Q 12-02-001NEETNEET 2026Top questionMedium
Three identical capacitors $P$, $Q$ and $S$, each of the capacitance $C$, are connected to a battery of voltage $V$, as shown in the figure. If the energy stored in the capacitor $P$ and total energy stored in the system are $U_P$ and $U_T$, respectively, then the ratio $\dfrac{U_P}{U_T}$ is :
Answer: (D) $1/6$
$P$ and $Q$ are in series (equivalent $C/2$), and this combination is in parallel with $S$ across the battery.
Charge on $P$ (and $Q$): $q = \dfrac{C}{2}V$, so
$$U_P = \frac{q^2}{2C} = \frac{C^2V^2/4}{2C} = \frac{CV^2}{8}$$
Equivalent capacitance: $C_{eq} = \dfrac{C}{2} + C = \dfrac{3C}{2}$, so
$$U_T = \frac{1}{2}\cdot\frac{3C}{2}V^2 = \frac{3CV^2}{4}$$
$$\frac{U_P}{U_T} = \frac{1/8}{3/4} = \frac{1}{6}$$
Solution by Sreeraj P, M.Sc Physics