Question

In the figure a 15 V battery is connected across capacitors of capacitances C1-Cg = 3.0 μF and C3-C5-1.5C2-1.5C4-5.5岠what are (a) the equivalent capacitance Ceq of the capacitors and (b) the charge stored by Ceq? What are (c) Vi and (d) qi of capacitor 1, (e) V2 and (f) q2 of capacitor 2, and (9) V3 and (h) q3 of capacitor 3? G C C3 G6 (a) Number (b) Number (c) Number (d) Number (e) Number (f) Number (g) Number (h) Number Units Units Units Units Units Units Units Units

Answer 1

a) C1 and C6 are parallel, the equivalent = 3+3 = 6 μF

C3 and C5 are in series, there equivalent = 5.5*5.5/11 = 2.75 μF

C4 and C2 are parallel with C3+C5 equivalent = 3.66+3.66+2.75 = 10.0833 μF

Ceq = C1-C3 equivalent in series with C2-C4-C3-C5 equivalent = 6*10.0833 / 16.0833 = 3.76 μF

b) Charge stored by Ceq = V Ceq = 15* 3.76 = 56.42 μC

c) V_{1} = (1/6)/((1/6)+(1/10.0833))* 15 = 9.4 V

d) q_{1} = C_{1}V_{1} = 3*9.4 = 28.2 μC

e) V_{2} = 15-9.4 = 5.6 V

f) q_{2} = C_{2}V_{2} = 3.66*5.6 = 20.53 μC

g) V_{3} = (1/5.5)/((1/5.5)+(1/15.5))* 5.6 = 2.8 V

h) q_{3} = C_{3}V_{3} = 5.5*2.8 = 15.4 μC