Question

Two condensers, one of capacity $C$ and other of capacity $\frac{C}{2}$ are connected to a $V$ - volt battery as shown in the figure. The work done in charging both the condensers fully is

• A. $\frac{1}{4}C{V}^2$
• B. $\frac{3}{4}C{V}^2$
• C. $\frac{1}{2}C{V}^2$
• D. $2C{V}^2$

Answer 1

The correct option is B $\frac{3}{4}C{V}^2$

As the capacitors are fully charged, the work done will be equal to the energy stored in a capacitor which is given by
$E=\frac{1}{2}C{V}^2$
And as they are connected in parallel, therefore the potential difference across each will be the same.
So for $1^{st}$ capacitor
$E_1=\frac{1}{2}C{V}^2$

For capacitor $2^{nd}$
$E_2=\frac{1}{2}\frac{C}{2}{V}^2=\frac{1}{4}C{V}^2$

So work done is
$W=E_1+E_2$
$\Rightarrow W=\frac{1}{2}C{V}^2+\frac{1}{4}C{V}^2=\frac{3}{4}C{V}^2$.