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 :

Step-by-step solution

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 pote