Question

What is the charge stored in C_1? What is the charge stored in C_2? What is the charge stored in C_3? What is the voltage V_1 across C_1? What is the voltage V_2 across C_2? What is the voltage V_2 across C_3? What is the charge stored in C_1? What is the charge stored in C_2? What is the charge stored in C_3?

Answer 1

Given,

C1 = 4F , C2 = 12 F and C3 = 1 F

The equivalent cap of the circuit will be :

C12 = C1 + C2 = 4 + 12 = 16 F

Ceq = C12 x C3 / C12 + C3 = 16 x 3 / (16 + 3) = 2.53 F

Charge in the circuit:

Q = CV = 2.53 x 12 = 30.36 F

We know that the same charge flows through the capacitors connected in series, so

C12 = C3 = 30.36 F

We know that, V1 = V2, since they are in parallel

Q1/C1 = Q2/C2

Q1/4 = Q2/12 =>Q2 = 3Q1

Also, Q1 + Q2 = 30.36

Q1 + 3Q1 = 30.36 => Q1 = 7.59 C

Q2 = 3 x 7.59 = 22.7 C

V1 = V2 = Q1/C1 = 7.59/4 = 1.9 V

V3 = V - V1(or V2) = 12 - 1.9 = 10.1 V

Hence,

a) C1 = 7.59 C ; C2 = 22.7 C and C3 = 33.6 C

b) V1 = V2 = 1.9 V and V3 = 10.1 V

c) Energy is given by:

E = 1/2 C V²

E1 = 0.5 x 4 x 10^-6 x 1.9 x 1.9 = 7.22 J

E2 = 0.5 x 12 x 10^-6 x 1.9 x 1.9 = 21.7 J

E3 = 0.5 x 1 x 10^-6 x 10.1 x 10.1 = 51 J