《电路》（英文版）Chpter 9 Problems

Basic Circuit Theory Chpter9 Problems Let vs=100 cos a t V in the circuit shown in Fig. 9-12.(a) Find the equivalent parallel RLC circuit and then determine resonant frequency @r, Q, and v(t).(b) Find i, (t),i2(t), and i3(t) (c)Calculate the average power loss in the 10 kQ2 resistor and the maximum energy stored in the inductor ①n50mn323r: Fig. 9-12 For prob. I 2 Obtain an expression for the input admittance of the network shown in Fig. 9-13 and then calculate @ and Q 10kQ2 34 mH(10/ 3 In the series RLC circuit of Fig. 9-14 a high-Q approximations are satisfactory.(a) At what value of o is the amplitude of the current i a maximum?(b) by how many rad/s would a have to be increased to reduce Im by 5% F 100cosot V H 4 For the network shown in Fig. 9-15 find the resonant frequency o and the quality factor Q 0.1H lu 20g 004v Fig 9-15 For prob. 4 DaLian Maritime University

Basic Circuit Theory Chpter9 Problems 1 Let v = 100 cos S ω t V in the circuit shown in Fig. 9-12. (a) Find the equivalent parallel RLC circuit and then determine resonant frequency ω r ,Q, and v(t). (b) Find i 1 (t), i (t), and i (t). (c) Calculate the average power loss in the 10 k 2 3 Ω resistor and the maximum energy stored in the inductor. + - + - (t) 1 i 2 i 50 v s v 3 i 10kΩ 40kΩ m H 1.25µ F Fig. 9-12 For prob.1. 2 Obtain an expression for the input admittance of the network shown in Fig. 9-13 and then calculate ω r and Q. + - F 4 8 10 − 1 • Ω I 10k m H 1 • I 5 10 Fig. 9-13 For prob.2. 3 In the series RLC circuit of Fig. 9-14 a high-Q approximations are satisfactory. (a) At what value of ω is the amplitude of the current i a maximum? (b) By how many rad/s would ω have to be increased to reduce I by 5%. m + - i 50Ω V 100p F 400µ H 100cosω t Fig. 9-14 For prob.3. 4 For the network shown in Fig. 9-15 find the resonant frequency ω r and the quality factor Q. - + 0.1 20Ω 0.04 0.1H C µ F v C v Fig. 9-15 For prob.4. DaLian Maritime University 1

Basic Circuit Theory Chpter9 Problems 5 Determine reasonably accurate values of @ and Q for the resonant network shown in Fig. 9-16 a and b 50g lkQ 22mH+20μF Ou F Fig. 9-16 For prob.5 6 A parallel RLC circuit has R=1 kQ2, c=47 u F, and L= 1l mH (a) Determine the resonant equency(in Hz)and Q.(b) If the circuit is exited by a steady-state I mA sinusoidal current source find the terminal voltage and the voltage across the capacitor 7 Let R=1 MQ2, L=lH, =1 u F, and 1=10 Z0 H A in the circuit of Fig 9-17.(a)Find @, and Q.(b) Calculate the current through the resistor and inductor R L 8 Find Y in for the network shown in Fig. 9-18 and determine andZngo,) 10-8F 04 4mH [ 10g Fig. 9-18 For prob. 8 9 Use the exact relationships to find R, L, and C for the parallel resonant circuit that has @, =103 rad/s, @,=118 rad/s, and ZG105)10Q2 10 A parallel resonant circuit is resonant at 400 Hz with Q=8 and R=500Q2 If a current source of 2mA is applied to the circuit, use approximation methods to find the cyclic frequency of the current if (a) the voltage across the circuit has a magnitude of 0.5V;(b) the resistor current has a magnitude of 0.5mA DaLian Maritime University

Basic Circuit Theory Chpter9 Problems 5 Determine reasonably accurate values of ω r and Q for the resonant network shown in Fig. 9-16 a and b. 2 20 0.1Ω 1kΩ µ F mH 250 Ω 0.15 Ω 20 2 µ F mH (a) (b) Fig. 9-16 For prob.5. 6 A parallel RLC circuit has R= 1 kΩ , C= 47 µ F, and L= 11 mH. (a) Determine the resonant frequency (in Hz) and Q. (b) If the circuit is exited by a steady-state 1 mA sinusoidal current source find the terminal voltage and the voltage across the capacitor. 7 Let R= 1 M Ω , L= 1H, C= 1 µ F, and • I = 10 o ∠0 µ A in the circuit of Fig.9-17. (a) Find ω r and Q. (b) Calculate the current through the resistor and inductor. + - R L C • I I C • • V I L • I LC • Fig. 9-17 For prob.7. 8 Find Y in for the network shown in Fig. 9-18 and determine ω r and Z (j in ω r ). + - Fig. 9-18 For prob.8. Yin 4.4mH Ω4 10 I R • 5 10 I R • 10 F −8 9 Use the exact relationships to find R, L, and C for the parallel resonant circuit that has ω1 =103 rad/s, ω 2 = 118 rad/s, and |Z(j105)|= 10Ω . 10 A parallel resonant circuit is resonant at 400 Hz with Q = 8 and R = 500Ω . If a current source of 2mA is applied to the circuit, use approximation methods to find the cyclic frequency of the current if (a) the voltage across the circuit has a magnitude of 0.5V; (b) the resistor current has a magnitude of 0.5mA. DaLian Maritime University 2

Basic Circuit Theory Chpter9 Problems Reference answers to Selected Problems 1:(a)4 krad/s, 40, 80 cos 4000t V;(b)2 cos 4000t, 400sin 4000t,-400sin4000t mA;(c)20 mW 2:4767krad/s.5244 3: (a)5 Mrad/s;(b)20.54 rad/s 4:4470rads.22.4 5:(a)5 krad/s, 40; (b)5 krad/s, 20 6:(a)65.37,221.3Hz;(b)lV 7:(a)Oo=1000rad/s,Qo=1000,(b)10mA 8:(a)(1000484×102+144×10-o)j44;(b)455kads,10kQ 9:12.309,15.19mH,542F 10:(a)443and357Hz;(b)497andl100Hz DaLian Maritime University

Basic Circuit Theory Chpter9 Problems Reference Answers to Selected Problems 1: (a) 4 krad/s, 40, 80 cos 4000t V; (b) 2 cos 4000t, 400sin 4000t, -400sin4000t mA; (c) 20 mW, 4mJ. 2: 47.67 krad/s, 52.44. 3: (a) 5 Mrad/s; (b) 20.54 rad/s. 4: 4470 rad/s, 22.4. 5: (a) 5 krad/s, 40; (b) 5 krad/s, 20. 6: (a) 65.37, 221.3 Hz; (b) 1V. 7: (a) ω 0 =1000 rad/s, Q =1000; (b) 10 mA. 0 8: (a) (1000-48.4 +j4.4 )/j4.4 8 2 10 ω− × ω4 10− × ω ; (b) 45.5 krad/s, 10 kΩ . 9: 12.30Ω ,15.19 mH, 5.42 µ F. 10: (a) 443 and 357 Hz; (b) 497 and 1100 Hz. DaLian Maritime University 3