Basic Circuit Theory Chpter8 Problems 1 (a) Find in Fig.8-20. (b) To what identical value should each of the 4? resistors be changed so that is 180 o out of phase with the source voltage? ? 2 V ? 2 V DaLian Maritime University 50 + - + - 2 ? VV°0/ ?4 ?4 ?? 4j ?? 4j ?4 ?? 4j Fig. 8-20 For prob.1. 2 Find v 3 (t) in the circuit of Fig.8-21 by using nodal analysis. ( - + A ?1 ?2 3 v F400μ mH4.0 3 i cos210 )3010 4 °+t ?1?1 3 (a) Find i 2 (t) in the circuit of Fig.8-22. (b) Change the control voltage from 3v 1 to 3v and again find i 2 (t). 2 Fig. 8-21 For prob.2. + - 3 - + + - 2 v A 1 v 2 i cos210 1 v t 4 10 ?20 mH4 mH1 F2μ Fig. 8-22 For prob.3. 4 For the circuit of Fig.8-23 find v (t) and v (t). R L + + - - ?2 L v R v F 4 1 μ A2 cos2 t 6 10 H2μ A 5 (a) Find the Thevenin equivalent of the network shown in Fig.8-24a. Fig. 8-23 For prob.4. (b) Find the Norton equivalent of the network shown in Fig.8-24b. + - (a) (b) Fig. 8-24 For prob.5. a b H2.0 ?80 H2 F01.0 μ cos250 t 3 10 ?k10 a b t 4 10 A V cos220 1 Basic Circuit Theory Chpter8 Problems 6 Find the output impedance of the network in Fig.8-25. + - ?12 1 1.0 ?? 3j ?20j '1 x v x v Fig. 8-25 For prob.6. 7 (a) Find the frequency-domain Norton equivalent of the network depicted in Fig.8-26. (b) Give element values for one network that this Norton equivalent (at ω =2000 rad/s). A a b i F20μ i ?250 t200 cos220 5.0 8 Use superposition to find in Fig.8-27. xI ? Fig. 8-26 For prob.7. -+-+ 1V°0/ ?? 1j ?1 ?1 ?1j V°0/ A°0/ 1 1 1 xI ? A°0/ 9 For the circuit of Fig.8-28 find the phase angle of the and graphically if = 90V and =150V. ? x V ? y V x V y V Fig. 8-27 For prob.8. + - + - - + +- V°0/201 xV ? yV ? 50 V°80/ 10 Use phasors and nodal analysis on the circuit of Fig.8-29 to find . ? 2 V Fig. 8-28 For prob.9. ?3 ?3j ?? 5j ?6 2 ? V BI ? A90/5 ° A0/10 ° Fig. 8-29 For prob.10. DaLian Maritime University 2 Basic Circuit Theory Chpter8 Problems 11 Find v X (t) in the circuit of Fig.8-30 if v =20cos1000t V and v =20sin1000t V. 1S 2S + - + - mF1.0 mH10 1s v ?25 x v 2s v Fig. 8-30 For prob.11. 12 Use mesh analysis to find i (t) in the circuit shown in Fig.8-31. X + - - + Fig. 8-31 For prob.12. x i Vt100 cos10 ?1 x v H04.0 ?1 ?1 ?1 F04.0 Reference Answers to Selected Problems 1: (a) 7.81 V; (b) 9.8? . o 7.128?∠ 2: 6.47 2 cos(10000t+44 ) V. o 3: (a) 11.09 2 cos(10000t+33.7 ) A; (b) 3.29 o 2 cos(10000t+170.5 ) A. o 4: (a) –4+2 cos(10 t-45 ) V; (b) 2 cos(10 t+135 ) V. 6 o 6 o 5: (a) 46.4 2 cos(1000t+21.8 ) V; (b) 17.9 o 2 cos(10000t+63.4 ) A. o 7: (a) 15.8 A, (1+j1) mS; (b) 1 mS, 0.54.18?∠ o μ F. 8: 1.58 . 43.18?∠ o 9: 65 and -61 , or -113 o and 13 . o o o 10: 34.4 V. 6.23∠ o 11: 70.7 cos(1000t-45 ) V. o 12: 1.213 cos(100t-76.0 ) A. o DaLian Maritime University 3