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Chapter 14 Inductance and RL Circuits

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. 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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. 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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Inductance Coils of wireCoils Inductors –ReactorsReactors –ChokesChokes

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Inductance (Cont.) Lenz’s law Symbol is L, unit is henry (H)henry (H)

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Inductance (Cont.) Strong and weak magnetic fields Self induction Transient responses

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. 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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Strength of Inductance

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. 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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Transient Responses Coil connected to dc voltage source

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Transient Responses (Cont.) Current builds up gradually when switch is closed Current decays gradually when switch opens

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. RL Circuits

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. RL Circuits (Cont.) L coil shorted through switch 2

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Transient Response Curves Graphs show charge and discharge circuits

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Transient Response Curves Time constant ( )Time constant ( ) –Inductance in henrys –Resistance in ohms

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What is inductance? The property in an electric circuit that resists a change in current

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. 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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. 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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What kind of circuit contains resistance and inductance? RL circuit

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Mutual Inductance Two coils close together Coupling Unity coupling

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Mutual Inductance (Cont.) –L M is mutual inductance –k is coefficient or percentage of coupling –L 1 and L 2 are inductances of coils

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Phase Relationship in Series Inductance Without mutual inductance –L T = L 1 + L 2 + L 3 …+ L N With mutual inductance –L T = L 1 + L 2 ± 2L M

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Phase Relationship in Parallel Inductance Without mutual inductance With mutual inductance

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What kind of inductance is produced by two coils within magnetic reach of each other? Mutual inductance

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. 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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Inductance in AC Circuits Inductance produces counter emf to oppose source voltage Reactance (X)Reactance (X) Inductive reactance (X L )Inductive reactance (X L )

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Induced Current and Voltage Counter emf is 180° out of phase with source voltage X L = 2 fL

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Induced Current and Voltage (Cont.) As frequency or inductance increases, inductive reactance increases

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Power in Inductive Circuits True power –P = I × E Reactive power –Measured in volt-ampere-reactive (VAR)volt-ampere-reactive (VAR) Apparent power –Measured in volt-amperes (VA)volt-amperes (VA) –Apparent power = E eff × I eff

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Power Factor (PF) True power = Apparent power × cos True power = E eff × I eff × cos

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Power Factor Example

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. A Purely Resistive Circuit

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Resistance and Inductance in an AC Circuit Different traits for added inductor

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Resistance and Inductance in an AC Circuit (Cont.) Impedance (Z)Impedance (Z) Pythagorean theorem Finding impedance Phase angle ( )Phase angle ( ) cos = PF

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. 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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Ohm’s Law for AC Circuits E = I × Z

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Ohm’s Law Example Reactance of L –X L = 2 × 3.14 × 60 Hz × 8 H –X L = 3014 Ω Impedance –Z = 5000 Ω

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Ohm’s Law Example (Cont.) Current –I = 0.04 A Voltage drops –E R = 0.04 A × 4000 Ω = 160 V Source voltage

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. 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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Parallel RL Circuits No phase difference among the elements Phase difference among total and branch currents

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Parallel RL Circuits (Cont.)

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Parallel RL Circuit Example Inductive reactance –X L = 6.28 × 100 Hz × 4 H = 2512 Ω Branch currents

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Parallel RL Circuit Example (Cont.) Phase angle –arctan 0.597 = 30.8° Total circuit current

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Parallel RL Circuit Example (Cont.) Impedance

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. 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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What is opposition to an alternating current due to inductance or capacitance called? Reactance

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. 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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What is the relationship between inductive reactance and frequency or inductance? They are in direct proportion

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review How is reactive power measured? Volt-ampere-reactive (VAR)

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. 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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Apparent power –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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Coil –An electronic component used to produce inductance in a circuit. Coupling –Percentage of mutual inductance between coils. Also called linkage.

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Henry (H) –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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Inductance –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 (X L ) –Opposition to an ac current as a result of inductance.

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Inductor –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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Mutual inductance –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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Power factor (PF) –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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Reactance (X) –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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Reactor –An electronic component used to produce inductance in a circuit. RL circuit –A circuit that contains resistance and inductance.

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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Self induction –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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Transient response –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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© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Volt-ampere (VA) –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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