What is the charge on each capacitor in the figure if ΔV=20V?
Q1, Q2, Q3 =
What is the potential difference across each capacitor in the figure
ΔV1, ΔV2, ΔV3 =
The trick is caps in series have the same charge and Q = VC.
V1C1 = V2C2 = V3C3 and V1+V2+V3 = 20 = V1+V1(C1/C2) + V1(C1/C3) = V1(1+12/4+12/6) = 6V1
ΔV1 = 20/6 = 10/3 V,
ΔV2 = 10/3 * 12µF/4µF = 10 V,
ΔV3 = 10/3 * 12µF/6µF = 20/3 V
The charge on all three caps = C1V1 = 10/3 *12µF = Q1 = 40µC <------
Q2 = V2C2 = 10*4µF = 40µC
Q3 = V3C3 = 20/3*6µF = 40µC
Check Ceq = 1/[1/12+1/4+1/6) = 2µF ---> Q = CeqV =2*20 = 40µC