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 U_P U_T is :
A. 1/6
From the given circuit diagram, capacitors P and Q are connected in series, and their combination is connected in parallel with capacitor S. The equivalent capacitance of the series combination of P and Q is: C_ PQ = C C C + C = C 2 The total equivalent capacitance of the system is: C_ eq = C_ PQ + C_S = C 2 + C = 3C 2 The total energy stored in the system is: U_T = 1 2 C_ eq V^2 = 1 2 ( 3C 2 ) V^2 = 3 4 C V^2 Since capacitors P and Q are identical and connected in series across the battery of voltage V, the potential difference across each of them is equal. Thus, the voltage across capacitor P is: V_P = V 2 The energy stored in capacitor P is: U_P = 1 2 C_P V_P^2 = 1 2 C ( V 2 )^2 = 1 8 C V^2 The ratio of the energy stored in capacitor P to the total energy stored in the system is: U_P U_T = 1 8 C V^2 3 4 C V^2 = 1 8 4 3 = 1 6 Answer: 1/6
Related: Physics — Capacitance · All PYQ Banks