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Examine Yourselves

Examine Yourselves. Moroni 10: 3

ronald
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Examine Yourselves

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  1. 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. Discussion #12 –Exam 1 Review

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

  3. 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! Discussion #12 –Exam 1 Review

  4. Exam 1 Review…Overview • Kirchoff’s current law • Kirchoff’s voltage law • Passive sign convention • Voltage/current dividers (Ohm’s Law) • Wheatstone bridge • Measuring Devices • Node voltage method • Mesh current method • Principle of superposition • Source transformation • Thévenin equivalent circuits • Norton equivalent circuits • Maximum power transfer • Dependent Sources Discussion #12 –Exam 1 Review

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

  6. Node a is2 is1 i2 + R2 _ Vs2 + _ Vs1 R4 i4 R3 i5 i3 R5 Exam 1 Review…KCL • What is Kirchoff’s current law? a) What is an expression for the current at Node a? Discussion #12 –Exam 1 Review

  7. Node a is2 is1 i2 + R2 _ Vs2 + _ Vs1 R4 i4 R3 i5 i3 R5 Exam 1 Review…KCL • What is Kirchoff’s current law? a) What is an expression for the current at Node a? Discussion #12 –Exam 1 Review

  8. Node a is2 is1 i2 + R2 _ Vs2 + _ Vs1 R4 i4 R3 i5 i3 R5 Exam 1 Review…KCL • What is Kirchoff’s current law? a) What is an expression for the current at Node a? b) what expressions for the current through R2 are valid? Discussion #12 –Exam 1 Review

  9. Node a is2 is1 i2 + R2 _ Vs2 + _ Vs1 R4 i4 R3 i5 i3 R5 Exam 1 Review…KCL • What is Kirchoff’s current law? a) What is an expression for the current at Node a? b) what expressions for the current through R2 are valid? Discussion #12 –Exam 1 Review

  10. Node a is2 is1 i2 + R2 _ Vs2 + _ Vs1 R4 i4 R3 i5 i3 R5 Exam 1 Review…KCL • What is Kirchoff’s current law? a) What is an expression for the current at Node a? b) what expressions for the current through R2 are valid? Discussion #12 –Exam 1 Review

  11. Exam 1 Review…KVL • What is Kirchoff’s voltage law? Discussion #12 –Exam 1 Review

  12. is i1 i3 i2 + R3 – + R2 – + R1 – + _ Vs Exam 1 Review…KVL • What is Kirchoff’s voltage law? • If Vs = 3V, what are the voltages across R1, R2, and R3? Discussion #12 –Exam 1 Review

  13. is i1 i3 i2 + R3 – + R2 – + R1 – + _ Vs Exam 1 Review…KVL • What is Kirchoff’s voltage law? • If Vs = 3V, what are the voltages across R1, R2, and R3? Discussion #12 –Exam 1 Review

  14. Exam 1 Review…Passive Sign • What is the passive sign convention? Discussion #12 –Exam 1 Review

  15. i i a b a b _ _ + + vba vab Exam 1 Review…Passive Sign • What is the passive sign convention? • Which element dissipates power and which generates power? Discussion #12 –Exam 1 Review

  16. i i a b a b _ _ + + vba vab Exam 1 Review…Passive Sign • What is the passive sign convention? • Which element dissipates power and which generates power? • Passive Element (load) • power dissipated = vi • power generated = -vi • Active Element (source) • power dissipated = -vi • power generated = vi Positive voltage Negative voltage Discussion #12 –Exam 1 Review

  17. ie = 2A – 3V + B ia + 10V – E D A id =3A C – 5V + Exam 1 Review…Passive Sign • What is the passive sign convention? • Find the power dissipated by each element Discussion #12 –Exam 1 Review

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

  19. Exam 1 Review…Passive Sign • What is the passive sign convention? • Find the power dissipated by each element ie = 2A – 3V + B ia = 5A + 10V – + 12V – + 10V – E D A id =3A C – 5V + Discussion #12 –Exam 1 Review

  20. Exam 1 Review…Dividers • What is a voltage/current divider? Discussion #12 –Exam 1 Review

  21. Exam 1 Review…Dividers • What is a voltage/current divider? Discussion #12 –Exam 1 Review

  22. + Vs _ Exam 1 Review…Dividers • What is a voltage/current divider? • Using a voltage divider find the voltage across R3 Vs = 3V, R1 = 10Ω, R2 = 6Ω, R3 = 8Ω – v1 + i R1 + v2 – R2 + v3 – R3 Discussion #12 –Exam 1 Review

  23. – v1 + i + R1 Vs _ + v2 – R2 + v3 – R3 Exam 1 Review…Dividers • What is a voltage/current divider? • Using a voltage divider find the voltage across R3 Vs = 3V, R1 = 10Ω, R2 = 6Ω, R3 = 8Ω Discussion #12 –Exam 1 Review

  24. i1 i3 i2 – R3 + – R1 + – R2 + is Exam 1 Review…Dividers • What is a voltage/current divider? • Using a current divider find i1 R1 = 10Ω, R2 = 2 Ω, R3 = 20 Ω, Is = 4A Discussion #12 –Exam 1 Review

  25. i1 i3 i2 – R3 + – R1 + – R2 + is Exam 1 Review…Dividers • What is a voltage/current divider? • Using a current divider find i1 R1 = 10Ω, R2 = 2 Ω, R3 = 20 Ω, Is = 4A Discussion #12 –Exam 1 Review

  26. c R1 R3 va vb a b + vs R2 Rx _ d Exam 1 Review…Wheatstone • What is the voltage across the terminals a and b of the Wheatstone bridge? Discussion #12 –Exam 1 Review

  27. c R1 R3 va vb a b + vs R2 Rx _ d Exam 1 Review…Wheatstone • What is the voltage across the terminals a and b of the Wheatstone bridge? Discussion #12 –Exam 1 Review

  28. Exam 1 Review…Measuring • How do measuring devices connect to circuits? Discussion #12 –Exam 1 Review

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

  30. R1 A + vs _ i R2 Exam 1 Review…Measuring • How do measuring devices connect to circuits? 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 Discussion #12 –Exam 1 Review

  31. + R2 – + v2 – V + vs _ i Exam 1 Review…Measuring • How do measuring devices connect to circuits? 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 Discussion #12 –Exam 1 Review

  32. R1 + R2 – W + vs _ i Exam 1 Review…Measuring • How do measuring devices connect to circuits? 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 Discussion #12 –Exam 1 Review

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

  34. R2 ia ib R4 R3 R1 Exam 1 Review…Node Voltage • What is the node voltage method of circuit analysis? • Find all unknown voltages ia = 1mA, ib = 2mA, R1 = 1kΩ, R2= 500Ω, R3 = 2.2kΩ, R4 = 4.7kΩ Discussion #12 –Exam 1 Review

  35. i2 vb Node b Node a va + R2 – + ib – + R4 – + R3 – + R1 – i1 i3 i4 vc Node c Exam 1 Review…Node Voltage • What is the node voltage method of circuit analysis? • Find all unknown voltages ia = 1mA, ib = 2mA, R1 = 1kΩ, R2= 500Ω, R3 = 2.2kΩ, R4 = 4.7kΩ • Label currents and voltages (polarities “arbitrarily” chosen) • Choose Node c (vc) as the reference node (vc = 0) • Define remaining n – 1 (2) voltages • va is independent • vb is independent • Apply KCL at nodes a and b + ia – Discussion #12 –Exam 1 Review

  36. i2 vb Node b Node a va + R2 – + ib – + R4 – + R3 – + R1 – i1 i3 i4 vc Node c Exam 1 Review…Node Voltage • What is the node voltage method of circuit analysis? • Find all unknown voltages ia = 1mA, ib = 2mA, R1 = 1kΩ, R2= 500Ω, R3 = 2.2kΩ, R4 = 4.7kΩ • Apply KCL at nodes a and b + ia – Discussion #12 –Exam 1 Review

  37. i2 vb Node b Node a va + R2 – + ib – + R4 – + R3 – + R1 – i1 i3 i4 vc Node c Exam 1 Review…Node Voltage • What is the node voltage method of circuit analysis? • Find all unknown voltages ia = 1mA, ib = 2mA, R1 = 1kΩ, R2= 500Ω, R3 = 2.2kΩ, R4 = 4.7kΩ • Express currents in terms of voltages + ia – Discussion #12 –Exam 1 Review

  38. i2 vb Node b Node a va + R2 – + ib – + R4 – + R3 – + R1 – i1 i3 i4 vc Node c Exam 1 Review…Node Voltage • What is the node voltage method of circuit analysis? • Find all unknown voltages ia = 1mA, ib = 2mA, R1 = 1kΩ, R2= 500Ω, R3 = 2.2kΩ, R4 = 4.7kΩ • Solve the n – 1 – m equations + ia – Discussion #12 –Exam 1 Review

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

  40. R4 ic R3 R1 R2 vs Is ia ib – + Exam 1 Review…Mesh Current • What is the mesh current method of circuit analysis? • Find the mesh currents Vs = 6V, Is = 0.5A, R1= 3Ω, R2= 8Ω, R3 = 6Ω, R4 = 4Ω Discussion #12 –Exam 1 Review

  41. +R4– ic +R3 – + R1– + R2 – vs Is ia ib – + Exam 1 Review…Mesh Current • What is the mesh current method of circuit analysis? • Find the mesh currents Vs = 6V, Is = 0.5A, R1= 3Ω, R2= 8Ω, R3 = 6Ω, R4 = 4Ω • Mesh current directions given • Voltage polarities chosen and labeled • Identify n – m (3) mesh currents • ia is dependent (ia = is) • ia is independent • ic is independent • Apply KVL around meshes b and c Discussion #12 –Exam 1 Review

  42. +R4– ic +R3 – + R1– + R2 – vs Is ia ib – + Exam 1 Review…Mesh Current • What is the mesh current method of circuit analysis? • Find the mesh currents Vs = 6V, Is = 0.5A, R1= 3Ω, R2= 8Ω, R3 = 6Ω, R4 = 4Ω • Apply KVL at nodes b and c Discussion #12 –Exam 1 Review

  43. +R4– ic +R3 – + R1– + R2 – vs Is ia ib – + Exam 1 Review…Mesh Current • What is the mesh current method of circuit analysis? • Find the mesh currents Vs = 6V, Is = 0.5A, R1= 3Ω, R2= 8Ω, R3 = 6Ω, R4 = 4Ω • Express voltages in terms of currents Discussion #12 –Exam 1 Review

  44. +R4– ic +R3 – + R1– + R2 – vs Is ia ib – + Exam 1 Review…Mesh Current • What is the mesh current method of circuit analysis? • Find the mesh currents Vs = 6V, Is = 0.5A, R1= 3Ω, R2= 8Ω, R3 = 6Ω, R4 = 4Ω • Solve the n – m equations Discussion #12 –Exam 1 Review

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

  46. R2 R1 R3 + vR – + – vs is Exam 1 Review…Superposition • What is the superposition method of circuit analysis? • Use superposition to find vR is= 12A, vs= 12V, R1= 1Ω, R2= 0.3Ω, R3 = 0.23Ω Discussion #12 –Exam 1 Review

  47. is Exam 1 Review…Superposition • What is the superposition method of circuit analysis? • Use superposition to find vR is= 12A, vs= 12V, R1= 1Ω, R2= 0.3Ω, R3 = 0.23Ω • Remove all sources except is • Source vs is replaced with short circuit – R2 + i2 + R1 – R3 + vR1 – i1 i3 Discussion #12 –Exam 1 Review

  48. is Exam 1 Review…Superposition • What is the superposition method of circuit analysis? • Use superposition to find vR is= 12A, vs= 12V, R1= 1Ω, R2= 0.3Ω, R3 = 0.23Ω Node a – R2 + i2 + R1 – R3 + vR1 – i1 i3 Discussion #12 –Exam 1 Review

  49. + – vs Exam 1 Review…Superposition • What is the superposition method of circuit analysis? • Use superposition to find vR is= 12A, vs= 12V, R1= 1Ω, R2= 0.3Ω, R3 = 0.23Ω • Remove all sources except vs • Source is is replaced with open circuit – R2 + i2 + R1 – R3 + vR2 – i1 i3 Discussion #12 –Exam 1 Review

  50. + – vs Exam 1 Review…Superposition • What is the superposition method of circuit analysis? • Use superposition to find vR is= 12A, vs= 12V, R1= 1Ω, R2= 0.3Ω, R3 = 0.23Ω Node a – R2 + i2 + R1 – R3 + vR2 – i1 i3 Discussion #12 –Exam 1 Review

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