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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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Chapter 14

Chapter 14

Inductance and RL Circuits


Objectives

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.


Objectives1

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.


Inductance

Inductance

  • Coils of wire

  • Inductors

    • Reactors

    • Chokes

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Inductance cont

Inductance (Cont.)

  • Lenz’s law

  • Symbol is L, unit is henry (H)

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Inductance cont1

Inductance (Cont.)

  • Strong and weak magnetic fields

  • Self induction

  • Transient responses

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Producing stronger and weaker magnetic fields

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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Strength of inductance

Strength of Inductance

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Self induction

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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Transient responses

Transient Responses

  • Coil connected to dc voltage source

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Transient responses cont

Transient Responses (Cont.)

  • Current builds up gradually when switch is closed

  • Current decays gradually when switch opens

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Rl circuits

RL Circuits

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Rl circuits cont

RL Circuits (Cont.)

  • L coil shorted through switch 2

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Transient response curves

Transient Response Curves

  • Graphs show charge and discharge circuits

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Transient response curves1

Transient Response Curves

  • Time constant ()

    • Inductance in henrys

    • Resistance in ohms

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Review

Review

What is inductance?

The property in an electric circuit that resists a change in current

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Review1

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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Review2

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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Review3

Review

What kind of circuit contains resistance and inductance?

RL circuit

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Mutual inductance

Mutual Inductance

  • Two coils close together

  • Coupling

  • Unity coupling

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Mutual inductance cont

Mutual Inductance (Cont.)

  • LMis mutual inductance

  • k is coefficient or percentage of coupling

  • L1 and L2 are inductances of coils

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Phase relationship in series inductance

Phase Relationship in Series Inductance

  • Without mutual inductance

    • LT = L1 + L2 + L3 …+ LN

  • With mutual inductance

    • LT = L1 + L2± 2LM

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Phase relationship in parallel inductance

Phase Relationship in Parallel Inductance

  • Without mutual inductance

  • With mutual inductance

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Review4

Review

What kind of inductance is produced by two coils within magnetic reach of each other?

Mutual inductance

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Review5

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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Inductance in ac circuits

Inductance in AC Circuits

  • Inductance produces counter emf to oppose source voltage

  • Reactance (X)

  • Inductive reactance (XL)

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Induced current and voltage

Induced Current and Voltage

  • Counter emf is 180° out of phase with source voltage

  • XL = 2fL

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Induced current and voltage cont

Induced Current and Voltage (Cont.)

  • As frequency or inductance increases, inductive reactance increases

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Power in inductive circuits

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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Power factor pf

Power Factor (PF)

  • True power = Apparent power × cos 

  • True power = Eeff × Ieff × cos 

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Power factor example

Power Factor Example

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A purely resistive circuit

A Purely Resistive Circuit

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Resistance and inductance in an ac circuit

Resistance and Inductance in an AC Circuit

  • Different traits for added inductor

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Resistance and inductance in an ac circuit cont

Resistance and Inductance in an AC Circuit (Cont.)

  • Impedance (Z)

  • Pythagorean theorem

  • Finding impedance

  • Phase angle ()

  • cos  = PF

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Resistance and inductance example

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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Ohm s law for ac circuits

Ohm’s Law for AC Circuits

  • E = I× Z

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Ohm s law example

Ohm’s Law Example

  • Reactance of L

    • XL = 2 × 3.14 × 60 Hz × 8 H

    • XL= 3014 Ω

  • Impedance

    • Z = 5000 Ω

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Ohm s law example cont

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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Ohm s law example cont1

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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Parallel rl circuits

Parallel RL Circuits

  • No phase difference among the elements

  • Phase difference among total and branch currents

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Parallel rl circuits cont

Parallel RL Circuits (Cont.)

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Parallel rl circuit example

Parallel RL Circuit Example

  • Inductive reactance

    • XL = 6.28 × 100 Hz × 4 H = 2512 Ω

  • Branch currents

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Parallel rl circuit example cont

Parallel RL Circuit Example (Cont.)

  • Phase angle

    • arctan 0.597 = 30.8°

  • Total circuit current

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Parallel rl circuit example cont1

Parallel RL Circuit Example (Cont.)

  • Impedance

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Inductive heating

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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Review6

Review

What is opposition to an alternating current due to inductance or capacitance called?

Reactance

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Review7

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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Review8

Review

What is the relationship between inductive reactance and frequency or inductance?

They are in direct proportion

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Review9

Review

How is reactive power measured?

Volt-ampere-reactive (VAR)

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For discussion

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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