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### Transcript of Chapter10 : Sinusoidal Steady-State Analysis electric circuit textbook solution

• PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 10, Problem 1. Determine i in the circuit of Fig. 10.50. Figure 10.50 For Prob. 10.1. Chapter 10, Solution 1. We first determine the input impedance. 1 1 10 10H j L j x j = = 111 0.1 10 1 F j j C j x = = 1 1 1 1 1 1.0101 0.1 1.015 5.653 10 0.1 1 o inZ j j j = + + + = = < 2 0 1.9704 5.653 1.015 5.653 o o o I < = = < < ( ) 1.9704cos(10 5.653 ) Ao i t t= + = 1.9704cos(10t+5.65) A
• PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 10, Problem 2. Solve for Vo in Fig. 10.51, using nodal analysis. Figure 10.51 For Prob. 10.2. Chapter 10, Solution 2. Consider the circuit shown below. 2 Vo j5 j4 40o V- At the main node, 4 40 (10 ) 2 5 4 o o o o V V V V j j j = + = + 40 3.98 5.71 A 10 o oV j = = < + _
• PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 10, Problem 3. Determine ov in the circuit of Fig. 10.52. Figure 10.52 For Prob. 10.3. Chapter 10, Solution 3. 4= 02)t4cos(2 -j1690-16)t4sin(16 = 8jLjH2 = 3j- )121)(4(j 1 Cj 1 F121 == The circuit is shown below. Applying nodal analysis, 8j61 2 3j4 16j- ooo + +=+ VVV o 8j6 1 3j4 1 12 3j4 16j- V + + +=+ = = + = 02.35-835.3 88.12207.1 15.33-682.4 04.0j22.1 56.2j92.3 oV Therefore, =)t(vo 3.835 cos(4t 35.02) V j8 1 6 -j3 4 -j16 V 20 A + Vo
• PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 10, Problem 4. Determine 1i in the circuit of Fig. 10.53. Figure 10.53 For Prob. 10.4. Chapter 10, Solution 4. 3 0.5 0.5 10 500H j L j x j = = 3 6 112 500 10 2 10 F j j C j x x = = Consider the circuit as shown below. I1 2000 V1 -j500 500o V j500 + 30I1 At node 1, + = 1 1 1 150 30 2000 500 500 V I V V j j But = 1 1 50 2000 V I + + = =1 1 1 1 1 50 50 4 30( ) 4 4 0 50 2000 V V j x j V j V V = =1 1 50 0 2000 V I =1( ) 0 Ai t + _
• PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 10, Problem 5. Find oi in the circuit of Fig. 10.54. Figure 10.54 For Prob. 10.5.
• PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 10, Solution 5. 3 0.25 0.25 4 10 1000H j L j x x j = = 3 6 112 125 4 10 2 10 F j j C j x x x = = Consider the circuit as shown below. Io 2000 Vo -j125 250o V j1000 + 10Io At node Vo, 25I160jV)14j1( 0I160jV16jV2j25V 0 125j I10V 1000j 0V 2000 25V oo oooo oooo =+ =+ = + + But Io = (25Vo)/2000 = + + = =++ 37.817768.1 94.58115.14 57.408.25 08.14j1 2j25 V 25V08.0j2jV)14j1( o oo Now to solve for io, = += + = = 06.4398.12 mA8784.0j367.12 2000 7567.1j2666.025 2000 V25 I o o io = 12.398cos(4x103 t + 4.06) mA. + _
• PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 10, Problem 6. Determine V x in Fig. 10.55. Figure 10.55 For Prob. 10.6. Chapter 10, Solution 6. Let Vo be the voltage across the current source. Using nodal analysis we get: 0 10j20 V 3 20 V4V oxo = + + where ox V 10j20 20 V + = Combining these we get: 30j60V)35.0j1(0 10j20 V 3 10j20 V4 20 V o ooo +=+= + + + = + = + + = 5.0j2 )3(20 Vor 5.0j2 30j60 V xo 29.11166 V.
• PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 10, Problem 7. Use nodal analysis to find V in the circuit of Fig. 10.56. Figure 10.56 For Prob. 10.7. Chapter 10, Solution 7. At the main node, ++ + = + + += + 50 1 30 j 20j40 1 V 3j196.5 20j40 058.31j91.115 50 V 30j V 306 20j40 V15120 o o V15408.124 0233.0j04.0 7805.4j1885.3 V o = + =
• PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 10, Problem 8. Use nodal analysis to find current oi in the circuit of Fig. 10.57. Let ( )+= 15200cos6 tis A. Figure 10.57 For Prob. 10.8. Chapter 10, Solution 8. ,200= 20j1.0x200jLjmH100 == 100j 10x50x200j 1 Cj 1 F50 6 == The frequency-domain version of the circuit is shown below. 0.1 Vo 40 V1 Io V2 + -j100 o 156 20 Vo j20 -
• PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. At node 1, 40 VV 100j V 20 V V1.0156 2111 1 o + +=+ or 21 025.0)01.0025.0(5529.17955.5 VVjj +=+ (1) At node 2, 21 2 1 21 V)2j1(V30 20j V V1.0 40 VV +=+= (2) From (1) and (2), BAVor 0 )5529.1j7955.5( V V )2j1(3 025.0)01.0j025.0( 2 1 = + = + Using MATLAB, V = inv(A)*B leads to 09.1613.110,23.12763.70 21 jVjV +== o21 o 17.82276.7 40 VV I = = Thus, A)17.82t200cos(276.7)t(i o o =
• PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 10, Problem 9. Use nodal analysis to find ov in the circuit of Fig. 10.58. Figure 10.58 For Prob. 10.9.
• PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 10, Solution 9. 33 10,010)t10cos(10 = 10jLjmH10 = 20j- )1050)(10(j 1 Cj 1 F50 6-3 = = Consider the circuit shown below. At node 1, 20j-202