\(C_{2}=\frac{3 \varepsilon_{0} A K_{2}}{d}\)

\(C_{3}=\frac{3 \varepsilon_{0} A K_{3}}{d}\)

\(\frac{1}{C_{e q}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}\)

\(\Rightarrow \quad C_{e q}=\frac{3 \varepsilon_{0} A K_{1} K_{2} K_{3}}{d\left(K_{1} K_{2}+K_{2} K_{3}+K_{3} K_{1}\right)}.........(i)\)

\(C_{1}=\frac{\varepsilon_{0} K_{1} A}{3 d}\)

\(C_{2}=\frac{\varepsilon_{0} K_{2} A}{3 d}\)

\(C_{3}=\frac{\varepsilon_{0} K_{3} A}{3 d}\)

\(C_{e q}^{\prime} =C_{1}+C_{2}+C_{3} \)

\( = \frac{{{\varepsilon _0}A}}{{3d}}({K_1} + {K_2} + {K_3}).........(ii)\)

Now,

\(\frac{{{E_1}}}{{{E_2}}} = \frac{{\frac{1}{2}{C_{eq}} \cdot {V^2}}}{{\frac{1}{2}C_{eq}^\prime {V^2}}} = \frac{{9{K_1}{K_2}{K_3}}}{{\left( {{K_1} + {K_2} + {K_3}} \right)\left( {{K_1}{K_2} + {K_2}{K_3} + {K_3}{K_1}} \right)}}\)