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Capacitors in Series and Parallel

  • #1
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Homework Statement


Fig. 25-39 shows a 12.0 V battery and four uncharged capacitors of capacitances C1 = 1.00 µF, C2 = 2.00 µF, C3 = 3.00 µF, and C4 = 4.00 µF. If only switch S1 is closed, what is the charge on (a) capacitor 1, (b) capacitor 2, (c) capacitor 3, and (d) capacitor 4? (figure at http://imgur.com/xOR2AU4)

xOR2AU4.png
[edit: Image inserted by moderator]

Homework Equations


q=CV
V is same for capacitors in parallel, P is same for capacitors in series

The Attempt at a Solution


a) C1 and C2 are parallel, as are C3 and C4.
Ct (capacitance of total) = 1/(C1+C2) + 1/(C3+C4) = 0.48
Q = (Ct*Vt) = 0.48*12 = 5.71 µC

Q1+Q2 = 5.71 (because both come from positive end of battery)
Q1/C1=Q2/C2
Q1/(1µF) = 2Q1/(2µF)
3Q1 = 5.71µC
Q1 = 1.9 µC

The correct answer is 9 µC, and I think I went wrong with the calculation of the initial capacitance, but I'm really not sure.
 

Answers and Replies

  • #2
ehild
Homework Helper
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1,802

Homework Statement


Fig. 25-39 shows a 12.0 V battery and four uncharged capacitors of capacitances C1 = 1.00 µF, C2 = 2.00 µF, C3 = 3.00 µF, and C4 = 4.00 µF. If only switch S1 is closed, what is the charge on (a) capacitor 1, (b) capacitor 2, (c) capacitor 3, and (d) capacitor 4? (figure at http://imgur.com/xOR2AU4)

Homework Equations


q=CV
V is same for capacitors in parallel, P is same for capacitors in series

The Attempt at a Solution


a) C1 and C2 are parallel, as are C3 and C4. [/B]
Ct (capacitance of total) = 1/(C1+C2) + 1/(C3+C4) = 0.48
Q = (Ct*Vt) = 0.48*12 = 5.71 µC

Q1+Q2 = 5.71 (because both come from positive end of battery)
Q1/C1=Q2/C2
Q1/(1µF) = 2Q1/(2µF)
3Q1 = 5.71µC
Q1 = 1.9 µC

The correct answer is 9 µC, and I think I went wrong with the calculation of the initial capacitance, but I'm really not sure.
Only switch 1 is closed. C1 and C2 are not parallel, neither are C3 and C4.
Also, you used wrong formula for the series equivalent of capacitors.
 

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