Three capacitors of capacitances 25 F , 30 F and 45 F are connected in parallel to a supply of 100 ~V . Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is 9 x E . The value of x is _____.

Step-by-step solution

In parallel combination : Potential difference is same across all aligned & Energy = 1 2 ( C ₁+ C ₂+ C ₃ ) V ^2 & = 1 2 (25+30+45) (100)^2 10⁻⁶=0.5= E aligned In series combination: Charge is same on all. aligned & 1 C _ equ = 1 C ₁ + 1 C ₂ + 1 C ₃ = 1 25 + 1 30 + 1 45 & 1 C _ equ = (18+15+10) 450 = 43 450 C _ equ = 450 43 & Energy = Q ^2 2 C ₁ + Q ^2 2 C ₂ + Q ^2 2 C ₃ & = Q ^2 2 [ 1 C ₁ + 1 C ₂ + 1 C ₃ ] & ( V C _ equ )^2 2 1 C _ equ = V ^2 C _ equ 2 & (100)^2 2 450 43 10⁻⁶ & 4.5 86 = 9 x E = 9 x 0.5 x =86 aligne