Question

Find the ratio of the potential differences that must be applied across the parallel and series combination of two identical capacitors so that the energy stored in the two cases becomes the same.

Answer 1

$C_2=2C_1.$

parallel combination:$C_{e}q=3C_1$

Energy $E=\frac{1}{2}\times C_{e}q\times V1²=\frac{3}{2}\times C_{1}V1²$

Series combination:$C_{e}q=\frac{C_1{C}_2}{C_1+C_2}=\frac{2C_1}{3}$

Energy$E=\frac{1}{2}\times \frac{2}{3}\times C_1\times {V_2}^2=\frac{1}{2}\times C_1\times {V_2}^2$

Equating energies, we get $V_1:V_2=\sqrt{2}:3$

The plot of energy vs Capacitance:

This will be linear if Voltage applied is assumed to be constant.