A network of 4 capacitors is connected to a battery as shown. The ratio of the charges on capacitors \(\mathrm{C}_{2}\) and \(\mathrm{C}_{4}\) is

Equivalent capacitance for three capacitors \(\mathrm{C}_{1}, \mathrm{C}_{2}\) and \(\left.\mathrm{C}_{3}\right)\) in series is given by
\(\begin{array}{l}
\frac{1}{\mathrm{C}_{\mathrm{eq}}}=\frac{1}{\mathrm{C}_{1}}+\frac{1}{\mathrm{C}_{2}}+\frac{1}{\mathrm{C}_{3}}=\frac{\mathrm{C}_{2} \mathrm{C}_{3}+\mathrm{C}_{3} \mathrm{C}_{1}+\mathrm{C}_{\mathrm{C}} \mathrm{C}_{2}}{\mathrm{C}_{\mathrm{C}} \mathrm{C} \mathrm{C}_{3}} \\
\Rightarrow \mathrm{C}_{\mathrm{eq}}=\frac{\mathrm{C}_{1} \mathrm{C}_{2} \mathrm{C}_{3}}{\mathrm{C}_{1} \mathrm{C}_{2}+\mathrm{C}_{2} \mathrm{C}_{3}+\mathrm{C}_{3} \mathrm{C}_{1}} \\
\Rightarrow \mathrm{C}_{\mathrm{eq}}=\frac{\mathrm{C}(2 \mathrm{C})(3 \mathrm{C})}{\mathrm{C}(2 \mathrm{C})+(2 \mathrm{C})(3 \mathrm{C})+(3 \mathrm{C}) \mathrm{C}}=\frac{6}{11} \mathrm{C}
\end{array}\)
\(\Rightarrow\) Charge on capacitors \(\left(\mathrm{C}_{1}, \mathrm{C}_{2} \& \mathrm{C}_{3}\right)\) in series
\(=\mathrm{C}_{\mathrm{eq}} \mathrm{V}=\frac{6 \mathrm{C}}{11} \mathrm{v}\)
Charge on capacitor \(\mathrm{C}_{4}=\mathrm{C}_{4} \mathrm{~V}=4 \mathrm{CV}\)
\(\frac{\text { Charge } \mathrm{onC}_{2}}{\text { Charge } \mathrm{onC}_{4}}=\frac{\frac{6 \mathrm{C}}{11} \mathrm{~V}}{4 \mathrm{CV}}=\frac{6}{11} \times \frac{1}{4}=\frac{3}{22}\)