Three capacitors having capacitances of 8.1 F , 8.8 F , and 5.0 F are connected

Question

Three capacitors having capacitances of 8.1 F , 8.8 F , and 5.0 F are connected in series across a 36-V potential difference.

Part A

What is the charge on the 5.0 F capacitor?

Express your answer using two significant figures.

Part B

What is the total energy stored in all three capacitors?

Express your answer using two significant figures.

Part C

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?

Express your answer using two significant figures.

3.76

Part D

What is the total energy now stored in the capacitors?

Express your answer using two significant figures.

Explanation / Answer

a)

equivalent capacitance

1/Ceq=1/8.1 +1/8.8 +1/5

Ceq=2.2878 uF

charge on 5uF is

Q=CeqV=(2.2878*10-6)*36

Q=8.24*10-5 C

b)

total energy stored

U=(1/2)CeqV2=(1/2)(2.2878*10-6)*362

U=1.4825*10-3 J

c)

total charge

Q=Q1+Q2+Q3=3*(8.24*10-5)=2.47*10-4 C

equivalent capacitance

Ceq=8.1+8.8+5 =21.9 uF

Voltage across each capacitor is

V1=V2=V3=(2.47*10-4)/(21.9*10-6)=11.28 Volts

d)

total energy stored is

U=(1/2)*(21.9*10-6)*11.282

U=1.393*10-3 J

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