Question

Three plates $P,Q,R$ each of area $A$ have separation $d$ between $P$ and $Q$ and also between $Q$ and $R$. The energy stored when the plates are fully charged is:-

• A. $\frac{2{\epsilon }_{0}A{V}^2}{d}$
• B. $\frac{{\epsilon }_{0}A{V}^2}{d}$
• C. $\frac{{\epsilon }_{0}A{V}^2}{2d}$
• D. $\frac{{\epsilon }_{0}A{V}^2}{4d}$

Answer 1

The correct option is B $\frac{{\epsilon }_{0}A{V}^2}{d}$

This can be redrawn as:

Both the capacitors are connected in parallel.
The equivalent capacitance,
$C_{eq}=2C=2\left(\frac{{\epsilon }_{0}A}{d}\right)$

Energy stored in the combination,
$U=\frac{C_{eq}{V}^2}{2}$
$U=\frac{1}{2}\left(\frac{2{\epsilon }_{0}A}{d}\right)V^2=\frac{{\epsilon }_{0}A{V}^2}{d}$