Question

A network of four capacitors of capacity equal to $C_1=C,C_2=2C,C_3=3C$ and $C_4=4C$ are connected to a battery as shown in the figure. The ratio of the charges on $C_2$ and $C_4$ is:

Answer 1

Capacitor $C_1,C_2,C_3$ are in series

Resultant capacitance $\frac{1}{C_s}=\frac{1}{C}+\frac{1}{2C}+\frac{1}{3C}$

$\therefore C_s=\frac{6C}{11}$

For capacitors in series charge on each one each capacitor is equal

Charge on capacitor $C_2$ is $Q^{\prime }=\frac{6}{11}CV$

Charge on capacitor $C_4$ is $Q=4CV$

\dfrac{Q'}{Q}=\dfrac{6}{11 \times4}=\dfrac{3}{22}$

The ratio of charges on $C_2$ and $C_4$ is $\frac{3}{22}$