1. Three capacitors are connected to a battery ash shown in the figure below. C

Question

1. Three capacitors are connected to a battery ash shown in the figure below. C1’s capacitance is three times the value of C2’s, and C3’s is five times the value of C2’s. a) If C2’s capacitance is just some number, C, what is the equivalent capacitance of the system in terms of C? b) State the ranking of the capacitors according to the charge they store from largest to smallest. c) Rank the capacitors according to the potential differences across them from largest to smallest. d) Assume C3 is now increased to seven times C2. Explain what happens to the charge stored by each capacitor.

Explanation / Answer

C2 = C, C1 = 3C, C3 = 5C

C2 and C3 are in parallel

C23 = C+5C = 6C

C1 and C23 are in sereis

C123 = C1*C23/(C1+C23) = (3C*6c)/(3C+6C)

Cnet =C123 = 2C

(b) Q = VC

in series combination charge is constant.

Q1 = Q2+Q3

In parallel combinaion voltage is constant

C3>C2

Q3 > Q2

Q1 > Q3 > Q2

(c) V3 = V2 > V1

(d) C3 = 7C2

C23 = C+7C = 8C

C123 = (3C*8C)/(3C+8C) = 2.182 C

Q = VC

V = Q/C = Q1/2.182C = 0.458 Vi

in series combination charge is constant

Q1 = VC1 = 0.458Vi*3C = 1.375 Qi

Q1 is changed to 1.375 times of initial value

Q23 = V23*C23

V23 = V2 = V3 = 1.375*Q2/8C

V23 = 0.172 V

V2 = V3 = 0.172 V

Q2 = 0.172V*C2 = 0.172 Q2i

Q2 is changed to 0.172 times of initial value

Q3 = 0.172V*7C2 = 1.2 Q3i

Q3 is changed to 1.2 times of initial value

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