Three capacitors having capacitances of 8.40, 8.40, and 4.20 μFμF, respectively, are connected in series across a 36.0-V potential difference. (a) What is the charge on the 4.20-μF4.20-μF capacitor? (b) The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other with the positively charged plates connected together. What is the voltage across each capacitor in the parallel combination?

a) Q=71.4 μ C

b) ΔV' = 10.2 V

Explanation:

Given that

C ₁ = 8.7 μF

C₂ = 8.2 μF

C₃ = 4.1 μF

The potential difference of the battery, ΔV = 34 V

When connected in series

1/C = 1/C ₁ + 1/C₂ + 1/C₃

1 / C = 1/8.4 + 1 / 8.4 + 1/4.2

C=2.1 μF

As we know that when capacitor are connected in series then they have same charge, Q

Q = C ΔV

Q = 2.1 x 34 μ C

Q=71.4 μ C

b)

As we know that when capacitor are connected in parallel then they have same voltage difference.

Q' = C' ΔV'

C' = C ₁+C₂+C₃ (For parallel connection)

C' = 8.4 + 8.4 + 4.2 μF

C'=21 μF

Q' = C' ΔV'

Q'=3 Q

3 x 71.4 = 21 ΔV'

ΔV' = 10.2 V