A network of four capacitors of capacity equal to C1 = C , C2 = 2C , C3 = 3C and C4 = 4C are connected to a battery as shown in the figure. The ratio of the charges on C2 and C4 is ?

A network of four capacitors of capacity equal to C1 = C , C2 = 2C , C3 = 3C and C4 = 4C are connected to a battery as shown in the figure. The ratio of the charges on C2 and C4 is ?

(a) \( \frac{4}{7} \)

(b) \( \frac{3}{22} \)

(c) \( \frac{7}{4} \)

(d) \( \frac{22}{3} \)

Answer :  (b) \( \frac{3}{22} \)

\( \frac{1}{C_s} = \frac{1}{3C} + \frac{1}{2C} + \frac{1}{C} \)

\( = \frac{2 + 3 + 6}{6C} \)

\( \frac{1}{C_s} = \frac{11}{6C} \Rightarrow C_s = \frac{6C}{11} \)

\( Q = C V = \frac{6}{11} C \cdot V \)

\( \frac{Q_s}{Q_4} = \frac{\frac{6}{11} C \cdot V}{4 C \cdot V} \)

\( = \frac{3}{22} \)