The effective capacitance of two capacitors of capacitances C₁^' and C₂^' (with ${{\mathrm{C}}_2}^{\mathrm{\prime }}>{{\mathrm{C}}_1}^{\mathrm{\prime }}$) connected in parallel is 25/6 times the effective capacitance when they are connected in series. The ratio $\frac{{\mathrm{C}}_2^{\mathrm{\prime }}}{{\mathrm{C}}_1^{\mathrm{\prime }}}$ is :

$$\begin{gathered} {\mathrm{C}}_1^{\mathrm{\prime }}+{\mathrm{C}}_2^{\mathrm{\prime }}=\frac{25}{6}\left(\frac{{\mathrm{C}}_1^{\mathrm{\prime }}{\mathrm{C}}_2^{\mathrm{\prime }}}{{\mathrm{C}}_1^{\mathrm{\prime }}+{\mathrm{C}}_2^{\mathrm{\prime }}}\right) \\ \Rightarrow 6{\left({\mathrm{C}}_1^{\mathrm{\prime }}+{\mathrm{C}}_2^{\mathrm{\prime }}\right)}^2=25{\mathrm{C}}_1^{\mathrm{\prime }}{\mathrm{C}}_2^{\mathrm{\prime }} \\ \Rightarrow 6{\mathrm{C}}_1^{\mathrm{\prime }2}+6{\mathrm{C}}_2^{\mathrm{\prime }2}-13{\mathrm{C}}_1^{\mathrm{\prime }}{\mathrm{C}}_2^{\mathrm{\prime }}=0 ...\left(1\right) \\ \mathrm{Let} {\mathrm{C}}_2^{\mathrm{\prime }}={\mathrm{xC}}_1^{\mathrm{\prime }} \\ \mathrm{eqn}. \left(1\right) \mathrm{becomes} 6{\mathrm{x}}^2-13\mathrm{x}+6=0 \\ \mathrm{x}=3/2\text{ or }\frac{2}{3} \\ \mathrm{Since} {\mathrm{C}}_2^{\mathrm{\prime }}>{\mathrm{C}}_1^{\mathrm{\prime }} \\ \mathrm{x}=\frac{2}{3} \mathrm{is} \mathrm{not} \mathrm{possible}. \end{gathered}$$