Solution of Fundamental of Electric Circuits

Chapter 1, Drift 1 How divers coulombs are represented by these amounts of electrons: (a) 6. 482 ? 1017 (b) 1. 24 ? 1018 (c) 2. 46 ? 1019 (d) 1. 628 ? 10 20 Chapter 1, Separation 1 (a) q = 6. 482x1017 x [-1. 602x10-19 C] = -0. 10384 C (b) q = 1. 24x1018 x [-1. 602x10-19 C] = -0. 19865 C (c) q = 2. 46x1019 x [-1. 602x10-19 C] = -3. 941 C (d) q = 1. 628x1020 x [-1. 602x10-19 C] = -26. 08 C Chapter 1, Drift 2. Particularize the popular eloquent through an atom if the carry progress is absorbed by (a) q(t ) = (3t + 8) mC (b) q(t ) = ( 8t 2 + 4t-2) C (c) q (t ) = 3e -t ? 5e ? 2 t nC (d) q(t ) = 10 sin 120? pC (e) q(t ) = 20e ? 4 t cos 50t ? C ( ) Chapter 1, Separation 2 (a) (b) (c) (d) (e) i = dq/dt = 3 mA i = dq/dt = (16t + 4) A i = dq/dt = (-3e-t + 10e-2t) nA i=dq/dt = 1200? cos 120? t pA i =dq/dt = ? e ? 4t (80 cos 50 t + 1000 sin 50 t ) ? A PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 1, Drift 3. Experience the carry q(t) eloquent through a cognizance if the popular is: (a) i (t ) = 3A, q(0) = 1C (b) i ( t ) = ( 2t + 5) mA, q(0) = 0 (c) i ( t ) = 20 cos(10t + ? / 6) ? A, q(0) = 2 ? C (d) i (t ) = 10e ? 30t sin 40tA, q(0) = 0 Chapter 1, Separation 3 (a) q(t) = ? i(t)dt + q(0) = (3t + 1) C (b) q(t) = ? (2t + s) dt + q(v) = (t 2 + 5t) mC q(t) = ? 10e -30t sin 40t + q(0) = (c) q(t) = ? 20 cos (10t + ? / 6 ) + q(0) = (2sin(10t + ? / 6) + 1) ? C (d) 10e -30t ( ? 0 sin 40 t - 40 cos t) 900 + 1600 = ? e - 30t (0. 16cos40 t + 0. 12 sin 40t) C Chapter 1, Drift 4. A popular of 3. 2 A progresss through a president. Estimate how abundantly carry passes through any cross-section of the president in 20 seconds. Chapter 1, Separation 4 q = it = 3. 2 x 20 = 64 C Chapter 1, Drift 5. Particularize the aggregate carry infections balance the span gap of 0 ? t ? 10s when 1 i (t ) = t A. 2 Chapter 1, Separation 5 1 t 2 10 q = ? idt = ? tdt = = 25 C 2 4 0 0 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. 10 Chapter 1, Drift 6. The carry entering a positive atom is shown in Fig. 1. 23. Experience the popular at: (a) t = 1 ms (b) t = 6 ms (c) t = 10 ms Figure 1. 23 Chapter 1, Separation 6 (a) At t = 1ms, i = (b) At t = 6ms, i = dq 80 = = 40 A dt 2 q = 0A dt dq 80 = = –20 A dt 4 (c) At t = 10ms, i = PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 1, Drift 7. The carry eloquent in a wire is plotted in Fig. 1. 24. Sketch the similar popular. Figure 1. 4 Chapter 1, Separation 7 ? 25A, dq ? i= = - 25A, dt ? ? 25A, ? 0< t> I = inv(Z)*V I= 1. 6196 mA –1. 0202 mA –2. 461 mA 3 mA –2. 423 mA PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 54. Find the intricacy populars i1, i2, and i3 in the circumference in Fig. 3. 99. Figure 3. 99 Chapter 3, Separation 54 Let the intricacy populars be in mA. For intricacy 1, ? 12 + 10 + 2 I 1 ? I 2 = 0 ? ?> 2 = 2 I 1 ? I 2 For intricacy 2, ? 10 + 3I 2 ? I 1 ? I 3 = 0 For intricacy 3, ? 12 + 2 I 3 ? I 2 = 0 ? ?> ? ?> (1) 10 = ? I 1 + 3I 2 ? I 3 (2) 12 = ? I 2 + 2 I 3 (3) Putting (1) to (3) in matrix create leads to ? 2 ? 1 0 ?? I 1 ? ? 2 ? ? ?? ? ? ? ? ? 1 3 ? 1?? I 2 ? = ? 10 ? ? 0 ? 1 2 ?? I ? ?12 ? ? ?? 3 ? ? ? Using MATLAB, ? ? > AI = B ? 5. 25 ? I = A B = ? 8. 5 ? ? ? ?10. 25? ? ? ?1 ? ? > I 1 = 5. 25 mA, I 2 = 8. 5 mA, I 3 = 10. 25 mA PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 55. In the circumference of Fig. 3. 100, explain for i1, i2, and i3. Figure 3. 100 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Separation 55 10 V b I2 i1 I2 + c 1A 1A 4A 6? I1 d I3 2? i2 4A a 12 ? I4 i3 4? +– I3 I4 8V 0 It is clear that I1 = 4 For intricacy 4, 12(I4 – I1) + 4(I4 – I3) – 8 = 0 6(I2 – I1) + 10 + 2I3 + 4(I3 – I4) = 0 or -3I1 + 3I2 + 3I3 – 2I4 = -5 (1) (2) (3) (4) For the superintricacy At node c, I2 = I 3 + 1 Solving (1), (2), (3), and (4) yields, I1 = 4A, I2 = 3A, I3 = 2A, and I4 = 4A At node b, At node a, At node 0, i1 = I2 – I1 = -1A i2 = 4 – I4 = 0A i3 = I4 – I3 = 2A PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 56. Particularize v1 and v2 in the circumference of Fig. 3. 101. Figure 3. 101 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Separation 56 + v1 – 2? 2? i2 2? 2? 2? + v2 12 V + – i1 i3 – For loop 1, 12 = 4i1 – 2i2 – 2i3 which leads to 6 = 2i1 – i2 – i3 For loop 2, 0 = 6i2 –2i1 – 2 i3 which leads to 0 = -i1 + 3i2 – i3 For loop 3, 0 = 6i3 – 2i1 – 2i2 which leads to 0 = -i1 – i2 + 3i3 In matrix create (1), (2), and (3) beseem, ? 2 ? 1 ? 1? ? i1 ? ?6? ? ? 1 3 ? 1? ?i ? = ? 0? ? ?? 2 ? ? ? ? ? 1 ? 1 3 ? ?i 3 ? ?0? ? ?? ? ? ? (1) (2) (3) 2 ? 1 ? 1 2 6 ? 1 ? = ? 1 3 ? 1 = 8, ? 2 = ? 1 3 ? 1 = 24 ? 1 ? 1 3 ? 1 0 3 2 ? 1 6 ? 3 = ? 1 3 0 = 24 , accordingly i2 = i3 = 24/8 = 3A, ? 1 ? 1 0 v1 = 2i2 = 6 volts, v = 2i3 = 6 volts PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 57. In the circumference in Fig. 3. 102, experience the prizes of R, V1, and V2 absorbed that io = 18 mA. Figure 3. 102 Chapter 3, Separation 57 Usurp R is in kilo-ohms. V2 = 4k? x18mA = 72V , V1 = 100 ? V2 = 100 ? 72 = 28V Popular through R is 3 3 iR = io , V1 = i R R ? > 28 = (18) R 3+ R 3+ R This leads to R = 84/26 = 3. 23 k ? PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 58. Experience i1, i2, and i3 the circumference in Fig. 3. 103. Figure 3. 103 Chapter 3, Separation 58 30 ? i2 30 ? 10 ? 10 ? 30 ? i1 + i3 20 V – For loop 1, 120 + 40i1 – 10i2 = 0, which leads to -12 = 4i1 – i2 For loop 2, 50i2 – 10i1 – 10i3 = 0, which leads to -i1 + 5i2 – i3 = 0 For loop 3, -120 – 10i2 + 40i3 = 0, which leads to 12 = -i2 + 4i3 Solving (1), (2), and (3), we get, i1 = -3A, i2 = 0, and i3 = 3A (1) (2) (3) PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 59. Rework Prob. 3. 30 using intricacy segregation. Chapter 3, Drift 30. Using nodal segregation, experience vo and io in the circumference of Fig. 3. 79. Figure 3. 79 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Separation 59 40 ? –+ I0 10 ? 20 ? i2 120 V + 100V + i1 – 4v0 + – 2I0 i2 i3 v0 80 ? – i3 For loop 1, -100 + 30i1 – 20i2 + 4v0 = 0, where v0 = 80i3 or 5 = 1. 5i1 – i2 + 16i3 For the supermesh, 60i2 – 20i1 – 120 + 80i3 – 4 v0 = 0, where v0 = 80i3 or 6 = -i1 + 3i2 – 12i3 Also, 2I0 = i3 – i2 and I0 = i2, hereafter, 3i2 = i3 ? 3 ? 2 32 ? ? ? 1 3 ? 12? ? ? ?1 ? 3 ? 0 ? ? ? i1 ? ?10? ?i ? = ? 6 ? ? 2? ? ? ?i 3 ? ? 0 ? ? ? ? ? (1) (2) (3) From (1), (2), and (3), 3 ? 32 3 10 32 3 ? 2 10 ? = ? 1 3 ? 12 = 5, ? 2 = ? 1 6 ? 12 = ? 28, ? 3 = ? 1 3 6 = ? 84 0 3 ? 1 0 0 ? 1 0 3 0 I0 = i2 = ? 2/? = -28/5 = -5. 6 A v0 = 8i3 = (-84/5)80 = -1. 344 kvolts PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 60. Estimate the force dissipated in each resistor in the circumference in Fig. 3. 104. Figure 3. 104 Chapter 3, Separation 60 0. 5i0 4? 10 V 8? v1 1? 10 V + v2 2? – i0 At node 1, (v1/1) + (0. 5v1/1) = (10 – v1)/4, which leads to v1 = 10/7 At node 2, (0. 5v1/1) + ((10 – v2)/8) = v2/2 which leads to v2 = 22/7 P1? = (v1)2/1 = 2. 041 watts, P2? = (v2)2/2 = 4. 939 watts P4? = (10 – v1)2/4 = 18. 38 watts, P8? = (10 – v2)2/8 = 5. 88 watts PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 61. Estimate the popular create io/is in the circumference of Fig. 3. 105. Figure 3. 105 Chapter 3, Separation 61 v1 is 20 ? v2 10 ? i0 + v0 – 30 ? – + 5v0 40 ? At node 1, is = (v1/30) + ((v1 – v2)/20) which leads to 60is = 5v1 – 3v2 But v2 = -5v0 and v0 = v1 which leads to v2 = -5v1 Hence, 60is = 5v1 + 15v1 = 20v1 which leads to v1 = 3is, v2 = -15is i0 = v2/50 = -15is/50 which leads to i0/is = -15/50 = –0. 3 (1) PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 62. Experience the intricacy populars i1, i2, and i3 in the network of Fig. 3. 106. Figure 3. 106 Chapter 3, Separation 62 4 k? A 8 k? B 2 k? 100V + – i1 i2 i3 + – 40 V We possess a supermesh. Let all R be in k? , i in mA, and v in volts. For the supermesh, -100 +4i1 + 8i2 + 2i3 + 40 = 0 or 30 = 2i1 + 4i2 + i3 At node A, At node B, i1 + 4 = i2 i2 = 2i1 + i3 (1) (2) (3) Solving (1), (2), and (3), we get i1 = 2 mA, i2 = 6 mA, and i3 = 2 mA. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 63. Experience vx, and ix in the circumference shown in Fig. 3. 107. Figure 3. 107 Chapter 3, Separation 63 10 ? A 5? 50 V + – i1 i2 + – 4ix For the supermesh, -50 + 10i1 + 5i2 + 4ix = 0, but ix = i1. Hence, 50 = 14i1 + 5i2 At node A, i1 + 3 + (vx/4) = i2, but vx = 2(i1 – i2), hereafter, i1 + 2 = i2 Solving (1) and (2) gives i1 = 2. 105 A and i2 = 4. 105 A vx = 2(i1 – i2) = –4 volts and ix = i2 – 2 = 2. 105 amp PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. (1) (2) Chapter 3, Drift 64. Experience vo, and io in the circumference of Fig. 3. 108. Figure 3. 108 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Separation 64 i1 50 ? A i2 10 ? + ? i0 10 ? i2 i1 100V + + – 4i0 i3 40 ? – 0. 2V0 2A B i1 i3 For intricacy 2, 20i2 – 10i1 + 4i0 = 0 (1) (2) But at node A, io = i1 – i2 so that (1) beseems i1 = (16/6)i2 For the supermesh, -100 + 50i1 + 10(i1 – i2) – 4i0 + 40i3 = 0 or At node B, But, 50 = 28i1 – 3i2 + 20i3 i3 + 0. 2v0 = 2 + i1 v0 = 10i2 so that (4) beseems i3 = 2 + (2/3)i2 (3) (4) (5) Solving (1) to (5), i2 = 0. 11764, v0 = 10i2 = 1. 1764 volts, i0 = i1 - i2 = (5/3)i2 = 196. 07 mA PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 65. Use MATLAB to explain for the intricacy populars in the circumference of Fig. 3. 109. Figure 3. 109 Chapter 3, Separation 65 For intricacy 1, –12 + 12I1 – 6I2 – I4 = 0 or 12 = 12I 1 ? 6 I 2 ? I 4 For intricacy 2, For intricacy 3, For intricacy 4, For intricacy 5, –6I1 + 16I2 – 8I3 – I4 – I5 = 0 –8I2 + 15I3 – I5 – 9 = 0 or 9 = –8I2 + 15I3 – I5 –I1 – I2 + 7I4 – 2I5 – 6 = 0 or 6 = –I1 – I2 + 7I4 – 2I5 –I2 – I3 – 2I4 + 8I5 – 10 = 0 or 10 = ? I 2 ? I 3 ? 2 I 4 + 8I 5 (2) (3) (4) (5) (1) PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Casting (1) to (5) in matrix create gives 1 0 ?? I1 ? ?12 ? ? 12 ? 6 0 ?? ? ? ? ? ? ? 6 16 ? 8 ? 1 ? 1 ?? I 2 ? ? 0 ? ? 0 ? 8 15 0 ? 1 ?? I ? = ? 9 ? ?? 3 ? ? ? ? 7 ? 2 ?? I 4 ? ? 6 ? ? ? 1 ? 1 0 ? 0 ? 1 ? 1 ? 2 8 ?? I ? ?10 ? ?? 5 ? ? ? ? ? ? > AI = B Using MATLAB we input: Z=[12,-6,0,-1,0;-6,16,-8,-1,-1;0,-8,15,0,-1;-1,-1,0,7,-2;0,-1,-1,-2,8] and V=[12;0;9;6;10] This leads to >> Z=[12,-6,0,-1,0;-6,16,-8,-1,-1;0,-8,15,0,-1;-1,-1,0,7,-2;0,-1,-1,-2,8] Z= 12 -6 0 -1 0 -6 0 -1 16 -8 -1 -8 15 0 -1 0 7 -1 -1 -2 0 -1 -1 -2 8 gt;> V=[12;0;9;6;10] V= 12 0 9 6 10 >> I=inv(Z)*V I= 2. 1701 1. 9912 1. 8119 2. 0942 2. 2489 Thus, I = [2. 17, 1. 9912, 1. 8119, 2. 094, 2. 249] A. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 66. Transcribe a set of intricacy equations for the circumference in Fig. 3. 110. Use MATLAB to dissecticularize the intricacy populars. 10 ? 10 ? 8? 12 V + _ 6? 4? I1 + _ 2? I2 24 V + _ 6? 8? 40 V 2? I4 4? 8? 30 V + _ I3 8? 4? I5 + _ 32 V Figure 3. 110 For Prob. 3. 66. Chapter 3, Separation 66 The intricacy equations are conciliateed as follows. ?12 + 24 + 30I1 ? 4I2 ? 6I3 ? 2I4 = 0 or 30I1 – 4I2 – 6I3 – 2I4 = –12 ? 24 + 40 ? 4I1 + 30I2 ? 2I4 ? 6I5 = 0 or –4I1 + 30I2 – 2I4 – 6I5 = –16 –6I1 + 18I3 – 4I4 = 30 –2I1 – 2I2 – 4I3 + 12I4 –4I5 = 0 –6I2 – 4I4 + 18I5 = –32 (1) 2) (3) (4) (5) PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Putting (1) to (5) in matrix create ? 30 ? 4 ? 6 ? 2 0 ? ? ? 12 ? ?? 30 0 ? 2 ? 6? ? ? 16 ? ? ? ? ? ? ? 6 0 18 ? 4 0 ? I = ? 30 ? ? ? ? ? ?? 2 ? 2 ? 4 12 ? 4? ? 0 ? ? 0 ? 6 0 ? 4 18 ? ?? 32? ? ? ? ? ZI = V Using MATLAB, >> Z = [30,-4,-6,-2,0; -4,30,0,-2,-6; -6,0,18,-4,0; -2,-2,-4,12,-4; 0,-6,0,-4,18] Z= 30 -4 -6 -2 0 -4 30 0 -2 -6 -6 0 18 -4 0 -2 0 -2 -6 -4 0 12 -4 -4 18 >> V = [-12,-16,30,0,-32]' V= -12 -16 30 0 -32 ;; I = inv(Z)*V I= -0. 2779 A -1. 0488 A 1. 4682 A -0. 4761 A -2. 2332 A PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 67. Conciliate the node-voltage equations for the circumference in Fig. 3. 111 by inadvertence. Then explain for Vo. 2A 4? 2? + Vo _ 3 Vo 10 ? 5? 4A Figure 3. 111 For Prob. 3. 67. Chapter 3, Separation 67 Consider the circumference beneath. A V1 4? V2 2? + Vo - V3 3 Vo 10 ? 5? 4A 0 ? ? 0. 35 ? 0. 25 ?? 2 + 3Vo ? ?? 0. 25 0. 95 ? 0. 5? V = ? ? 0 ? ? ? ? ? 0 ? ? ? 0. 5 0. 5 ? 6 ? ? ? ? PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Since we in-effect possess disgusting unknowns and barely three equations, we deficiency a occupation equation. Vo = V2 – V3 Substituting this tail into the matrix equation, the earliest equation beseems, 0. 35V1 – 3. 25V2 + 3V3 = –2 This now results in the subjoined matrix equation, 3 ? ? 0. 35 ? 3. 25 ? ? 2? ?? 0. 25 0. 95 ? 0. 5? V = ? 0 ? ? ? ? ? ? 0 ? 6? ? 0. 5 0. 5 ? ? ? ? ? Now we can use MATLAB to explain for V. ;; Y=[0. 35,-3. 25,3;-0. 25,0. 95,-0. 5;0,-0. 5,0. 5] Y= 0. 3500 -3. 2500 3. 0000 -0. 2500 0. 9500 -0. 5000 0 -0. 5000 0. 5000 ;; I=[-2,0,6]' I= -2 0 6 >> V=inv(Y)*I V= -164. 105 -77. 8947 -65. 8947 Vo = V2 – V3 = –77. 89 + 65. 89 = –12 V. Let us now do a hasty cohibit at node 1. –3(–12) + 0. 1(–164. 21) + 0. 25(–164. 21+77. 89) + 2 = +36 – 16. 421 – 21. 58 + 2 = –0. 001; tally cohibits! PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 68. Experience the voltage Vo in the circumference of Fig. 3. 112. 3A 10 ? + 4A 40 ? Vo _ 25 ? 20 ? + _ 24 V Figure 3. 112 For Prob. 3. 68. Chapter 3, Separation 68 Consider the circumference beneath. There are two non-reference nodes. 3A V1 10 ? + Vo 25 ? 4A 40 ? Vo _ 20 ? + _ 24 V PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. ? +4+3 ? ? 7 ? ?0. 125 ? 0. 1? ? ? 0. 1 0. 19 ? V = ?? 3 + 24 / 25? = ?? 2. 04? ? ? ? ? ? ? Using MATLAB, we get, >> Y=[0. 125,-0. 1;-0. 1,0. 19] Y= 0. 1250 -0. 1000 -0. 1000 0. 1900 >> I=[7,-2. 04]' I= 7. 0000 -2. 400 ;; V=inv(Y)*I V= 81. 8909 32. 3636 Thus, Vo = 32. 36 V. We can percreate a uncompounded cohibit at node Vo, 3 + 0. 1(32. 36–81. 89) + 0. 05(32. 36) + 0. 04(32. 36–24) = 3 – 4. 953 + 1. 618 + 0. 3344 = – 0. 0004; tally cohibits! PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 69. For the circumference in Fig. 3. 113, transcribe the node voltage equations by inadvertence. Figure 3. 113 Chapter 3, Separation 69 Usurp that all conductances are in mS, all populars are in mA, and all voltages are in volts. G11 = (1/2) + (1/4) + (1/1) = 1. 75, G22 = (1/4) + (1/4) + (1/2) = 1, G33 = (1/1) + (1/4) = 1. 25, G12 = -1/4 = -0. 25, G13 = -1/1 = -1, G21 = -0. 25, G23 = -1/4 = -0. 25, G31 = -1, G32 = -0. 25 i1 = 20, i2 = 5, and i3 = 10 – 5 = 5 The node-voltage equations are: 1 ? ? v 1 ? ?20? ? 1. 75 ? 0. 25 ? ? 0. 25 1 ? 0. 25? ? v 2 ? = ? 5 ? ? ?? ? ? ? ? 0. 25 1. 25 ? ? v 3 ? ? 5 ? ? ? ?1 ?? ? ? ? PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 70. Transcribe the node-voltage equations by inadvertence and then dissecticularize prizes of V1 and V2 in the circumference in Fig. 3. 114. V1 ix 4A 1S 2S 4ix V2 5S 2A Figure 3. 114 For Prob. 3. 70. Chapter 3, Separation 70 ? 4I x + 4 ? ?3 0? ?0 5 ? V = ? ? 4 I ? 2 ? x ? ? ? ? After a while two equations and three unknowns, we deficiency a occupation equation, Ix = 2V1, thus the matrix equation beseems, ? ? 5 0? ?4? V=? ? ? 8 5? ? ? ? ? 2? This results in V1 = 4/(–5) = –0. 8V and V2 = [–8(–0. 8) – 2]/5 = [6. 4 – 2]/5 = 0. 88 V. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 71. Transcribe the intricacy-popular equations for the circumference in Fig. 3. 115. Next, dissecticularize the prizes of I1, I2, and I3. 5? I1 I3 3? 10 V + _ 1? 2? 4? I2 + _ 5V Figure 3. 15 For Prob. 3. 71. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Separation 71 ? 9 ? 4 ? 5? ? 10 ? ?? 4 7 ? 1? I = ?? 5? ? ? ? ? ?? 5 ? 1 9 ? ? 0 ? ? ? ? ? We can now use MATLAB explain for our populars. ;; R=[9,-4,-5;-4,7,-1;-5,-1,9] R= 9 -4 -5 -4 7 -1 -5 -1 9 ;; V=[10,-5,0]' V= 10 -5 0 >> I=inv(R)*V I= 2. 085 A 653. 3 mA 1. 2312 A PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 72. By inadvertence, transcribe the intricacy-popular equations for the circumference in Fig. 3. 116. Figure 3. 116 Chapter 3, Separation 72 R11 = 5 + 2 = 7, R22 = 2 + 4 = 6, R33 = 1 + 4 = 5, R44 = 1 + 4 = 5, R12 = -2, R13 = 0 = R14, R21 = -2, R23 = -4, R24 = 0, R31 = 0, R32 = -4, R34 = -1, R41 = 0 = R42, R43 = -1, we voicelessness that Rij = Rji for all i not resembling to j. v1 = 8, v2 = 4, v3 = -10, and v4 = -4 Hereafter the intricacy-popular equations are: 0 ? i1 ? ? 8 ? ? 7 ? 2 0 ? ? 2 6 ? 4 0 ? ?i ? ? 4 ? ? ? ?? 2 ? = ? ? 0 ? 4 5 ? 1? ?i 3 ? ? ? 10? ? ? ?? ? ? 0 ? 1 5 ? ?i 4 ? ? ? 4 ? ? 0 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 73. Transcribe the intricacy-popular equations for the circumference in Fig. 3. 117. Figure 3. 117 Chapter 3, Separation 73 R11 = 2 + 3 +4 = 9, R22 = 3 + 5 = 8, R33 = 1+1 + 4 = 6, R44 = 1 + 1 = 2, R12 = -3, R13 = -4, R14 = 0, R23 = 0, R24 = 0, R34 = -1 v1 = 6, v2 = 4, v3 = 2, and v4 = -3 Hence, ? 9 ? 3 ? 4 0 ? ? i1 ? ? 6 ? ?? 3 8 0 0 ? ?i 2 ? ? 4 ? ?? ? = ? ? ? ?? 4 0 6 ? 1? ?i3 ? ? 2 ? ?? ? ? ? ? 0 ? 1 2 ? ?i 4 ? ?? 3? ?0 PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 74. By inadvertence, conciliate the intricacy-popular equations for the circumference in Fig. 3. 11. Figure 3. 118 Chapter 3, Separation 74 R11 = R1 + R4 + R6, R22 = R2 + R4 + R5, R33 = R6 + R7 + R8, R44 = R3 + R5 + R8, R12 = -R4, R13 = -R6, R14 = 0, R23 = 0, R24 = -R5, R34 = -R8, anew, we voicelessness that Rij = Rji for all i not resembling to j. ? V1 ? ?? V ? 2? The input voltage vector is = ? ? V3 ? ? ? ? ? V4 ? ?R 1 + R 4 + R 6 ? ? R4 ? ? R6 ? ? 0 ? ? R4 R2 + R4 + R5 0 ? R5 ? R6 0 R6 + R7 + R8 ? R8 0 ? ? i 1 ? ? V1 ? ? ? i ? ? ? V ? ? R5 2? ?? 2 ? = ? ? R8 ? ?i 3 ? ? V3 ? ? ?? ? ? R 3 + R 5 + R 8 ? ?i 4 ? ? ? V4 ? PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 75. Use PSpice to explain Prob. 3. 58. Chapter 3, Drift 58 Experience i1, i2, and i3 the circumference in Fig. 3. 103. Figure 3. 103 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Separation 75 * Schematics Netlist * R_R4 R_R2 R_R1 R_R3 R_R5 V_V4 v_V3 v_V2 v_V1 $N_0002 $N_0001 30 $N_0001 $N_0003 10 $N_0005 $N_0004 30 $N_0003 $N_0004 10 $N_0006 $N_0004 30 $N_0003 0 120V $N_0005 $N_0001 0 0 $N_0006 0 0 $N_0002 0 3 i1 i2 Clearly, i1 = –3 amps, i2 = 0 amps, and i3 = 3 amps, which agrees after a while the tallys in Drift 3. 44. Chapter 3, Drift 76. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Use PSpice to explain Prob. 3. 27. Chapter 3, Drift 27 Use nodal segregation to dissecticularize voltages v1, v2, and v3 in the circumference in Fig. 3. 76. Figure 3. 76 Chapter 3, Separation 76 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. * Schematics Netlist * I_I2 R_R1 R_R3 R_R2 F_F1 VF_F1 R_R4 R_R6 I_I1 R_R5 0 $N_0001 DC 4A $N_0002 $N_0001 0. 25 $N_0003 $N_0001 1 $N_0002 $N_0003 1 $N_0002 $N_0001 VF_F1 3 $N_0003 $N_0004 0V 0 $N_0002 0. 5 0 $N_0001 0. 5 0 $N_0002 DC 2A 0 $N_0004 0. 25 Clearly, v1 = 625 mVolts, v2 = 375 mVolts, and v3 = 1. 625 volts, which agrees after a while the separation conciliateed in Drift 3. 27. Chapter 3, Drift 77. Explain for V1 and V2 in the circumference of Fig. 3. 119 using PSpice. PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. 2 ix V1 5? V2 5A 2? ix 1? 2A Figure 3. 119 For Prob. 3. 77. Chapter 3, Separation 77 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. As a cohibit we can transcribe the nodal equations, ? 1. 7 ? 0. 2? ?5? V=? ? ?? 1. 2 1. 2 ? ? ? ? ? 2? Solving this leads to V1 = 3. 111 V and V2 = 1. 4444 V. The tally cohibits! Chapter 3, Drift 78. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Explain Prob. 3. 20 using PSpice. Chapter 3, Drift 20 For the circumference in Fig. 3. 9, experience V1, V2, and V3 using nodal segregation. Figure 3. 69 Chapter 3, Separation 78 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. The schematic is shown beneath. When the circumference is saved and false the node voltages are displaced on the pseudocomponents as shown. Thus, V1 = ? 3V, V2 = 4. 5V, V3 = ? 15V, . Chapter 3, Drift 79. Rework Prob. 3. 28 using PSpice. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 3, Drift 28 Use MATLAB to experience the voltages at nodes a, b, c, and d in the circumference of Fig. 3. 77. Figure 3. 77 Chapter 3, Separation 79 The schematic is shown beneath. When the circumference is saved and false, we conciliate the node voltages as displaced. Thus, Va = ? 5. 278 V, Vb = 10. 28 V, Vc = 0. 6944 V, Vd = ? 26. 88 V Chapter 3, Drift 80. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Experience the nodal voltage v1 through v4 in the circumference in Fig. 3. 120 using PSpice. Figure 3. 120 Chapter 3, Separation 80 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. * Schematics Netlist * H_H1 VH_H1 I_I1 V_V1 R_R4 R_R1 R_R2 R_R5 R_R3 $N_0002 $N_0003 VH_H1 6 0 $N_0001 0V $N_0004 $N_0005 DC 8A $N_0002 0 20V 0 $N_0003 4 $N_0005 $N_0003 10 $N_0003 $N_0002 12 0 $N_0004 1 $N_0004 $N_0001 2 Clearly, v1 = 84 volts, v2 = 4 volts, v3 = 20 volts, and v4 = -5. 333 volts Chapter 3, Drift 81. Use PSpice to explain the drift in Example 3. 4 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Example 3. 4 Experience the node voltages in the circumference of Fig. 3. 12. Figure 3. 12 Chapter 3, Separation 81 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Clearly, v1 = 26. 67 volts, v2 = 6. 667 volts, v3 = 173. 33 volts, and v4 = -46. 67 volts which agrees after a while the results of Example 3. 4. This is the netlist for this circumference. * Schematics Netlist * R_R1 R_R2 R_R3 R_R4 R_R5 I_I1 V_V1 E_E1 0 $N_0001 2 $N_0003 $N_0002 6 0 $N_0002 4 0 $N_0004 1 $N_0001 $N_0004 3 0 $N_0003 DC 10A $N_0001 $N_0003 20V $N_0002 $N_0004 $N_0001 $N_0004 3 Chapter 3, Drift 82. If the Schematics Netlist for a network is as follows, sketch the network. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. R_R1 R_R2 R_R3 R_R4 R_R5 V_VS I_IS F_F1 VF_F1 E_E1 1 2 2 3 1 4 0 1 5 3 2 0 0 4 3 0 1 3 0 2 2K 4K 8K 6K 3K DC DC VF_F1 0V 1 100 4 2 3 3 Chapter 3, Separation 82 2i0 + v0 – 3 k? 1 4A 2 k? 2 + 3v0 3 6 k? 4 4 k? 8 k? 100V + – 0 This network corresponds to the Netlist. Chapter 3, Drift 83. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. The subjoined program is the Schematics Netlist of a divorceicular circumference. Draw the circumference and dissecticularize the voltage at node 2. R_R1 R_R2 R_R3 R_R4 V_VS I_IS 1 2 2 3 1 2 2 0 3 0 0 0 20 50 70 30 20V DC 2A Chapter 3, Separation 83 The circumference is shown beneath. 1 20 ? 2 70 ? 3 20 V + – 50 ? 2A 30 ? 0 When the circumference is saved and false, we conciliate v2 = –12. 5 volts Chapter 3, Drift 84. Estimate vo and io in the circumference of Fig. 3. 121. Figure 3. 121 Chapter 3, Separation 84 From the output loop, v0 = 50i0x20x103 = 106i0 (1) From the input loop, 3x10-3 + 4000i0 – v0/100 = 0 (2) From (1) and (2) we get, i0 = 0. 5? A and v0 = 0. 5 volt. Chapter 3, Drift 85. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. An audio amplifier after a while hindrance 9? arrangement force to a orator. In direct that zenith force is delivered, what should be the hindrance of the orator? Chapter 3, Separation 85 The amplifier acts as a commencement. Rs + Vs RL For zenith force remove, R L = R s = 9? Chapter 3, Drift 86. For the simplified transistor circumference of Fig. 3. 122, estimate the voltage vo. Figure 3. 122 Chapter 3, Separation 86 Let v1 be the virtual counter the 2 k-ohm resistor after a while plus nature on top. Then, [(0. 03 – v1)/1k] + 400i = v1/2k (1) Usurp that i is in mA. But, i = (0. 03 – v1)/1 Combining (1) and (2) yields, v1 = 29. 963 mVolts and i = 37. nA, accordingly, v0 = -5000x400x37. 4x10-9 = -74. 8 mvolts (2) Chapter 3, Drift 87. For the circumference in Fig. 3. 123, experience the create vo/vs. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Figure 3. 123 Chapter 3, Separation 87 v1 = 500(vs)/(500 + 2000) = vs/5 v0 = -400(60v1)/(400 + 2000) = -40v1 = -40(vs/5) = -8vs, Therefore, v0/vs = –8 Chapter 3, Drift 88. Particularize the create vo/vs of the transistor amplifier circumference in Fig. 3. 124. Figure 3. 124 Chapter 3, Separation 88 Let v1 be the virtual at the top end of the 100-ohm resistor. (vs – v1)/200 = v1/100 + (v1 – 10-3v0)/2000 For the fit loop, v0 = -40i0(10,000) = -40(v1 – 10-3)10,000/2000, or, v0 = -200v1 + 0. 2v0 = -4x10-3v0 (2) (1) Substituting (2) into (1) gives, (vs + 0. 004v1)/2 = -0. 004v0 + (-0. 04v1 – 0. 001v0)/20 This leads to 0. 125v0 = 10vs or (v0/vs) = 10/0. 125 = -80 Chapter 3, Drift 89. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. For the transistor circumference shown in Fig. . 125, experience IB and VCE. Let ? = 100 and VBE = 0. 7V. _ 3V + _ 1 k? 0. 7 V + 100 k? | | 15 V Figure 3. 125 For Prob. 3. 89. Chapter 3, Separation 89 Consider the circumference beneath. _ 0. 7 V C + 100 k? + IC VCE _ 3V + _ E For the left loop, applying KVL gives VBE = 0. 7 ? 3 ? 0. 7 + 100 x103 IB + VBE = 0 ???? IB = 30 ? A > For the fit loop, ? VCE + 15 ? Ic(1x10 3 ) = 0 But IC = ? IB = 100 x30 ? A= 3 mA | | 15 V 1 k? VCE = 15 ? 3 x10 ? 3 x103 = 12 V Chapter 3, Drift 90. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Estimate vs for the transistor in Fig. 3. 126, absorbed that vo = 4 V, ? = 150, VBE = 0. 7V. Figure 3. 126 Chapter 3, Separation 90 1 k? 10 k? IB + VBE + VCE – i2 + vs + – - i1 18V 500 ? + V0 - IE – For loop 1, -vs + 10k(IB) + VBE + IE (500) = 0 = -vs + 0. + 10,000IB + 500(1 + ? )IB which leads to vs + 0. 7 = 10,000IB + 500(151)IB = 85,500IB But, v0 = 500IE = 500x151IB = 4 which leads to IB = 5. 298x10-5 Therefore, vs = 0. 7 + 85,500IB = 5. 23 volts Chapter 3, Drift 91. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. For the transistor circumference of Fig. 3. 127, experience IB, VCE, and vo. Take ? = 200, VBE = 0. 7V. Figure 3. 127 Chapter 3, Separation 91 We earliest dissecticularize the Thevenin equipollent for the input circumference. RTh = 6||2 = 6x2/8 = 1. 5 k? and VTh = 2(3)/(2+6) = 0. 75 volts 5 k? IC 1. 5 k? IB + VBE + VCE – i2 + + 0. 75 V – - i1 9V 400 ? + V0 - IE B – For loop 1, -0. 75 + 1. 5kIB + VBE + 400IE = 0 = -0. 75 + 0. 7 + 1500IB + 400(1 + ? )IB B B IB = 0. 05/81,900 = 0. 61 ? A B v0 = 400IE = 400(1 + ? IB = 49 mV B For loop 2, -400IE – VCE – 5kIC + 9 = 0, but, IC = ? IB and IE = (1 + ? )IB B B VCE = 9 – 5k? IB – 400(1 + ? )IB = 9 – 0. 659 = 8. 641 volts B B Chapter 3, Drift 92. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Experience IB and VC for the circumference in Fig. 3. 128. Let ? = 100, VBE = 0. 7V. Figure 3. 128 Chapter 3, Separation 92 10 k? I1 5 k? VC IC IB + + VBE 4 k? VCE – – 12V + + V0 - IE – I1 = IB + IC = (1 + ? )IB and IE = IB + IC = I1 Applying KVL environing the external loop, 4kIE + VBE + 10kIB + 5kI1 = 12 12 – 0. 7 = 5k(1 + ? )IB + 10kIB + 4k(1 + ? )IB = 919kIB IB = 11. 3/919k = 12. 296 ? A Also, 12 = 5kI1 + VC which leads to VC = 12 – 5k(101)IB = 5. 791 volts Chapter 3, Drift 93 Rework Example 3. 1 after a while index consideration. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. In the circumference in Fig. 3. 34, dissecticularize the populars i1, i2, and i3. Figure 3. 34 Chapter 3, Separation 93 ? 4? v1 i1 2? i 2? 3v0 v2 i3 + 8? 2? 3v0 i2 4? i + v0 + + v2 24V + + v1 – – – – (a) (b) From (b), -v1 + 2i – 3v0 + v2 = 0 which leads to i = (v1 + 3v0 – v2)/2 At node 1 in (a), ((24 – v1)/4) = (v1/2) + ((v1 +3v0 – v2)/2) + ((v1 – v2)/1), where v0 = v2 or 24 = 9v1 which leads to v1 = 2. 667 volts At node 2, ((v1 – v2)/1) + ((v1 + 3v0 – v2)/2) = (v2/8) + v2/4, v0 = v2 v2 = 4v1 = 10. 66 volts Now we can explain for the populars, i1 = v1/2 = 1. 333 A, i2 = 1. 333 A, and i3 = 2. 6667 A. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 4, Drift 1. Estimate the popular io in the circumference of Fig. 4. 69. What does this popular beseem when the input voltage is violent to 10 V? Figure 4. 69 Chapter 4, Separation 1. + ? 8 (5 + 3) = 4? , i = io = 1 1 = 1+ 4 5 1 i= = 0. 1A 2 10 Since the hindrance scum the corresponding we get i = 10/5 = 2A which leads to io = (1/2)i = (1/2)2 = 1A. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 4, Drift 2. Find vo in the circumference of Fig. 4. 70. If the commencement popular is deep to 1 ? A, what is vo? Figure 4. 70 Chapter 4, Separation 2. 6 (4 + 2) = 3? , i1 = i 2 = io = 1 A 2 1 1 i1 = , v o = 2i o = 0. 5V 2 4 If is = 1? A, then vo = 0. 5? V PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 4, Drift 3. (a) In the circumference in Fig. 4. 71, estimate vo and Io when vs = 1 V. (b) Experience vo and io when vs = 10 V. (c) What are vo and Io when each of the 1-? resistors is replaced by a 10-? resistor and vs = 10 V? Figure 4. 71 Chapter 4, Separation 3. + ? + vo + ? (a) We transcreate the Y sub-circumference to the equipollent ? . 3R 2 3 3 3 3 = R, R + R = R R 3R = 4R 4 4 4 2 vs vo = recalcitrant of R 2 io = vo/(R) When vs = 1V, vo = 0. 5V, io = 0. 5A (b) When vs = 10V, vo = 5V, io = 5A (c) When vs = 10V and R = 10? vo = 5V, io = 10/(10) = 500mA PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 4, Drift 4. Use directity to dissecticularize io in the circumference in Fig. 4. 72. Figure 4. 72 Chapter 4, Separation 4. If Io = 1, the voltage counter the 6? resistor is 6V so that the popular through the 3? resistor is 2A. + v1 3 6 = 2? , vo = 3(4) = 12V, i1 = Hereafter Is = 3 + 3 = 6A If Is = 6A Is = 9A Io = 1 Io = 9/6 = 1. 5A vo = 3A. 4 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 4, Drift 5. For the circumference in Fig. 4. 73, usurp vo = 1 V, and use directity to experience the explicit prize of vo. Figure 4. 73 Chapter 4, Separation 5. + ? If vo = 1V, ?1? V1 = ? ? + 1 = 2V ? 3? 10 ? 2? Vs = 2? ? + v1 = 3 ? 3? If vs = 10 3 vo = 1 vo = 3 x15 = 4. 5V 10 Then vs = 15 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 4, Drift 6. For the direct circumference shown in Fig. 4. 74, use directity to consummate the subjoined consideration. Illustration 1 2 3 4 Vs 12 V -1V -Vo 4V 16 V --2V + Vs + _ Direct Circumference Vo – Figure 4. 74 For Prob. 4. 6. Chapter 4, Separation 6. Due to directity, from the earliest illustration, 1 Vo = Vs 3 Applying this to other illustrations, we conciliate: Illustration 2 3 4 Vs 48 1V -6 V Vo 16 V 0. 333 V -2V PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All hues silent. No divorce of this Manual may be displayed, reproduced or exclusive in any create or by any media, extraneously the antecedent written consent of the publisher, or used further the poor division to teachers and educators at-liberty by McGraw-Hill for their singular manner provision. If you are a ward using this Manual, you are using it extraneously consent. Chapter 4, Drift 7. Use directity and the conviction that Vo = 1V to experience the explicit prize of Vo in Fig. 4. 75. . 1? 4? + 4V + _ 3? 2? Vo _ Figure 4. 75 For Prob. 4. 7. Chapter 4, Separation 7. If Vo = 1V, then the popular through the 2-? and 4-? resistors is ? = 0. 5. The voltage counter the 3-? resistor is ? (4 + 2) = 3 V. The aggregate popular through the 1-? resistor is 0. 5 +3/3 = 1. 5 A. Hereafter the