How much charge does a 14 V battery have to supply to fully charge a 2.9 F capac
ID: 1586094 • Letter: H
Question
How much charge does a 14 V battery have to supply to fully charge a 2.9 F capacitor and a 4.5 F capacitor when they’re in parallel? a)Express your answer to two significant figures and include the appropriate units. b)How much energy does the battery have to supply in this case? Express your answer to two significant figures and include the appropriate units. c)How much charge does a 14 V battery have to supply to fully charge a 2.9 F capacitor and a 4.5 F capacitor when they’re in series? Express your answer to two significant figures and include the appropriate units. d)How much energy does the battery have to supply in this case? Express your answer to two significant figures and include the appropriate units.
Explanation / Answer
C=Q/V
Q = CV
When the two capacitors are connected in parallel , the voltage applied on both are the same as 10V.
Charge in C1 = Q1 = C1*V = 2.9e-6*14 = 4.06e-5 C
Charge in C2 = Q2 = C2*V = 4.5e-6*14 = 6.3e-5 C
Total Q1 + Q2 = 1.0e-4 C
Energy needed = 0.5 QV =0.5 * 1.0e-4*14 = 7 J
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When connected in series, both have the same charge Q.
Charge in C1 = Q = C1 *V1 = 2.9e-6*V1
Charge in C21 = Q = C2* V2 = 4.5 e-6*V2
Hence
Q = 2.9e-6*V1 = 4.5 e-6*V2
V1 = 1.55 V2
V1 + V2 = 14
1.55 V2 =14
V2 = 9.03 Volt
Q = 4.5 e-6*V2 = 4.5 e-6*9.03 = 4.06e-5 C
Energy needed = 0.5 Q V = 0.5*4.06e-5*14 = 2.8e-4 J
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