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 r ω ,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 ? resistor and the maximum energy stored in the inductor. + - + - )(t 1 i 2 i v 50 s v 3 i ?k10 ?k40 F25.1 μHm 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 r ω and Q. + - F 4 8 10 ? 1 ? I ?k10 Hm 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 ?50 V 100 Fp Hμ 400 tωcos100 Fig. 9-14 For prob.3. 4 For the network shown in Fig. 9-15 find the resonant frequency r ω and the quality factor Q. - + 1.0 ?20 04.0 H1.0 C vFμ C v Fig. 9-15 For prob.4. DaLian Maritime University 1 Basic Circuit Theory Chpter9 Problems 5 Determine reasonably accurate values of r ω and Q for the resonant network shown in Fig. 9-16 a and b. 202 ?1.0 ?k1 Fμ Hm ?250 ?15.0 20 2 Fμ Hm (a) (b) Fig. 9-16 For prob.5. 6 A parallel RLC circuit has R= 1 k? , C= 47μ 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? , L= 1H, C= 1μ F, and ? I = 10 o 0∠ μ A in the circuit of Fig.9-17. (a) Find r ω and Q. (b) Calculate the current through the resistor and inductor. + - C LR ? I CI ? ? V LI ? LCI ? Fig. 9-17 For prob.7. 8 Find Y in for the network shown in Fig. 9-18 and determine r ω and Z (j in r ω ). + - Fig. 9-18 For prob.8. in Y mH4.4 ? 4 10 RI ? 5 10 RI ? F10 8? 9 Use the exact relationships to find R, L, and C for the parallel resonant circuit that has 1 ω =103 rad/s, 2 ω = 118 rad/s, and |Z(j105)|= 10? . 10 A parallel resonant circuit is resonant at 400 Hz with Q = 8 and R = 500? . 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, 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) 0 ω =1000 rad/s, Q =1000; (b) 10 mA. 0 8: (a) (1000-48.4 +j4.4 )/j4.4 28 10 ω ? × ω 4 10 ? × ω ; (b) 45.5 krad/s, 10 k? . 9: 12.30 ,15.19 mH, 5.42? μ F. 10: (a) 443 and 357 Hz; (b) 497 and 1100 Hz. DaLian Maritime University 3