6311 13j 3k3 cb 1

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Unformatted text preview: C4 6.00 " 10!6 F 0 4.00 " 10!6 F The circuit is equivalent to the circuit shown in Figure 24.15e. C1234 # V1234 # V # 28.0 V Q1234 # C1234V # . 2.40 " 10!6 F / . 28.0 V / # 67.2 $ C Figure 24.15e Now build back up the original circuit, step by step. C1234 represents C123 and C4 in series (Figure 24.15f). Q123 # Q4 ! Q1234 # 67.2 $ C (charge same for capacitors in series) Figure 24.15f Q123 67.2 $ C # # 11.2 V C123 6.00 $ F Q 67.2 $ C # 16.8 V V4 # 4 # C4 4.00 $ F Note that V4 0 V123 # 16.8 V 0 11.2 V # 28.0 V, as it should. Then V123 # Capacitance and Dielectrics 24-5 Next consider the circuit as written in Figure 24.15g. V3 # V12 # 28.0 V ! V4 V3 # 11.2 V Q3 # C3V3 # . 4.00 $ F / .11.2 V / Q3 # 44.8 $ C Q12 ! C12V12 # . 2.00 $ F /.11.2 V / Q12 # 22.4 $ C Figure 24.15g Finally, consider the original circuit, as shown in Figure 24.15h. Q1 # Q2 # Q12 # 22.4 $ C (charge same for capacitors in series) Q 22.4 $ C V1 # 1 # # 5.6 V C1 4.00 $ F V2 # Q2 22.4 $ C # # 5.6 V C2 4.00 $ F Figure 24.15h Note that V1 0 V2 # 11.2 V, which equals V3 as it should. Summary: Q1 # 22.4 $ C, V1 # 5.6 V Q2 # 22.4 $ C, V2 # 5.6 V Q3 # 44.8 $ C, V3 # 11.2 V Q4 # 67.2 $ C, V4 # 16.8 V (c) Vad # V3 # 11.2 V EVALUATE:! V1 0 V2 0 V4 # V , or V3 0 V4 # V . Q1 # Q2 , Q1 0 Q3 # Q4 and Q4 # Q1234 . 24.16. IDENTIFY:! The two capacitors are in series. The equivalent capacitance is given by 1 1 1 #0 . Ceq C1 C2 SET UP:! For capacitors in series the charges are the same and the potentials add to give the potential across the network. 1 1 1 1 1 EXECUTE:! (a) #0 # 0 # 5.33 " 105 F!1 . Ceq # 1.88 " 10!6 F . Then !6 Ceq C1 C2 (3.0 " 10 F) (5.0 " 10!6 F) Q # VCeq # (52.0 V)(1.88 " 10!6 F) # 9.75 " 10!5 C . Each capacitor has charge 9.75 " 10!5 C . (b) V1 # Q / C1 # 9.75 " 10!5 C 3.0 " 10!6 F # 32.5 V . V2 # Q / C2 # 9.75 " 10!5 C 5.0 " 10!6 F # 19.5 V . 24.17. EVALUATE:! V1 0 V2 # 52.0 V , which is equal to the applied potential Vab . The...
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This document was uploaded on 03/11/2014 for the course PHYSICS 240 at University of Michigan.

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