Two capacitors, C₁ and C₂ 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 C₁ and C₂ respectively, so that the energy stored in the two cases becomes same. The ratio V_s to V_p is

Step-by-step solution

Let C₁ = C and C₂ = 2C . Equivalent capacitance in series combination: C_s = C₁ C₂ C₁ + C₂ = C 2C C + 2C = 2C 3 Equivalent capacitance in parallel combination: C_p = C₁ + C₂ = C + 2C = 3C Energy stored in series combination: U_s = 1 2 C_s V_s^2 = 1 2 ( 2C 3 ) V_s^2 Energy stored in parallel combination: U_p = 1 2 C_p V_p^2 = 1 2 (3C) V_p^2 Given that U_s = U_p : 1 2 ( 2C 3 ) V_s^2 = 1 2 (3C) V_p^2 2 3 V_s^2 = 3 V_p^2 V_s^2 V_p^2 = 9 2 V_s V_p = 3 2 The ratio V_s : V_p is 3 : 2 . Answer: 3 : 2