}{2}\left(\frac{3 \mathrm{C}}{2}\right) \mathrm{V}^2 \\
& \mathrm{~W}=\frac{3}{4} \mathrm{CV}^2
\end{aligned}$
.
