1. ECEN 301Discussion #12 –Exam 1 Review1 Examine Yourselves Moroni 10: 3 3 Behold, I would exhort you that when ye shall read these things, if it be wisdom in God that ye should read them, that ye would remember how merciful the Lord hath been unto the children of men, from the creation of Adam even down until the time that ye shall receive these things, and ponder it in your hearts. 2 Cor. 13: 5 5 Examine yourselves, whether ye be in the faith; prove your own selves.

2. ECEN 301Discussion #12 – Exam 1 Review2 Lecture 12 – Exam 1 Review Chapters 2 - 3

3. ECEN 301Discussion #12 –Exam 1 Review3 Exam 1 13 – 16 Feb (Monday – Thursday) – Testing Center Chapters 2 and 3 About 23 -25 questions 20 multiple choice (answer on bubble sheet!) 2 points each 3 long answer (show your work!) 5 points each Closed book! Calculators not allowed Time limit 3 hours (plan on 1-3 hours) Suggestions: study lecture slides, examples in book, and homework. Practice!

4. ECEN 301Discussion #12 –Exam 1 Review4 Exam 1 Review…Overview 1.Kirchoff’s current law 2.Kirchoff’s voltage law 3.Passive sign convention 4.Voltage/current dividers (Ohm’s Law) 5.Wheatstone bridge 6.Measuring Devices 7.Node voltage method 8.Mesh current method 9.Principle of superposition 10.Source transformation 11.Thévenin equivalent circuits 12.Norton equivalent circuits 13.Maximum power transfer 14.Dependent Sources

5. ECEN 301Discussion #12 –Exam 1 Review5 Exam 1 Review…KCL 1.What is Kirchoff’s current law?

6. ECEN 301Discussion #12 –Exam 1 Review6 Exam 1 Review…KCL 1.What is Kirchoff’s current law? a) What is an expression for the current at Node a? V s1 + _ V s2 + _ R2R2 R3R3 R4R4 R5R5 i s1 i2i2 i s2 i4i4 i3i3 i5i5 Node a

7. ECEN 301Discussion #12 –Exam 1 Review7 Exam 1 Review…KCL 1.What is Kirchoff’s current law? a) What is an expression for the current at Node a? V s1 + _ V s2 + _ R2R2 R3R3 R4R4 R5R5 i s1 i2i2 i s2 i4i4 i3i3 i5i5 Node a

8. ECEN 301Discussion #12 –Exam 1 Review8 Exam 1 Review…KCL 1.What is Kirchoff’s current law? a) What is an expression for the current at Node a? b) what expressions for the current through R 2 are valid? V s1 + _ V s2 + _ R2R2 R3R3 R4R4 R5R5 i s1 i2i2 i s2 i4i4 i3i3 i5i5 Node a

9. ECEN 301Discussion #12 –Exam 1 Review9 Exam 1 Review…KCL 1.What is Kirchoff’s current law? a) What is an expression for the current at Node a? b) what expressions for the current through R 2 are valid? V s1 + _ V s2 + _ R2R2 R3R3 R4R4 R5R5 i s1 i2i2 i s2 i4i4 i3i3 i5i5 Node a

10. ECEN 301Discussion #12 –Exam 1 Review10 Exam 1 Review…KCL 1.What is Kirchoff’s current law? a) What is an expression for the current at Node a? b) what expressions for the current through R 2 are valid? V s1 + _ V s2 + _ R2R2 R3R3 R4R4 R5R5 i s1 i2i2 i s2 i4i4 i3i3 i5i5 Node a

11. ECEN 301Discussion #12 –Exam 1 Review11 Exam 1 Review…KVL 2.What is Kirchoff’s voltage law?

12. ECEN 301Discussion #12 –Exam 1 Review12 Exam 1 Review…KVL 2.What is Kirchoff’s voltage law? a)If V s = 3V, what are the voltages across R 1, R 2, and R 3 ? isis i1i1 i2i2 i3i3 +R1–+R1– VsVs + _ +R2–+R2– +R3–+R3–

13. ECEN 301Discussion #12 –Exam 1 Review13 Exam 1 Review…KVL isis i1i1 i2i2 i3i3 +R1–+R1– VsVs + _ +R2–+R2– +R3–+R3– 2.What is Kirchoff’s voltage law? a)If V s = 3V, what are the voltages across R 1, R 2, and R 3 ?

14. ECEN 301Discussion #12 –Exam 1 Review14 Exam 1 Review…Passive Sign 3.What is the passive sign convention?

15. ECEN 301Discussion #12 –Exam 1 Review15 Exam 1 Review…Passive Sign 3.What is the passive sign convention? a)Which element dissipates power and which generates power? + v ab _ a b i v ba _ a b i +

16. ECEN 301Discussion #12 –Exam 1 Review16 Exam 1 Review…Passive Sign 3.What is the passive sign convention? a)Which element dissipates power and which generates power? + v ab _ a b i v ba _ a b i + Active Element (source) power dissipated = -vi power generated = vi Passive Element (load) power dissipated = vi power generated = -vi Positive voltageNegative voltage

17. ECEN 301Discussion #12 –Exam 1 Review17 Exam 1 Review…Passive Sign 3.What is the passive sign convention? b)Find the power dissipated by each element B E + 10V – – 3V + A D C – 5V + i e = 2A i d =3A iaia

18. ECEN 301Discussion #12 –Exam 1 Review18 Exam 1 Review…Passive Sign 3.What is the passive sign convention? b)Find the power dissipated by each element B E + 10V – – 3V + A D C – 5V + i e = 2A i d =3A a iaia Loop1 +va–+va– NB: since load D and load E share the same nodes their voltages will be the same + 10V –

19. ECEN 301Discussion #12 –Exam 1 Review19 Exam 1 Review…Passive Sign 3.What is the passive sign convention? b)Find the power dissipated by each element B E + 10V – – 3V + A D C – 5V + i e = 2A i d =3A + 10V – + 12V – i a = 5A

20. ECEN 301Discussion #12 –Exam 1 Review20 Exam 1 Review…Dividers 4.What is a voltage/current divider?

21. ECEN 301Discussion #12 –Exam 1 Review21 Exam 1 Review…Dividers 4.What is a voltage/current divider?

22. ECEN 301Discussion #12 –Exam 1 Review22 Exam 1 Review…Dividers 4.What is a voltage/current divider? a)Using a voltage divider find the voltage across R 3 V s = 3V, R1 = 10Ω, R 2 = 6Ω, R 3 = 8Ω VsVs + _ – v 1 + R1R1 + v 3 – R3R3 R2R2 +v2–+v2– i

23. ECEN 301Discussion #12 –Exam 1 Review23 Exam 1 Review…Dividers 4.What is a voltage/current divider? a)Using a voltage divider find the voltage across R 3 V s = 3V, R1 = 10Ω, R 2 = 6Ω, R 3 = 8Ω VsVs + _ – v 1 + R1R1 + v 3 – R3R3 R2R2 +v2–+v2– i

24. ECEN 301Discussion #12 –Exam 1 Review24 Exam 1 Review…Dividers 4.What is a voltage/current divider? a)Using a current divider find i 1 R 1 = 10Ω, R 2 = 2 Ω, R 3 = 20 Ω, I s = 4A i1i1 i2i2 i3i3 –R1+–R1+ isis –R2+–R2+ –R3+–R3+

25. ECEN 301Discussion #12 –Exam 1 Review25 Exam 1 Review…Dividers 4.What is a voltage/current divider? a)Using a current divider find i 1 R 1 = 10Ω, R 2 = 2 Ω, R 3 = 20 Ω, I s = 4A i1i1 i2i2 i3i3 –R1+–R1+ isis –R2+–R2+ –R3+–R3+

26. ECEN 301Discussion #12 –Exam 1 Review26 Exam 1 Review…Wheatstone 5.What is the voltage across the terminals a and b of the Wheatstone bridge? vsvs + _ R2R2 R1R1 R3R3 RxRx ba vava vbvb c d

27. ECEN 301Discussion #12 –Exam 1 Review27 Exam 1 Review…Wheatstone 5.What is the voltage across the terminals a and b of the Wheatstone bridge? vsvs + _ R2R2 R1R1 R3R3 RxRx ba vava vbvb c d

28. ECEN 301Discussion #12 –Exam 1 Review28 Exam 1 Review…Measuring 6.How do measuring devices connect to circuits?

29. ECEN 301Discussion #12 –Exam 1 Review29 Exam 1 Review…Measuring 6.How do measuring devices connect to circuits? Ω R NB: the resistance of an element can only be measured when the element is disconnected from all other circuit elements

30. ECEN 301Discussion #12 –Exam 1 Review30 Exam 1 Review…Measuring 6.How do measuring devices connect to circuits? R1R1 i R2R2 vsvs + _ A NB: 1. the ammeter must be connected in series with the circuit element 2. the ammeter should not restrict the flow of current (i.e. cause a voltage drop) – an ideal ammeter has zero resistance

31. ECEN 301Discussion #12 –Exam 1 Review31 Exam 1 Review…Measuring 6.How do measuring devices connect to circuits? i +R2–+R2– vsvs + _ V +v2–+v2– NB: 1. the voltmeter must be connected in parallel with the circuit element 2. the voltmeter should not draw any current away from the element – an ideal voltmeter has infinite resistance

32. ECEN 301Discussion #12 –Exam 1 Review32 Exam 1 Review…Measuring 6.How do measuring devices connect to circuits? R1R1 i +R2–+R2– vsvs + _ W NB: 1. the wattmeter must be connected in parallel with the circuit element, but also in series with the circuit. – a wattmeter is simply the combination of a voltmeter and an ammeter

33. ECEN 301Discussion #12 –Exam 1 Review33 Exam 1 Review…Node Voltage 7.What is the node voltage method of circuit analysis?

34. ECEN 301Discussion #12 –Exam 1 Review34 Exam 1 Review…Node Voltage 7.What is the node voltage method of circuit analysis? a)Find all unknown voltages i a = 1mA, i b = 2mA, R 1 = 1kΩ, R 2 = 500Ω, R 3 = 2.2kΩ, R 4 = 4.7kΩ iaia R1R1 R3R3 R 2 ibib R4R4

35. ECEN 301Discussion #12 –Exam 1 Review35 Exam 1 Review…Node Voltage 7.What is the node voltage method of circuit analysis? a)Find all unknown voltages i a = 1mA, i b = 2mA, R 1 = 1kΩ, R 2 = 500Ω, R 3 = 2.2kΩ, R 4 = 4.7kΩ +ia–+ia– 1.Label currents and voltages (polarities “arbitrarily” chosen) 2.Choose Node c (v c ) as the reference node (v c = 0) 3.Define remaining n – 1 (2) voltages  v a is independent  v b is independent 4.Apply KCL at nodes a and b +R1–+R1– +R3–+R3– + R 2 – +ib–+ib– i2i2 i1i1 i3i3 +R4–+R4– i4i4 Node a Node b Node c vava vbvb vcvc

36. ECEN 301Discussion #12 –Exam 1 Review36 Exam 1 Review…Node Voltage 7.What is the node voltage method of circuit analysis? a)Find all unknown voltages i a = 1mA, i b = 2mA, R 1 = 1kΩ, R 2 = 500Ω, R 3 = 2.2kΩ, R 4 = 4.7kΩ +ia–+ia– +R1–+R1– +R3–+R3– + R 2 – +ib–+ib– i2i2 i1i1 i3i3 +R4–+R4– i4i4 Node a Node b Node c vava vbvb vcvc 4.Apply KCL at nodes a and b

37. ECEN 301Discussion #12 –Exam 1 Review37 Exam 1 Review…Node Voltage 7.What is the node voltage method of circuit analysis? a)Find all unknown voltages i a = 1mA, i b = 2mA, R 1 = 1kΩ, R 2 = 500Ω, R 3 = 2.2kΩ, R 4 = 4.7kΩ +ia–+ia– +R1–+R1– +R3–+R3– + R 2 – +ib–+ib– i2i2 i1i1 i3i3 +R4–+R4– i4i4 Node a Node b Node c vava vbvb vcvc 4.Express currents in terms of voltages

38. ECEN 301Discussion #12 –Exam 1 Review38 Exam 1 Review…Node Voltage 7.What is the node voltage method of circuit analysis? a)Find all unknown voltages i a = 1mA, i b = 2mA, R 1 = 1kΩ, R 2 = 500Ω, R 3 = 2.2kΩ, R 4 = 4.7kΩ +ia–+ia– +R1–+R1– +R3–+R3– + R 2 – +ib–+ib– i2i2 i1i1 i3i3 +R4–+R4– i4i4 Node a Node b Node c vava vbvb vcvc 5.Solve the n – 1 – m equations

39. ECEN 301Discussion #12 –Exam 1 Review39 Exam 1 Review…Mesh Current 8.What is the mesh current method of circuit analysis?

40. ECEN 301Discussion #12 –Exam 1 Review40 Exam 1 Review…Mesh Current 8.What is the mesh current method of circuit analysis? a)Find the mesh currents V s = 6V, I s = 0.5A, R 1 = 3Ω, R 2 = 8Ω, R 3 = 6Ω, R 4 = 4Ω R2R2 R 1 R 4 R 3 IsIs vsvs –+–+ iaia ibib icic

41. ECEN 301Discussion #12 –Exam 1 Review41 Exam 1 Review…Mesh Current 8.What is the mesh current method of circuit analysis? a)Find the mesh currents V s = 6V, I s = 0.5A, R 1 = 3Ω, R 2 = 8Ω, R 3 = 6Ω, R 4 = 4Ω 1.Mesh current directions given 2.Voltage polarities chosen and labeled 3.Identify n – m (3) mesh currents  i a is dependent (i a = i s )  i a is independent  i c is independent 4.Apply KVL around meshes b and c +R2–+R2– + R 1 – +R 4 – +R 3 – IsIs vsvs –+–+ iaia ibib icic

42. ECEN 301Discussion #12 –Exam 1 Review42 Exam 1 Review…Mesh Current 8.What is the mesh current method of circuit analysis? a)Find the mesh currents V s = 6V, I s = 0.5A, R 1 = 3Ω, R 2 = 8Ω, R 3 = 6Ω, R 4 = 4Ω 4.Apply KVL at nodes b and c +R2–+R2– + R 1 – +R 4 – +R 3 – IsIs vsvs –+–+ iaia ibib icic

43. ECEN 301Discussion #12 –Exam 1 Review43 Exam 1 Review…Mesh Current 8.What is the mesh current method of circuit analysis? a)Find the mesh currents V s = 6V, I s = 0.5A, R 1 = 3Ω, R 2 = 8Ω, R 3 = 6Ω, R 4 = 4Ω 4.Express voltages in terms of currents +R2–+R2– + R 1 – +R 4 – +R 3 – IsIs vsvs –+–+ iaia ibib icic

44. ECEN 301Discussion #12 –Exam 1 Review44 Exam 1 Review…Mesh Current 8.What is the mesh current method of circuit analysis? a)Find the mesh currents V s = 6V, I s = 0.5A, R 1 = 3Ω, R 2 = 8Ω, R 3 = 6Ω, R 4 = 4Ω +R2–+R2– + R 1 – +R 4 – +R 3 – IsIs vsvs –+–+ iaia ibib icic 5.Solve the n – m equations

45. ECEN 301Discussion #12 –Exam 1 Review45 Exam 1 Review…Superposition 9.What is the superposition method of circuit analysis?

46. ECEN 301Discussion #12 –Exam 1 Review46 Exam 1 Review…Superposition 9.What is the superposition method of circuit analysis? a)Use superposition to find v R i s = 12A, v s = 12V, R 1 = 1Ω, R 2 = 0.3Ω, R 3 = 0.23Ω R1R1 R2R2 R3R3 vsvs +–+– isis +vR–+vR–

47. ECEN 301Discussion #12 –Exam 1 Review47 Exam 1 Review…Superposition 9.What is the superposition method of circuit analysis? a)Use superposition to find v R i s = 12A, v s = 12V, R 1 = 1Ω, R 2 = 0.3Ω, R 3 = 0.23Ω +R1–+R1– –R2+–R2+ i1i1 i2i2 R3R3 i3i3 isis + v R1 – 1.Remove all sources except i s Source v s is replaced with short circuit

48. ECEN 301Discussion #12 –Exam 1 Review48 Exam 1 Review…Superposition 9.What is the superposition method of circuit analysis? a)Use superposition to find v R i s = 12A, v s = 12V, R 1 = 1Ω, R 2 = 0.3Ω, R 3 = 0.23Ω +R1–+R1– –R2+–R2+ i1i1 i2i2 R3R3 i3i3 isis + v R1 – Node a

49. ECEN 301Discussion #12 –Exam 1 Review49 Exam 1 Review…Superposition 9.What is the superposition method of circuit analysis? a)Use superposition to find v R i s = 12A, v s = 12V, R 1 = 1Ω, R 2 = 0.3Ω, R 3 = 0.23Ω +R1–+R1– –R2+–R2+ i1i1 i2i2 R3R3 i3i3 + v R2 – 2.Remove all sources except v s Source i s is replaced with open circuit vsvs +–+–

50. ECEN 301Discussion #12 –Exam 1 Review50 Exam 1 Review…Superposition 9.What is the superposition method of circuit analysis? a)Use superposition to find v R i s = 12A, v s = 12V, R 1 = 1Ω, R 2 = 0.3Ω, R 3 = 0.23Ω +R1–+R1– –R2+–R2+ i1i1 i2i2 R3R3 i3i3 + v R2 – vsvs +–+– Node a

51. ECEN 301Discussion #12 –Exam 1 Review51 Exam 1 Review…Superposition 9.What is the superposition method of circuit analysis? a)Use superposition to find v R i s = 12A, v s = 12V, R 1 = 1Ω, R 2 = 0.3Ω, R 3 = 0.23Ω R1R1 R2R2 R3R3 vsvs +–+– isis +vR–+vR–

52. ECEN 301Discussion #12 –Exam 1 Review52 Exam 1 Review…Source Transform 10.How are voltage sources transformed to current sources (and vice-versa)? vsvs +–+– RsRs a b isis RpRp a b

53. ECEN 301Discussion #12 –Exam 1 Review53 Exam 1 Review…Source Transform 10.How are voltage sources transformed to current sources (and vice-versa)? vsvs +–+– RsRs a b isis RpRp a b

54. ECEN 301Discussion #12 –Exam 1 Review54 Exam 1 Review…Thévenin 11.What is the Thévenin theorem?

55. ECEN 301Discussion #12 –Exam 1 Review55 Exam 1 Review…Thévenin 11.What is the Thévenin theorem? a)find i L by finding the Thévenin equivalent circuit v s = 10V, R 1 = 4Ω, R 2 = 6Ω, R 3 = 10Ω, R L = 10Ω R2R2 R 1 RLRL R 3 vsvs +–+– iLiL

56. ECEN 301Discussion #12 –Exam 1 Review56 Exam 1 Review…Thévenin 11.What is the Thévenin theorem? a)find i L by finding the Thévenin equivalent circuit v s = 10V, R 1 = 4Ω, R 2 = 6Ω, R 3 = 10Ω, R L = 10Ω 1.Compute R T Remove R L +R2–+R2– +R 1 –+ R 3 – vsvs +–+–

57. ECEN 301Discussion #12 –Exam 1 Review57 Exam 1 Review…Thévenin 11.What is the Thévenin theorem? a)find i L by finding the Thévenin equivalent circuit v s = 10V, R 1 = 4Ω, R 2 = 6Ω, R 3 = 10Ω, R L = 10Ω 1.Compute R T Remove R L Zero sources +R2–+R2– +R 1 –+ R 3 –

58. ECEN 301Discussion #12 –Exam 1 Review58 Exam 1 Review…Thévenin 11.What is the Thévenin theorem? a)find i L by finding the Thévenin equivalent circuit v s = 10V, R 1 = 4Ω, R 2 = 6Ω, R 3 = 10Ω, R L = 10Ω 1.Compute R T Remove R L Zero sources Compute R T = R EQ R EQ

59. ECEN 301Discussion #12 –Exam 1 Review59 Exam 1 Review…Thévenin 11.What is the Thévenin theorem? a)find i L by finding the Thévenin equivalent circuit v s = 10V, R 1 = 4Ω, R 2 = 6Ω, R 3 = 10Ω, R L = 10Ω 1.Compute R T 2.Compute v T R2R2 R 1 RLRL R 3 vsvs +–+– iLiL

60. ECEN 301Discussion #12 –Exam 1 Review60 Exam 1 Review…Thévenin 11.What is the Thévenin theorem? a)find i L by finding the Thévenin equivalent circuit v s = 10V, R 1 = 4Ω, R 2 = 6Ω, R 3 = 10Ω, R L = 10Ω 1.Compute R T 2.Compute v T a)Remove the load b)Define v oc +R2–+R2– +R 1 –+ R 3 – vsvs +–+– + v oc –

61. ECEN 301Discussion #12 –Exam 1 Review61 Exam 1 Review…Thévenin 11.What is the Thévenin theorem? a)find i L by finding the Thévenin equivalent circuit v s = 10V, R 1 = 4Ω, R 2 = 6Ω, R 3 = 10Ω, R L = 10Ω 1.Compute R T 2.Compute v T a)Remove the load b)Define v oc c)Choose a network analysis method Voltage divider +R2–+R2– +R 1 –+ R 3 – vsvs +–+– + v oc – i i 3 = 0

62. ECEN 301Discussion #12 –Exam 1 Review62 Exam 1 Review…Thévenin 11.What is the Thévenin theorem? a)find i L by finding the Thévenin equivalent circuit v s = 10V, R 1 = 4Ω, R 2 = 6Ω, R 3 = 10Ω, R L = 10Ω 1.Compute R T 2.Compute v T a)Remove the load b)Define v oc c)Choose a network analysis method Voltage divider d)V T = V oc +R2–+R2– +R 1 –+ R 3 – vsvs +–+– + v oc – i i 3 = 0

63. ECEN 301Discussion #12 –Exam 1 Review63 Exam 1 Review…Thévenin 11.What is the Thévenin theorem? a)find i L by finding the Thévenin equivalent circuit v s = 10V, R 1 = 4Ω, R 2 = 6Ω, R 3 = 10Ω, R L = 10Ω iLiL vTvT +–+– RTRT RLRL iLiL NB: i L is the same in both circuits R2R2 R 1 RLRL R 3 vsvs +–+–

64. ECEN 301Discussion #12 –Exam 1 Review64 Exam 1 Review…Thévenin 11.What is the Thévenin theorem? a)find i L by finding the Thévenin equivalent circuit v s = 10V, R 1 = 4Ω, R 2 = 6Ω, R 3 = 10Ω, R L = 10Ω vTvT +–+– RTRT RLRL iLiL

65. ECEN 301Discussion #12 –Exam 1 Review65 Exam 1 Review…Norton 12.What is the Norton theorem?

66. ECEN 301Discussion #12 –Exam 1 Review66 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω isis R1R1 R2R2 RLRL R 3 – + vsvs

67. ECEN 301Discussion #12 –Exam 1 Review67 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω vsvs isis R1R1 R2R2 R 3 – + vsvs 1.Compute R N Remove R L

68. ECEN 301Discussion #12 –Exam 1 Review68 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω R1R1 R2R2 R 3 1.Compute R N Remove R L Zero sources

69. ECEN 301Discussion #12 –Exam 1 Review69 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω 1.Compute R N Remove R L Zero sources Compute R N = R EQ R EQ

70. ECEN 301Discussion #12 –Exam 1 Review70 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω 1.Compute R N 2.Compute i N isis R1R1 R2R2 RLRL R 3 – + vsvs

71. ECEN 301Discussion #12 –Exam 1 Review71 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω 1.Compute R N 2.Compute i N a)Short circuit the load b)Define i sc isis R1R1 R2R2 R 3 – + vsvs i sc

72. ECEN 301Discussion #12 –Exam 1 Review72 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω 1.Compute R N 2.Compute i N a)Short circuit the load b)Define i sc c)Choose a network analysis method Node voltage isis +R1–+R1– +R2–+R2– + R 3 – – + vsvs i sc Node a Node b Node d i1i1 i2i2 i3i3 iviv

73. ECEN 301Discussion #12 –Exam 1 Review73 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω 2.Compute i N c)Choose a network analysis method Node voltage isis +R1–+R1– +R2–+R2– + R 3 – – + vsvs i sc Node a Node b Node d i1i1 i2i2 i3i3 iviv 1.v a is independent 2.v b is dependent (actually v a and v b are dependent on each other but choose v b ) v b = v a + v s

74. ECEN 301Discussion #12 –Exam 1 Review74 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω 2.Compute i N c)Choose a network analysis method Node voltage isis +R1–+R1– +R2–+R2– + R 3 – – + vsvs i sc Node a Node b Node d i1i1 i2i2 i3i3 iviv

75. ECEN 301Discussion #12 –Exam 1 Review75 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω 2.Compute i N c)Choose a network analysis method Node voltage isis +R1–+R1– +R2–+R2– + R 3 – – + vsvs i sc Node a Node b Node d i1i1 i2i2 i3i3 iviv

76. ECEN 301Discussion #12 –Exam 1 Review76 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω 2.Compute i N c)Choose a network analysis method Node voltage isis +R1–+R1– +R2–+R2– + R 3 – – + vsvs i sc Node a Node b Node d i1i1 i2i2 i3i3 iviv

77. ECEN 301Discussion #12 –Exam 1 Review77 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω 2.Compute i N c)Choose a network analysis method Node voltage isis +R1–+R1– +R2–+R2– + R 3 – – + vsvs i sc Node a Node b Node d i1i1 i2i2 i3i3 iviv

78. ECEN 301Discussion #12 –Exam 1 Review78 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω 2.Compute i N c)Choose a network analysis method Node voltage d)i N = i sc isis +R1–+R1– +R2–+R2– + R 3 – – + vsvs i sc i1i1 i2i2 i3i3 iviv

79. ECEN 301Discussion #12 –Exam 1 Review79 Exam 1 Review…Norton 12.What is the Norton theorem? a)Find the Norton equivalent circuit v s = 6V, i s = 2A, R 1 = 6Ω, R 2 = 3Ω, R 3 = 2Ω, R L = 10Ω isis R1R1 R2R2 RLRL R 3 – + vsvs iNiN RNRN RLRL

80. ECEN 301Discussion #12 –Exam 1 Review80 Exam 1 Review…Max Power 13.What is the maximum power theorem?

81. ECEN 301Discussion #12 –Exam 1 Review81 Exam 1 Review…Max Power 13.What is the maximum power theorem? a)Find the maximum power delivered to the load v s = 18V, R 1 = 3Ω, R 2 = 6Ω, R 3 = 2Ω R2R2 R 1 RLRL R 3 vsvs +–+–

82. ECEN 301Discussion #12 –Exam 1 Review82 Exam 1 Review…Max Power 13.What is the maximum power theorem? a)Find the maximum power delivered to the load v s = 18V, R 1 = 3Ω, R 2 = 6Ω, R 3 = 2Ω 1.Find Thévenin equivalent circuit (previously found) vTvT +–+– RTRT RLRL

83. ECEN 301Discussion #12 –Exam 1 Review83 Exam 1 Review…Max Power 13.What is the maximum power theorem? a)Find the maximum power delivered to the load v s = 18V, R 1 = 3Ω, R 2 = 6Ω, R 3 = 2Ω vTvT +–+– RTRT RLRL 1.Find Thévenin equivalent circuit 2.Set R L = R T 3.Calculate P LMax

84. ECEN 301Discussion #8 – Network Analysis84 Exam 1 Review… Controlled Sources Network analysis with controlled sources: Initially treat controlled sources as ideal sources In addition to equations obtained by node/mesh analysis there will be the constraint equation (the controlled source equation) Substitute constraint equation into node/mesh equations

85. ECEN 301Discussion #8 – Network Analysis85 Exam 1 Review… Controlled Sources 14. find the gain (A v = v out /v in ) R 1 = 1Ω, R 2 = 0.5Ω, R 3 = 0.25Ω, R 4 = 0.25Ω, R 5 = 0.25Ω R2R2 R 1 R 4 R 3 v in +–+– –+–+ R5R5 +v–+v– + v out – 2v

86. ECEN 301Discussion #8 – Network Analysis86 Exam 1 Review… Controlled Sources 14. find the gain (A v = v out /v in ) R 1 = 1Ω, R 2 = 0.5Ω, R 3 = 0.25Ω, R 4 = 0.25Ω, R 5 = 0.25Ω R2R2 + R 1 – +R 4 – +R 3 – v in +–+– –+–+ R5R5 +v–+v– iaia icic ibib + v out – 2v Choose mesh analysis – simpler than node analysis 1.Mesh current directions chosen 2.Voltage polarities chosen and labeled 3.Identify n – m (3) mesh currents  i a is independent  i c is independent 4.Apply KVL around meshes a, b, and c

87. ECEN 301Discussion #8 – Network Analysis87 Exam 1 Review… Controlled Sources 14. find the gain (A v = v out /v in ) R 1 = 1Ω, R 2 = 0.5Ω, R 3 = 0.25Ω, R 4 = 0.25Ω, R 5 = 0.25Ω v in +–+– R2R2 + R 1 – +R 4 – +R 3 – –+–+ R5R5 +v–+v– iaia icic ibib + v out – 2v 4.Apply KVL at nodes a, b, and c

88. ECEN 301Discussion #8 – Network Analysis88 Exam 1 Review… Controlled Sources 14. find the gain (A v = v out /v in ) R 1 = 1Ω, R 2 = 0.5Ω, R 3 = 0.25Ω, R 4 = 0.25Ω, R 5 = 0.25Ω R2R2 + R 1 – +R 4 – +R 3 – v in +–+– –+–+ R5R5 +v–+v– iaia icic ibib + v out – 2v 5.Solve the n – m equations

89. ECEN 301Discussion #8 – Network Analysis89 Exam 1 Review… Controlled Sources 14. find the gain (A v = v out /v in ) R 1 = 1Ω, R 2 = 0.5Ω, R 3 = 0.25Ω, R 4 = 0.25Ω, R 5 = 0.25Ω R2R2 + R 1 – +R 4 – +R 3 – v in +–+– –+–+ R5R5 +v–+v– iaia icic ibib + v out – 2v 5.Solve the n – m equations (Matrices)

90. ECEN 301Discussion #8 – Network Analysis90 Exam 1 Review… Controlled Sources 14. find the gain (A v = v out /v in ) R 1 = 1Ω, R 2 = 0.5Ω, R 3 = 0.25Ω, R 4 = 0.25Ω, R 5 = 0.25Ω R2R2 + R 1 – +R 4 – +R 3 – v in +–+– –+–+ R5R5 +v–+v– iaia icic ibib + v out – 2v 5.Solve the n – m equations (Matrices)

91. ECEN 301Discussion #8 – Network Analysis91 Exam 1 Review… Controlled Sources 14. find the gain (A v = v out /v in ) R 1 = 1Ω, R 2 = 0.5Ω, R 3 = 0.25Ω, R 4 = 0.25Ω, R 5 = 0.25Ω R2R2 + R 1 – +R 4 – +R 3 – v in +–+– –+–+ R5R5 +v–+v– iaia icic ibib + v out – 2v  Find the gain

92. ECEN 301Discussion #12 –Exam 1 Review92 Exam 1 Review…Thévenin P.114 Find the Thévenin equivalent resistance v s = 20V, R 1 = 1MΩ, R 2 = 2kΩ, R 3 = 3kΩ, R 4 = 6kΩ, R 5 = 6kΩ, R 6 = 3kΩ, R 7 = 2kΩ, R L = 10Ω R6R6 R 5 RLRL R 7 R 3 R1R1 R2R2 vsvs +–+– R4R4 NB: the answer to this problem in the book is wrong!!

93. ECEN 301Discussion #12 –Exam 1 Review93 Exam 1 Review…Thévenin P.114 Find the Thévenin equivalent resistance v s = 20V, R 1 = 1MΩ, R 2 = 2kΩ, R 3 = 3kΩ, R 4 = 6kΩ, R 5 = 6kΩ, R 6 = 3kΩ, R 7 = 2kΩ, R L = 10Ω R6R6 R 5 R 7 R 3 R1R1 R2R2 vsvs +–+– R4R4 1.Compute R T Remove R L

94. ECEN 301Discussion #12 –Exam 1 Review94 Exam 1 Review…Thévenin P.114 Find the Thévenin equivalent resistance v s = 20V, R 1 = 1MΩ, R 2 = 2kΩ, R 3 = 3kΩ, R 4 = 6kΩ, R 5 = 6kΩ, R 6 = 3kΩ, R 7 = 2kΩ, R L = 10Ω R6R6 R 5 R 7 R 3 R1R1 R2R2 R4R4 1.Compute R T Remove R L Zero sources

95. ECEN 301Discussion #12 –Exam 1 Review95 Exam 1 Review…Thévenin P.114 Find the Thévenin equivalent resistance v s = 20V, R 1 = 1MΩ, R 2 = 2kΩ, R 3 = 3kΩ, R 4 = 6kΩ, R 5 = 6kΩ, R 6 = 3kΩ, R 7 = 2kΩ, R L = 10Ω R6R6 R 5 R 7 R 3 R1R1 R2R2 R4R4 1.Compute R T Remove R L Zero sources Consider now – what resistance would the LOAD see?

96. ECEN 301Discussion #12 –Exam 1 Review96 Exam 1 Review…Thévenin P.114 Find the Thévenin equivalent resistance v s = 20V, R 1 = 1MΩ, R 2 = 2kΩ, R 3 = 3kΩ, R 4 = 6kΩ, R 5 = 6kΩ, R 6 = 3kΩ, R 7 = 2kΩ, R L = 10Ω R6R6 R 5 R 7 R 3 R1R1 R2R2 R4R4 1.Compute R T Remove R L Zero sources Imagine we connected a 1A current source – in which branches would current flow? isis

97. ECEN 301Discussion #12 –Exam 1 Review97 Exam 1 Review…Thévenin P.114 Find the Thévenin equivalent resistance v s = 20V, R 1 = 1MΩ, R 2 = 2kΩ, R 3 = 3kΩ, R 4 = 6kΩ, R 5 = 6kΩ, R 6 = 3kΩ, R 7 = 2kΩ, R L = 10Ω R6R6 R 5 R 7 R 3 R1R1 R2R2 R4R4 1.Compute R T Remove R L Zero sources Imagine we connected a 1A current source – in which branches would current flow? isis

98. ECEN 301Discussion #12 –Exam 1 Review98 Exam 1 Review…Thévenin P.114 Find the Thévenin equivalent resistance v s = 20V, R 1 = 1MΩ, R 2 = 2kΩ, R 3 = 3kΩ, R 4 = 6kΩ, R 5 = 6kΩ, R 6 = 3kΩ, R 7 = 2kΩ, R L = 10Ω R6R6 R 5 R 7 R 3 R1R1 R2R2 R4R4 1.Compute R T Remove R L Zero sources No current would get to here isis

99. ECEN 301Discussion #12 –Exam 1 Review99 Exam 1 Review…Thévenin P.114 Find the Thévenin equivalent resistance v s = 20V, R 1 = 1MΩ, R 2 = 2kΩ, R 3 = 3kΩ, R 4 = 6kΩ, R 5 = 6kΩ, R 6 = 3kΩ, R 7 = 2kΩ, R L = 10Ω R6R6 R 5 R 7 There are only 3 resistors to consider 1.Compute R T Remove R L Zero sources Compute R T = R EQ