Three capacitors with capacitances C1 38 F C2 43 F and C3

Three capacitors, with capacitances C1 = 3.8 ?F, C2 = 4.3 ?F, and C3 = 5.7 ?F, are connected to a 20 -V voltage source, as shown in the figure. What is the charge on capacitor C2 ?

Solution

for parallel combination:

Cp = C2 + C3 = 4.3 + 5.7 = 10 uF

for series comb.:

Ceq = C1*Cp/(C1+Cp)

Ceq = 3.8*10/(13.8) = 2.75 uF

Ceq = 2.75*10^-6 F

we know that

Q = CV

Qt = Ceq*V = 2.75*10^-6*20 = 55*10^-6 C

Now first we need to calculate Voltage in parallel comb.

Cp = 10 uF

Vp = Qp/Cp = 55*10^-6/(10*10^-6)

Vp = 5.5 V

Now we know that Voltage V is common between parallel capacitors.

V in C2 = 5.5 V

V in C3 = 5.5 V