2. Inductance and RL Circuits
Chapter 14
Inductance and RL Circuits

3. Objectives Define the terms inductor and inductance.
Explain how inductance affects a current.
Describe an RL circuit’s transient response.
Define mutual inductance.
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4. 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.
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5. Inductance Coils of wire Inductors Reactors Chokes
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6. Inductance (Cont.) Lenz’s law Symbol is L, unit is henry (H)
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7. Inductance (Cont.) Strong and weak magnetic fields Self induction
Transient responses
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8. 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
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9. Strength of Inductance
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10. 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
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11. Transient Responses Coil connected to dc voltage source
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12. Transient Responses (Cont.)
Current builds up gradually when switch is closed
Current decays gradually when switch opens
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13. RL Circuits © Goodheart-Willcox Co., Inc.
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14. RL Circuits (Cont.) L coil shorted through switch 2
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15. Transient Response Curves
Graphs show charge and discharge circuits
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16. Transient Response Curves
Time constant ()
Inductance in henrys
Resistance in ohms
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17. Review What is inductance?
The property in an electric circuit that resists a change in current
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18. 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
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19. Review What is a transient response?
The response of the current and voltage in a circuit after an instant change in applied voltage
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20. Review What kind of circuit contains resistance and inductance?
RL circuit
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21. Mutual Inductance Two coils close together Coupling Unity coupling
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22. Mutual Inductance (Cont.)
LM is mutual inductance
k is coefficient or percentage of coupling
L1 and L2 are inductances of coils
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23. Phase Relationship in Series Inductance
Without mutual inductance
LT = L1 + L2 + L3 …+ LN
With mutual inductance
LT = L1 + L2 ± 2LM
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24. Phase Relationship in Parallel Inductance
Without mutual inductance
With mutual inductance
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25. Review
What kind of inductance is produced by two coils within magnetic reach of each other?
Mutual inductance
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26. Review
What is the degree to which the lines of force of one coil link with the windings of the second coil called?
Coupling
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27. Inductance in AC Circuits
Inductance produces counter emf to oppose source voltage
Reactance (X)
Inductive reactance (XL)
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28. Induced Current and Voltage
Counter emf is 180° out of phase with source voltage
XL = 2fL
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29. Induced Current and Voltage (Cont.)
As frequency or inductance increases, inductive reactance increases
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30. 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
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31. Power Factor (PF) True power = Apparent power × cos 
True power = Eeff × Ieff × cos 
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32. Power Factor Example © Goodheart-Willcox Co., Inc.
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33. A Purely Resistive Circuit
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34. Resistance and Inductance in an AC Circuit
Different traits for added inductor
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35. Resistance and Inductance in an AC Circuit (Cont.)
Impedance (Z)
Pythagorean theorem
Finding impedance
Phase angle ()
cos  = PF
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36. 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
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37. Ohm’s Law for AC Circuits
E = I × Z
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38. Ohm’s Law Example Reactance of L Impedance XL = 2 × 3.14 × 60 Hz × 8 H
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39. Ohm’s Law Example (Cont.)
Current
I = 0.04 A
Voltage drops
ER = 0.04 A × 4000 Ω = 160 V
Source voltage
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40. 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
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41. Parallel RL Circuits No phase difference among the elements
Phase difference among total and branch currents
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42. Parallel RL Circuits (Cont.)
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43. Parallel RL Circuit Example
Inductive reactance
XL = 6.28 × 100 Hz × 4 H = 2512 Ω
Branch currents
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44. Parallel RL Circuit Example (Cont.)
Phase angle
arctan = 30.8°
Total circuit current
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45. Parallel RL Circuit Example (Cont.)
Impedance
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46. 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
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47. Review
What is opposition to an alternating current due to inductance or capacitance called?
Reactance
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48. 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
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49. Review
What is the relationship between inductive reactance and frequency or inductance?
They are in direct proportion
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50. Review How is reactive power measured? Volt-ampere-reactive (VAR)
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51. For Discussion
Discuss the relationship between induction and frequency.
Discuss the differences between apparent power and true power.
How can an inductive circuit be completely 180 degrees out of phase?
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52. Glossary Apparent power Choke
Power apparently used in a circuit as a product of current times voltage.
Choke
An electronic component used to produce inductance in a circuit.
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53. Glossary Coil Coupling
An electronic component used to produce inductance in a circuit.
Coupling
Percentage of mutual inductance between coils. Also called linkage.
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54. Glossary Henry (H) Impedance (Z)
Unit of measure of inductance. A coil has one henry of inductance if an emf of one volt is induced when current through an inductor is changing at a rate of one ampere per second.
Impedance (Z)
Total resistance to the flow of an alternating current as a result of resistance and reactance.
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55. Glossary Inductance Inductive reactance (XL)
1. Inherent property of an electric circuit that opposes a change in current. 2. Property of a circuit whereby energy may be stored in a magnetic field.
Inductive reactance (XL)
Opposition to an ac current as a result of inductance.
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56. Glossary Inductor Lenz’s law
An electronic component used to produce inductance in a circuit.
Lenz’s law
Induced emf in any circuit is always in such a direction as to oppose the effect that produces it.
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57. Glossary Mutual inductance Phase angle ()
Two coils located so the magnetic flux of one coil can link with turns of the other coil. The change in flux of one coil will cause an emf in the other.
Phase angle ()
The angle between vector Z and vector R in an ac circuit.
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58. Glossary Power factor (PF) Pythagorean theorem
Relationship between the true power and apparent power of a circuit.
Pythagorean theorem
The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
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59. Glossary Reactance (X) Reactive power
Opposition to alternating current as result of inductance or capacitance.
Reactive power
Power used by a reactive component of a circuit.
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60. Glossary Reactor RL circuit
An electronic component used to produce inductance in a circuit.
RL circuit
A circuit that contains resistance and inductance.
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61. Glossary Self induction Time constant ()
emf is self-induced when it is induced in a current-carrying conductor.
Time constant ()
Time period required for the voltage of a capacitor in an RC circuit to increase to 63.2% of maximum value or decrease to 36.7% of maximum value.
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62. Glossary Transient response True power Unity coupling
Response to momentary signal or force.
True power
Actual power absorbed in a circuit.
Unity coupling
Two coils positioned so all lines of magnetic flux of one cell cut across all turns of the second coil.
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63. Glossary Volt-ampere (VA) Volt-ampere-reactive (VAR) Wattless power
Unit measure of apparent power.
Volt-ampere-reactive (VAR)
Unit measure of reactive power.
Wattless power
Power not consumed in an ac circuit due to reactance.
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