Two capacitors of capacitances, $C_1$ and $C_2$, are connected in parallel. If two-third of the total charge is shared by capacitor $C_1$. The ratio of $C_1$ to $C_2$ is given by

2 : 1

The correct answer is Option (2) → 2 : 1

For capacitors in parallel, voltage across each is the same:

$Q_1 = C_1 V$, $Q_2 = C_2 V$, total charge $Q = Q_1 + Q_2 = (C_1 + C_2) V$

Given: $Q_1 = \frac{2}{3} Q = \frac{2}{3} (C_1 + C_2) V$

Also, $Q_1 = C_1 V$

So, $C_1 V = \frac{2}{3} (C_1 + C_2) V \Rightarrow C_1 = \frac{2}{3} (C_1 + C_2)$

$3 C_1 = 2 C_1 + 2 C_2 \Rightarrow C_1 = 2 C_2$

∴ Ratio $C_1 : C_2 = 2 : 1$