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P2213_HW09_solns_Fall2008

# P2213_HW09_solns_Fall2008 - Physics 2213 HW#9 Solutions...

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- 1 - Physics 2213 HW #9 — Solutions Fall 2008 24.59 [Capacitor Network] (a) Replace series and parallel combinations of capacitors by their equivalents. The network is sketched below. 1 5 8.4 F C C μ = = 2 3 4 4.2 F C C C μ = = = Simplify the circuit by replacing the capacitor combinations by their equivalents: 3 4 and C C are in series and can be replaced by 34 C : 34 3 4 1 1 1 C C C = + 3 4 34 3 4 1 C C C C C + = ( )( ) 3 4 34 3 4 4.2 F 4.2 F 2.1 F 4.2 F 4.2 F C C C C C μ μ μ μ μ = = = + + 2 34 and C C are in parallel and can be replaced by their equivalent: 234 2 34 C C C = + 234 4.2 F 2.1 F C μ μ = + 234 6.3 F C μ = 1 5 234 , and C C C are in series and can be replaced by eq C : eq 1 5 234 1 1 1 1 C C C C = + + eq 1 2 1 8.4 F 6.3 F C μ μ = + eq 2.5 F C μ = Note: For capacitors in series the equivalent capacitor is smaller than any of those in series. For capacitors in parallel the equivalent capacitance is larger than any of those in parallel. (b) In each equivalent network apply the rules for Q and V for capacitors in series and parallel; start with the simplest network and work back to the original circuit. The equivalent circuit is drawn below. eq eq Q C V = ( )( ) eq 2.5 F 220 V 550 C Q μ μ = = 1 5 234 550 C Q Q Q μ = = = (capacitors in series have same charge) 1 1 1 550 C 65 V 8.4 F Q V C μ μ = = = 5 5 5 550 C 65 V 8.4 F Q V C μ μ = = =

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- 2 - 234 234 234 550 C 87 V 6.3 F Q V C μ μ = = = Now draw the network as: 2 34 234 87 V V V V = = = capacitors in parallel have the same potential ( )( ) 2 2 2 4.2 F 87 V 370 C Q C V μ μ = = = ( )( ) 34 34 34 2.1 F 87 V 180 C Q C V μ μ = = = Finally, consider the original circuit (see below). 3 4 34 180 C Q Q Q μ = = = capacitors in series have the same charge 3 3 3 180 C 43 V 4.2 F Q V C μ μ = = = 4 4 4 180 C 43 V 4.2 F Q V C μ μ = = = Summary: 1 1 550 C, 65 V Q V μ = = 2 2 370 C, 87 V Q V μ = = 3 3 180 C, 43 V Q V μ = = 4 4 180 C, 43 V Q V μ = = 5 5 550 C, 65 V Q V μ = = Note: 3 4 2 1 2 5 and 220 V V V V V V V + = + + = (apart from some small rounding error) 1 2 3 5 2 4 and Q Q Q Q Q Q = + = + 24.60 [Throw the Switch] Apply the rules for combining capacitors in series and in parallel. With the switch open each pair of 3.00 F μ and 6.00 F μ capacitors are in series with each other and each pair is in parallel with the other pair. When the switch is closed each pair of 3.00 F μ and 6.00 F μ capacitors are in parallel with each other and the two pairs are in series.
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P2213_HW09_solns_Fall2008 - Physics 2213 HW#9 Solutions...

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