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Chapter 14

Chapter 14. Inductance and RL Circuits. Objectives. Define the terms inductor and inductance. Explain how inductance affects a current. Describe an RL circuit’s transient response. Define mutual inductance. Objectives. Describe the effect of inductance in ac circuits.

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Chapter 14

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  1. Chapter 14 Inductance and RL Circuits

  2. Objectives • Define the terms inductor and inductance. • Explain how inductance affects a current. • Describe an RL circuit’s transient response. • Define mutual inductance. Permission granted to reproduce for educational use only.

  3. Objectives • Describe the effect of inductance in ac circuits. • Explain and compare true power and apparent power. • Use various measuring and computing methods to determine the values of currents and voltages in inductive circuits. Permission granted to reproduce for educational use only.

  4. Inductance • Coils of wire • Inductors • Reactors • Chokes Permission granted to reproduce for educational use only.

  5. Inductance (Cont.) • Lenz’s law • Symbol is L, unit is henry (H) Permission granted to reproduce for educational use only.

  6. Inductance (Cont.) • Strong and weak magnetic fields • Self induction • Transient responses Permission granted to reproduce for educational use only.

  7. Producing Stronger and Weaker Magnetic Fields • Stronger magnetic field produces stronger induced voltage • Large inductors wound on laminated iron cores • Small inductors have powdered iron or air cores Permission granted to reproduce for educational use only.

  8. Strength of Inductance Permission granted to reproduce for educational use only.

  9. Self Induction • Expanding or collapsing magnetic field cutting across coil wires • Counter emf induced • Strength depends on • Number of turns of wire in coil • Link between length of coil and its diameter • Permeability of core Permission granted to reproduce for educational use only.

  10. Transient Responses • Coil connected to dc voltage source Permission granted to reproduce for educational use only.

  11. Transient Responses (Cont.) • Current builds up gradually when switch is closed • Current decays gradually when switch opens Permission granted to reproduce for educational use only.

  12. RL Circuits Permission granted to reproduce for educational use only.

  13. RL Circuits (Cont.) • L coil shorted through switch 2 Permission granted to reproduce for educational use only.

  14. Transient Response Curves • Graphs show charge and discharge circuits Permission granted to reproduce for educational use only.

  15. Transient Response Curves • Time constant () • Inductance in henrys • Resistance in ohms Permission granted to reproduce for educational use only.

  16. Review What is inductance? The property in an electric circuit that resists a change in current Permission granted to reproduce for educational use only.

  17. Review What is Lenz’s law? The field created by induced current is of such a polarity that it opposes the field of the permanent magnet Permission granted to reproduce for educational use only.

  18. Review What is a transient response? The response of the current and voltage in a circuit after an instant change in applied voltage Permission granted to reproduce for educational use only.

  19. Review What kind of circuit contains resistance and inductance? RL circuit Permission granted to reproduce for educational use only.

  20. Mutual Inductance • Two coils close together • Coupling • Unity coupling Permission granted to reproduce for educational use only.

  21. Mutual Inductance (Cont.) • LMis mutual inductance • k is coefficient or percentage of coupling • L1 and L2 are inductances of coils Permission granted to reproduce for educational use only.

  22. Phase Relationship in Series Inductance • Without mutual inductance • LT = L1 + L2 + L3 …+ LN • With mutual inductance • LT = L1 + L2± 2LM Permission granted to reproduce for educational use only.

  23. Phase Relationship in Parallel Inductance • Without mutual inductance • With mutual inductance Permission granted to reproduce for educational use only.

  24. Review What kind of inductance is produced by two coils within magnetic reach of each other? Mutual inductance Permission granted to reproduce for educational use only.

  25. Review What is the degree to which the lines of force of one coil link with the windings of the second coil called? Coupling Permission granted to reproduce for educational use only.

  26. Inductance in AC Circuits • Inductance produces counter emf to oppose source voltage • Reactance (X) • Inductive reactance (XL) Permission granted to reproduce for educational use only.

  27. Induced Current and Voltage • Counter emf is 180° out of phase with source voltage • XL = 2fL Permission granted to reproduce for educational use only.

  28. Induced Current and Voltage (Cont.) • As frequency or inductance increases, inductive reactance increases Permission granted to reproduce for educational use only.

  29. Power in Inductive Circuits • True power • P = I× E • Reactive power • Measured in volt-ampere-reactive (VAR) • Apparent power • Measured in volt-amperes (VA) • Apparent power = Eeff × Ieff Permission granted to reproduce for educational use only.

  30. Power Factor (PF) • True power = Apparent power × cos  • True power = Eeff × Ieff × cos  Permission granted to reproduce for educational use only.

  31. Power Factor Example Permission granted to reproduce for educational use only.

  32. A Purely Resistive Circuit Permission granted to reproduce for educational use only.

  33. Resistance and Inductance in an AC Circuit • Different traits for added inductor Permission granted to reproduce for educational use only.

  34. Resistance and Inductance in an AC Circuit (Cont.) • Impedance (Z) • Pythagorean theorem • Finding impedance • Phase angle () • cos  = PF Permission granted to reproduce for educational use only.

  35. Resistance and Inductance Example • Given an impedance of 500 Ω and an applied ac voltage of 100 V, find the current • True power = 100 V × 0.2 A × cos 53.1° = 12 W • Wattless power Permission granted to reproduce for educational use only.

  36. Ohm’s Law for AC Circuits • E = I× Z Permission granted to reproduce for educational use only.

  37. Ohm’s Law Example • Reactance of L • XL = 2 × 3.14 × 60 Hz × 8 H • XL= 3014 Ω • Impedance • Z = 5000 Ω Permission granted to reproduce for educational use only.

  38. Ohm’s Law Example (Cont.) • Current • I = 0.04 A • Voltage drops • ER = 0.04 A × 4000 Ω = 160 V • Source voltage Permission granted to reproduce for educational use only.

  39. Ohm’s Law Example (Cont.) • Phase angle • Apparent power = 0.04 A × 200 V = 8 VA • True power = 0.04 A × 200 V × 0.8 True power = 6.4 W Permission granted to reproduce for educational use only.

  40. Parallel RL Circuits • No phase difference among the elements • Phase difference among total and branch currents Permission granted to reproduce for educational use only.

  41. Parallel RL Circuits (Cont.) Permission granted to reproduce for educational use only.

  42. Parallel RL Circuit Example • Inductive reactance • XL = 6.28 × 100 Hz × 4 H = 2512 Ω • Branch currents Permission granted to reproduce for educational use only.

  43. Parallel RL Circuit Example (Cont.) • Phase angle • arctan 0.597 = 30.8° • Total circuit current Permission granted to reproduce for educational use only.

  44. Parallel RL Circuit Example (Cont.) • Impedance Permission granted to reproduce for educational use only.

  45. Inductive Heating • A magnetic field generates hysteresis and eddy currents • Amount of heat is due to the intensity of the magnetic field and frequency of applied ac • Uses include induction stoves and annealing Permission granted to reproduce for educational use only.

  46. Review What is opposition to an alternating current due to inductance or capacitance called? Reactance Permission granted to reproduce for educational use only.

  47. Review Because counter emf opposes source voltage, what is the phase relationship between the two? The counter emf is 180 degrees out of phase with the source voltage Permission granted to reproduce for educational use only.

  48. Review What is the relationship between inductive reactance and frequency or inductance? They are in direct proportion Permission granted to reproduce for educational use only.

  49. Review How is reactive power measured? Volt-ampere-reactive (VAR) Permission granted to reproduce for educational use only.

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