HAPTE 0 Sinusoidl Stedy-Stte Anlysis 42 EVIEW QUESTIONS 0. The voltge cross the cpcitor in Fig. 0.43 is: () 5 0 V () 7.07 45 V (c) 7.07 45 V (d) 5 45 V Ω 0.5 efer to the circuit in Fig. 0.47 nd oserve tht the two sources do not hve the sme frequency. The current i x (t) cn e otined y: () source trnsformtion () the superposition theorem (c) PSpice 0 0 V j Ω H Ω i x Figure 0.43 For eview Question 0.. sin 2t V F sin 0t V 0.2 The vlue of the current I o in the circuit in Fig. 0.44 is: () 4 0 A () 2.4 90 A (c) 0.6 0 A (d) A 3 0 A j8 Ω I o j Figure 0.44 For eview Question 0.2. 0.3 Using nodl nlysis, the vlue of in the circuit of Fig. 0.45 is: () 24 V () 8 V (c) 8 V (d) 24 V Figure 0.47 For eview Question 0.5. 0.6 For the circuit in Fig. 0.48, the Thevenin impednce t terminls - is: () () 0.5 j0.5 (c) 0.5 j0.5 (d) j2 (e) j2 Ω H 5 cos t V F Figure 0.48 For eview Questions 0.6 nd 0.7. j6 Ω 4 90 A j3 Ω 0.7 In the circuit of Fig. 0.48, the Thevenin voltge t terminls - is: () 3.535 45 V () 3.535 45 V (c) 7.07 45 V (d) 7.07 45 V Figure 0.45 For eview Question 0.3. 0.4 In the circuit of Fig. 0.46, current i(t) is: () 0 cos t A () 0 sin t A (c) 5 cos t A (d) 5 sin t A (e) 4.472 cos(t 63.43 ) A 0.8 efer to the circuit in Fig. 0.49. The Norton equivlent impednce t terminls - is: () j4 () j2 (c) j2 (d) j4 H F j Ω 0 cos t V i(t) 6 0 V j Figure 0.46 For eview Question 0.4. Figure 0.49 For eview Questions 0.8 nd 0.9.
422 PAT 2 A ircuits 0.9 The Norton current t terminls - in the circuit of Fig. 0.49 is: () 0 A ().5 90 A (c).5 90 A (d) 3 90 A 0.0 PSpice cn hndle circuit with two independent sources of different frequencies. () True () Flse Answers: 0.c, 0.2, 0.3d, 0.4, 0.5, 0.6c, 0.7, 0.8, 0.9d, 0.0. POBLEMS Section 0.2 Nodl Anlysis 0. Find in the circuit in Fig. 0.50. 0.4 ompute (t) in the circuit of Fig. 0.53. i x H 0.25 F 3 Ω H 0 cos(t 45 ) V F 5 sin(t 30 ) V 6 sin (4t 0 ) V Figure 0.53 For Pro. 0.4. 0.5i x Ω Figure 0.50 For Pro. 0.. 0.2 For the circuit depicted in Fig. 0.5 elow, determine. 0.3 Determine in the circuit of Fig. 0.52. 0.5 Use nodl nlysis to find in the circuit of Fig. 0.54. 20 Ω 50 mf 0 mh 2 F 0 cos 0 3 t V 20 Ω 4 30 Ω 6 sin 4t V Ω 6 Ω 2 cos 4t A Figure 0.54 For Pro. 0.5. Figure 0.52 For Pro. 0.3. 0.6 Using nodl nlysis, find (t) in the circuit in Fig. 0.55. 0 Ω H 0.02 F 20 sin ( 0t 4) V 4 cos ( 0t 3) A Figure 0.5 For Pro. 0.2.
HAPTE 0 Sinusoidl Stedy-Stte Anlysis 423 0.25 F H 0.9 Solve for the current I in the circuit of Fig. 0.58 using nodl nlysis. 5 0 A 8 sin (2t 30 ) V 0.5 F cos 2t A j Ω I Figure 0.55 For Pro. 0.6. 20 90 V j 2I 0.7 By nodl nlysis, find in the circuit in Fig. 0.56. 2 Figure 0.58 For Pro. 0.9. 0.0 Using nodl nlysis, find V nd V 2 in the circuit of Fig. 0.59. 0 Ω 0 Ω V j5 Ω V 2 20 sin000t A 20 Ω 50 mf 0 mh j2 A 20 Ω j0 Ω j A Figure 0.56 For Pro. 0.7. 0.8 lculte the voltge t nodes nd 2 in the circuit of Fig. 0.57 using nodl nlysis. Figure 0.59 For Pro. 0.0. 0. By nodl nlysis, otin current I o in the circuit in Fig. 0.60. j 20 30 A 00 20 V j I o Ω 2 3 Ω j j 0 Ω j j5 Ω Figure 0.57 For Pro. 0.8. Figure 0.60 For Pro. 0.. 0.2 Use nodl nlysis to otin in the circuit of Fig. 0.6 elow. 8 Ω j6 Ω j5 Ω 4 45 A V x 2V x j Ω j Figure 0.6 For Pro. 0.2.
424 PAT 2 A ircuits 0.3 Otin in Fig. 0.62 using nodl nlysis. j Section 0.3 Mesh Anlysis 0.7 Otin the mesh currents I nd I 2 in the circuit of Fig. 0.66. 2 0 V j 0.2 V s I 2 I 2 L Figure 0.62 For Pro. 0.3. 0.4 efer to Fig. 0.63. If (t) = V m sin ωt nd (t) = A sin(ωt φ), derive the expressions for A nd φ. Figure 0.66 For Pro. 0.7. 0.8 Solve for in Fig. 0.67 using mesh nlysis. (t) L (t) 0 cos 2t V 0.25 F 6 sin 2t V Figure 0.67 For Pro. 0.8. Figure 0.63 For Pro. 0.4. 0.5 For ech of the circuits in Fig. 0.64, find /V i for ω = 0, ω, nd ω 2 = /L. 0.9 ework Pro. 0.5 using mesh nlysis. 0.20 Using mesh nlysis, find I nd I 2 in the circuit of Fig. 0.68. L j0 Ω 40 Ω V i V i L 40 30 V I I j20 Ω 2 50 0 V () () Figure 0.68 For Pro. 0.20. Figure 0.64 For Pro. 0.5. 0.6 For the circuit in Fig. 0.65, determine /V s. 0.2 By using mesh nlysis, find I nd I 2 in the circuit depicted in Fig. 0.69. j 3 Ω V s 2 L 3 Ω I 30 20 V I 2 j Ω j6 Ω j Figure 0.65 For Pro. 0.6. Figure 0.69 For Pro. 0.2.
HAPTE 0 Sinusoidl Stedy-Stte Anlysis 425 0.22 epet Pro. 0. using mesh nlysis. 0.23 Use mesh nlysis to determine current I o in the circuit of Fig. 0.70 elow. 0.24 Determine nd I o in the circuit of Fig. 0.7 using mesh nlysis. I o 2 0 A j j 0 90 V Ω 4 0 A Ω j 4 30 A 3 I o j Section 0.4 Figure 0.73 For Pro. 0.29. Superposition Theorem Figure 0.7 For Pro. 0.24. 0.30 Find in the circuit shown in Fig. 0.74 using superposition. 0.25 ompute I in Pro. 0.9 using mesh nlysis. 0.26 Use mesh nlysis to find I o in Fig. 0.28 (for Exmple 0.0). 0 cos 4t V H 8 V 0.27 lculte I o in Fig. 0.30 (for Prctice Pro. 0.0) using mesh nlysis. 0.28 ompute in the circuit of Fig. 0.72 using mesh nlysis. Figure 0.74 For Pro. 0.30. j j3 Ω 0.3 Using the superposition principle, find i x in the circuit of Fig. 0.75. 4 90 A 2 0 V 8 F 3 Ω i x 5 cos(2t 0 ) A 4 H 0 cos(2t 60 ) V 2 0 A Figure 0.72 For Pro. 0.28. 0.29 Using mesh nlysis, otin I o in the circuit shown in Fig. 0.73. Figure 0.75 For Pro. 0.3. 0.32 ework Pro. 0.2 using the superposition theorem. 0.33 Solve for (t) in the circuit of Fig. 0.76 using the superposition principle. 80 Ω I o j60 Ω 20 Ω 00 20 V j40 Ω j40 Ω 60 30 V Figure 0.70 For Pro. 0.23.
426 PAT 2 A ircuits 6 Ω 20 Ω 0.4 mh 2 cos 3t V v 2 F o 4 sin 2t A 0 V 5 cos 0 5 t V 0.2 mf 80 Ω Figure 0.76 For Pro. 0.33. Figure 0.80 For Pro. 0.37. 0.34 Determine in the circuit of Fig. 0.77. 0 sin(3t 30 ) V Ω 6 F 24 V 2 cos 3t 0.38 Solve Pro. 0.20 using source trnsformtion. 0.39 Use the method of source trnsformtion to find I x in the circuit of Fig. 0.8. Figure 0.77 For Pro. 0.34. 0.35 Find in the circuit in Fig. 0.78 using superposition. 20 mf j j I x 60 0 V 6 Ω 5 90 A j3 Ω 50 cos 2000t V 40 mh 80 Ω 00 Ω Figure 0.8 For Pro. 0.39. 2 sin 4000t A 60 Ω 24 V Figure 0.78 For Pro. 0.35. 0.40 Use the concept of source trnsformtion to find in the circuit of Fig. 0.82. Section 0.5 Source Trnsformtion 0.36 Using source trnsformtion, find i in the circuit of Fig. 0.79. 3 Ω i j3 Ω j 20 0 V j j 5 Ω 8 sin(200t 30 ) A 5 mh Figure 0.82 For Pro. 0.40. mf Figure 0.79 For Pro. 0.36. 0.37 Use source trnsformtion to find in the circuit in Fig. 0.80. Section 0.6 Thevenin nd Norton Equivlent ircuits 0.4 Find the Thevenin nd Norton equivlent circuits t terminls - for ech of the circuits in Fig. 0.83.
HAPTE 0 Sinusoidl Stedy-Stte Anlysis 427 j20 Ω 0 Ω 0.44 For the circuit depicted in Fig. 0.86, find the Thevenin equivlent circuit t terminls -. 50 30 V j0 Ω () j5 Ω 8 Ω 5 45 A j0 Ω j6 Ω Figure 0.86 For Pro. 0.44. 4 0 A 8 Ω j0 Ω 0.45 epet Pro. 0. using Thevenin s theorem. () 0.46 Find the Thevenin equivlent of the circuit in Fig. 0.87 s seen from: () terminls - () terminls c-d Figure 0.83 For Pro. 0.4. c d 0.42 For ech of the circuits in Fig. 0.84, otin Thevenin nd Norton equivlent circuits t terminls -. 0 Ω j 6 Ω j 20 0 V j5 Ω 4 0 A j 2 0 A () 30 Ω Figure 0.87 For Pro. 0.46. 0.47 Solve Pro. 0.3 using Thevenin s theorem. 0.48 Using Thevenin s theorem, find in the circuit in Fig. 0.88. 3 20 45 V 60 Ω j0 Ω () j5 Ω 2 cos t V 4 F 8 F Figure 0.84 For Pro. 0.42. 0.43 Find the Thevenin nd Norton equivlent circuits for the circuit shown in Fig. 0.85. 5 Ω j0 Ω Figure 0.88 For Pro. 0.48. 0.49 Otin the Norton equivlent of the circuit depicted in Fig. 0.89 t terminls -. 5 mf 60 20 V j20 Ω 4 cos(200t 30 ) V 0 H 2 kω Figure 0.85 For Pro. 0.43. Figure 0.89 For Pro. 0.49.
428 PAT 2 A ircuits 0.50 For the circuit shown in Fig. 0.90, find the Norton equivlent circuit t terminls -. 00 kω 0 nf 3 60 A 60 Ω 40 Ω j80 Ω j30 Ω 50 kω vo Figure 0.90 For Pro. 0.50. 0.5 ompute in Fig. 0.9 using Norton s theorem. 5 cos 2t V Figure 0.94 For Pro. 0.54. 0.55 ompute (t) in the op mp circuit in Fig. 0.95 if = 4 cos 0 4 t V. 50 kω 4 F 4 H 2 F nf 00 kω Figure 0.9 For Pro. 0.5. 0.52 At terminls -, otin Thevenin nd Norton equivlent circuits for the network depicted in Fig. 0.92. Tke ω = 0 rd/s. 2 sin vt V 0 mf 0 Ω 2 cos vt Figure 0.92 For Pro. 0.52. Section 0.7 Op Amp A ircuits 0.53 For the differentitor shown in Fig. 0.93, otin /V s. Find (t) when (t) = V m sin ωt nd ω = /. Figure 0.93 For Pro. 0.53. vo 2 0.54 The circuit in Fig. 0.94 is n integrtor with feedck resistor. lculte (t) if = 2 cos 4 0 4 t V. Figure 0.95 For Pro. 0.55. 0.56 If the input impednce is defined s Z in = V s /I s, find the input impednce of the op mp circuit in Fig. 0.96 when = 0 k, 2 = 20 k, = 0 nf, 2 = 20 nf, nd ω = 5000 rd/s. I s 2 V s 2 Z in Figure 0.96 For Pro. 0.56. 0.57 Evlute the voltge gin A v = /V s in the op mp circuit of Fig. 0.97. Find A v t ω = 0, ω, ω = /, nd ω = / 2 2. V s 2 Figure 0.97 For Pro. 0.57. 2 Vo
HAPTE 0 Sinusoidl Stedy-Stte Anlysis 429 0.58 In the op mp circuit of Fig. 0.98, find the closed-loop gin nd phse shift if = 2 = nf, = 2 = 00 k, 3 = 20 k, 4 = 40 k, nd ω = 2000 rd/s. 0.6 For the op mp circuit in Fig. 0.0, otin (t). 20 kω 0 kω 0. mf 0.2 mf 40 kω 2 2 4 vo 5 cos 0 3 t V 3 Figure 0.0 For Pro. 0.6. Figure 0.98 For Pro. 0.58. 0.59 ompute the closed-loop gin /V s for the op mp circuit of Fig. 0.99. 0.62 Otin (t) for the op mp circuit in Fig. 0.02 if = 4 cos(000t 60 ) V. 50 kω 20 kω 0.2 mf 3 2 2 0. mf 0 kω Figure 0.99 For Pro. 0.59. 0.60 Determine (t) in the op mp circuit in Fig. 0.00 elow. Figure 0.02 For Pro. 0.62. Section 0.8 A Anlysis Using PSpice 0.63 Use PSpice to solve Exmple 0.0. 0.64 Solve Pro. 0.3 using PSpice. 20 kω 0 kω 0.5 mf 2 sin 400t V 0.25 mf 0 kω 40 kω 20 kω Figure 0.00 For Pro. 0.60.
430 PAT 2 A ircuits 0.65 Otin in the circuit of Fig. 0.03 using PSpice. j 3 0 A j Ω V x Figure 0.03 For Pro. 0.65. 2V x 0.66 Use PSpice to find V, V 2, nd V 3 in the network of Fig. 0.04. 0.68 Use PSpice to find nd in the circuit of Fig. 0.06 elow. Section 0.9 Applictions 0.69 The op mp circuit in Fig. 0.07 is clled n inductnce simultor. Show tht the input impednce is given y where Z in = V in I in = jωl eq L eq = 3 4 2 2 3 4 8 Ω I in V in V j0 Ω j0 Ω V 2 V 3 60 30 V j j 4 0 A Figure 0.04 For Pro. 0.66. Figure 0.07 For Pro. 0.69. 0.70 Figure 0.08 shows Wien-ridge network. Show tht the frequency t which the phse shift etween the input nd output signls is zero is f = 2 π, nd tht the necessry gin is A v = /V i = 3t tht frequency. 0.67 Determine V, V 2, nd V 3 in the circuit of Fig. 0.05 using PSpice. j0 Ω j V Ω V 2 V 3 V i 2 4 0 A 8 Ω j6 Ω j 2 0 A Figure 0.05 For Pro. 0.67. Figure 0.08 For Pro. 0.70. 0.7 onsider the oscilltor in Fig. 0.09. () Determine the oscilltion frequency. 20 mf 6 cos 4t V 0.5 4 0 Ω 25 mf Figure 0.06 For Pro. 0.68.
HAPTE 0 Sinusoidl Stedy-Stte Anlysis 43 () Otin the minimum vlue of for which oscilltion tkes plce. 20 kω 0 kω 80 kω 0.4 mh 2 nf (Hint: Set the imginry prt of the impednce in the feedck circuit equl to zero.) 0.74 Design olpitts oscilltor tht will operte t 50 khz. 0.75 Figure 0.2 shows Hrtley oscilltor. Show tht the frequency of oscilltion is f o = 2π (L L 2 ) f Figure 0.09 For Pro. 0.7. i 0.72 The oscilltor circuit in Fig. 0.0 uses n idel op mp. () lculte the minimum vlue of o tht will cuse oscilltion to occur. () Find the frequency of oscilltion. L 2 L MΩ 00 kω 0 mh 2 nf Figure 0.0 For Pro. 0.72. o 0 kω Figure 0.2 A Hrtley oscilltor; for Pro. 0.75. 0.76 efer to the oscilltor in Fig. 0.3. () Show tht V 2 = 3 j (ωl/ /ωl) () Determine the oscilltion frequency f o. (c) Otin the reltionship etween nd 2 in order for oscilltion to occur. 0.73 Figure 0. shows olpitts oscilltor. Show tht the oscilltion frequency is f o = 2π L T where T = 2 /( 2 ). Assume i X 2. 2 Vo L V 2 L f i Figure 0.3 For Pro. 0.76. L 2 Figure 0. A olpitts oscilltor; for Pro. 0.73.