Question

Consider the arrangement of three plates X, Y and Z each of the area $A$ and separation $d$. The energy stored when the plates are fully charged is

• A. ${\epsilon }_{o}A\frac{V^2}{2d}$
• B. ${\epsilon }_{o}A\frac{V^2}{d}$
• C. $2{\epsilon }_{o}A\frac{V^2}{d}$
• D. $3{\epsilon }_{o}A\frac{V^2}{d}$

Answer 1

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

This circuit will contain two capacitors with capacitance $C=\frac{A{ϵ}_0}{d}$ and they are in parallel.
Thus, net capacitance is $C_{eq}=C+C=2C=\frac{2A{ϵ}_0}{d}$
Energy stored $U=\frac{1}{2}{C}_{eq}{V}^2=\frac{1}{2}\left(\frac{2A{ϵ}_0}{d}\right)(V{)}^2=\frac{A{ϵ}_0{V}^2}{d}$