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(B) Let $C_1 = C$ and $C_2 = 2C$. For series combination, the equivalent capacitance is $C_s = \frac{C_1 C_2}{C_1 + C_2} = \frac{C 	imes 2C}{C + 2C}

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$3 : \sqrt{2}$

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(B) Let $C_1 = C$ and $C_2 = 2C$. For series combination, the equivalent capacitance is $C_s = \frac{C_1 C_2}{C_1 + C_2} = \frac{C 	imes 2C}{C + 2C} = \frac{2C^2}{3C} = \frac{2}{3}C$. The energy stored in series is $U_s = \frac{1}{2} C_s V_s^2 = \frac{1}{2} (\frac{2}{3}C) V_s^2 = \frac{1}{3} C V_s^2$. For parallel combination, the equivalent capacitance is $C_p = C_1 + C_2 = C + 2C = 3C$. The energy stored in parallel is $U_p = \frac{1}{2} C_p V_p^2 = \frac{1}{2} (3C) V_p^2 = \frac{3}{2} C V_p^2$. Given that the energy stored is the same, $U_s = U_p$. $\frac{1}{3} C V_s^2 = \frac{3}{2} C V_p^2$. $\frac{V_s^2}{V_p^2} = \frac{3}{2} 	imes 3 = \frac{9}{2}$. Taking the square root on both sides, $\frac{V_s}{V_p} = \sqrt{\frac{9}{2}} = \frac{3}{\sqrt{2}}$. Thus, the ratio $V_s : V_p = 3 : \sqrt{2}$.

Two capacitors, $C_1$ and $C_2$ have their capacitances in the ratio $1:2$. $V_s$ and $V_p$ are the potential differences applied across the series and parallel combination of $C_1$ and $C_2$ respectively, so that the energy stored in the two cases becomes same. The ratio $V_s$ to $V_p$ is

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