A 10F and a 32F capacitor are connected in series across a 2

A 10-F and a 3.2-F capacitor are connected in series across a 24-V battery. What voltage is required to charge a parallel combination of the two capacitors to the same total energy?

Solution

for series combination

Ceq = C1*C2/(C1+C2)

Ceq = 10*3.2/13.2 = 2.42 F

V = 24

U = 0.5*CV^2 = 0.5*2.42*24^2

U = 696.96 J

2.

for parallel combination

Ceq = C1 + C2

Ceq = 10 + 3.2 = 13.2 F

U = 0.5*C*V^2

V = sqrt(2U/C)

V = sqrt(2*696.96/13.2)

V = 10.28 V