A 9.0 capacitor and a 7.0 F capacitor are connected in ser es across a 5.0 kV Po

Question

A 9.0 capacitor and a 7.0 F capacitor are connected in ser es across a 5.0 kV Potential difference. The charged capacitors are then disconnected from the source and connected to each other with terminals or like sign together, Find the charge on eac capacitor (in mC) and the voltage across each capacitor (in V). (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) 9.0 F capacitor charge 15601x mc 7.0 capacitor charge voltage 2480 mC Additional Materials eBook

Explanation / Answer

In series , equivalent capacitance is given as

Cs = C1 C2/(C1 + C2) = 9 x 7/(9 + 7) = 3.94 uF

charge in each capacitor is given as

Q1 = Q2 = Cs V = 3.94 x 5000 = 19.7 mC

after they are connected in parallel , let the charge on them be Q1' and Q2' respectively

using conservation of charge ,

Q1' + Q2' = Q1 + Q2 = 2 x 19.7 = 39.4 mC

Q1' + Q2' = 39.4 mC eq-1

Also

Q1'/C1 = Q2'/C2

Q1'/9 = Q2'/7

Q1' = 1.3 Q2' eq-2

using eq-1 and eq-2

1.3 Q2' + Q2' = 39.4 mC

Q2' = 17.13 mC

using eq-2

Q1' = 1.3 Q2' = 1.3 x 17.13 = 22.3 mC

V = electric potential on each = Q1'/C1 = 22.3 x 10-3/(9 x 10-6) = 2477.8

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