How much energy must a 24-V battery expend to charge a C 1 = 0.41 F and a C 2 =

Question

How much energy must a 24-V battery expend to charge a C1 = 0.41 F and a C2 = 0.17 F capacitor fully when they are placed in parallel?

Express your answer to two significant figures and include the appropriate units

1.67×104 J

CORRECT

Part B

How much charge flowed from the battery in that case?

Express your answer to two significant figures and include the appropriate units.

1.67×104 J

CORRECT

Part B

How much charge flowed from the battery in that case?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Parallel Capacitors: C(total) = C1 + C2
Series Capacitors : C(total) = 1/C1 + 1/C2 => (C1C2) / (C1 + C2)
Energy in a capacitor: U = (1/2)CV²

a) When caps in parallel: C(total) = .41 x 10^(-6) + .17 x 10^(-6)

= 0.58 x 10^(-6) F.

U = (1/2)(0.58x 10^(-6))(24)² = 1.67×104 J

Q=CV
= 0.58 x 10^(-6) F. x 24
= 13.92 x 10^(-6) F.

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