The potential difference that must be applied across the series and parallel combination of 4 identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is

The equivalent capacitance for series combination,
\(C_1=\frac{C}{4}...(i)\)
\(\therefore \quad\) Potential energy, \(\mathrm{U}_1=\frac{1}{2} \mathrm{C}_1 \mathrm{~V}_1^2\)...(ii)
The equivalent capacitance for parallel combination,
\(C_2=4 C...(iii)\)
\(\therefore \quad\) Potential energy, \(U_2=\frac{1}{2} C_2 V_2^2\)...(iv)
Given that, \(\mathrm{U}_1=\mathrm{U}_2\)
\(\begin{array}{ll}
\therefore & \mathrm{C}_1 \mathrm{~V}_1^2=\mathrm{C}_2 \mathrm{~V}_2^2 \\
\therefore & \frac{\mathrm{~V}_1}{\mathrm{~V}_2}=\sqrt{\frac{\mathrm{C}_2}{\mathrm{C}_1}} \\
\therefore & \frac{\mathrm{~V}_1}{\mathrm{~V}_2}=\sqrt{\frac{4 \mathrm{C}}{\frac{\mathrm{C}}{4}}}=\sqrt{\frac{16}{1}} \\
\therefore & \frac{\mathrm{~V}_1}{\mathrm{~V}_2}=\frac{4}{1}
\end{array}\)
...(From(ii) and (iv))
...(From (i) and (iii))