Physics Book Solutions

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Unformatted text preview: L 2, ra L!0 !0 A # # C # ln( rb ra ) ln((d 0 ra ) ra ) ln(1 0 d ra ) d d EVALUATE:! (b) At the scale of part (a) the cylinders appear to be flat, and so the capacitance should appear like that of flat plates. IDENTIFY:! Initially the capacitors are connected in parallel to the source and we can calculate the charges Q1 and EXECUTE:! (a) d 11 ra : C # 24.56. Q2 . 2C SET UP:! After they are reconnected, the charges add and the voltages are the same, so Ceq # C1 0 C2 , as for Q2 on each. After they are reconnected to each other the total charge is Q # Q2 ! Q1 . U # 1 CV 2 # 2 capacitors in parallel. Capacitance and Dielectrics 24-15 EXECUTE:! Originally Q1 # C1V1 # (9.0 \$ F) (28 V) # 2.52 " 10!4 C and Q2 # C2V2 # (4.0 \$ F)(28 V) # 1.12 " 10!4 C . Ceq # C1 0 C2 # 13.0 \$ F . The original energy stored is U # 1 CeqV 2 # 1 (13.0 " 10!6 F)(28 V)2 # 5.10 " 10!3 J . 2 2 Disconnect and flip the capacitors, so now the total charge is Q # Q2 ! Q1 # 1.4 " 10!4 C and the equivalent capacitance is still the same, Ceq # 13.0 \$ F . The new energy stored is U # 24.57. Q2 (1.4 " 10!4 C) 2 # # 7.54 " 10!4 J . The change in 2Ceq 2(13.0 " 10!6 F) stored energy is BU # 7.45 " 10!4 J ! 5.10 " 10!3 J # !4.35 " 10!3 J . EVALUATE:! When they are reconnected, charge flows and thermal energy is generated and energy is radiated as electromagnetic waves. IDENTIFY:! Simplify the network by replacing series and parallel combinations by their equivalent. The stored energy in a capacitor is U # 1 CV 2 . 2 SET UP:! For capacitors in series the voltages add and the charges are the same; 1 1 1 #0 0 %. For capacitors Ceq C1 C2 Q . U # 1 CV 2 . 2 V EXECUTE:! (a) Find Ceq for the network by replacing each series or parallel combination by its equivalent. The successive simplified circuits are shown in Figure 24.57a–c. U tot # 1 CeqV 2 # 1 (2.19 " 10!6 F)(12.0 V)2 # 1.58 " 10!4 J # 158 \$ J 2 2 in parallel the voltages are the same and the charg...
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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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