The ratio of potential difference that must be applied across parallel and series combination of two capacitors C ₁ and C ₂ with their capacitance in the ratio 1: 2 so that energy stored in these two cases becomes same is

Step-by-step solution

Given: C ₁: C ₂=1: 2 aligned C ₂ & =2 C ₁ C _ P & = C ₁+ C ₂= C ₁+2 C ₁=3 C ₁ C _ S & = C ₁ C ₂ C ₁+ C ₂ = 2 C ₁^2 3 C ₁ = 2 3 C ₁ aligned Let V_P and V_S be the potentials applied across the parallel and series combinations respectively, then using E = 1 2 CV ^2 we can write, aligned & 1 2 C _ P V _ P ^2= 1 2 C _ S V _ s ^2 & V _ P ^2 ~V _ S ^2 = C _ S C _ P & V _ P V _ S = 2 3 C ₁ 3 C ₁ = 2 3 aligned