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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 $\frac{U_P}{U_T}$ is:
Detailed Solution
P and Q are in series, so each gets charge $\frac{CV}{2}$; S is directly across V with charge CV. $U_P=\frac{1}{2}\frac{(CV/2)^2}{C}=\frac{1}{8}CV^2$. $U_T=\frac{1}{8}CV^2+\frac{1}{8}CV^2+\frac{1}{2}CV^2=\frac{3}{4}CV^2$. $\frac{U_P}{U_T}=\frac{1/8}{3/4}=\frac{1}{6}$.