Question

What are the charge on and the potential difference across each capacitor in the figure (Figure 1) if ΔV = 6.0 V ?

Part A

Q1

Part B

V1

Part C

Q2

Part D

V2

Part E

Q3

Part F

V3

Answer 1

here c1 = 4*10^-6 F

c2 = 12*10^-6 F

c3 = 2*10^-6 F

ΔV = 6.0 V

here c1 and c2 are in parallel combination

c12 = c1+c2 = (4+12)*10^-6 = 16*10^-6 F

c3 and c12 are in sereis combiantion

c tot = c3*c12/c12+c3 = 2*10^-6*16*10^-6/(2+16)*10^-6

c tot = 1.78*10^-6 F

from the relation

q = cv

q = 1.78*10^-6*6 = 10.68*10^-6 C

in a sereis combination charge is same across the capacitors

so

q12 = q3 = 10.68*10^-6 C

v3 = q3/c3 = 5.34 V

v12 = q12/c12 = 0.67 V

in a parallel combination voltage is same across the capacitors

v12 = v1 = v2 = 0.67V

q1 = c1v1 = 2.68*10^-6 C

q2 = c2v2 = 8.04*10^-6 C