chapter 14 inductance and rl circuits © goodheart-willcox co., inc.permission granted to reproduce...

Chapter 14

Inductance and RL Circuits

© 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.


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.


Inductance

• Coils of wire• Inductors

– Reactors– Chokes


Inductance (Cont.)

• Lenz’s law

• Symbol is L, unit is henry (H)

t

ILE


Inductance (Cont.)

• Strong and weak magnetic fields

• Self induction

• Transient responses


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


Strength of Inductance


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


Transient Responses

• Coil connected to dc voltage source


Transient Responses (Cont.)

• Current builds up gradually when switch is closed

• Current decays gradually when switch opens


RL Circuits


RL Circuits (Cont.)

• L coil shorted through switch 2


Transient Response Curves

• Graphs show charge and discharge circuits


Transient Response Curves

• Time constant ()

– Inductance in henrys– Resistance in ohms

R

L


Review

What is inductance?

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


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


Review

What is a transient response?

The response of the current and voltage in a circuit after an instant change in applied voltage


Review

What kind of circuit contains resistance and inductance?

RL circuit


Mutual Inductance

• Two coils close together

• Coupling

• Unity coupling


Mutual Inductance (Cont.)

– LM is mutual inductance

– k is coefficient or percentage of coupling

– L1 and L2 are inductances of coils

21M L LL k


Phase Relationship in Series Inductance

• Without mutual inductance– LT = L1 + L2 + L3 …+ LN

• With mutual inductance– LT = L1 + L2 ± 2LM


Phase Relationship in Parallel Inductance

• Without mutual inductance

• With mutual inductance

N321T LLLLL

1

1

1

1

1

21

21T LL

LLL


Review

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

Mutual inductance


Review

What is the degree to which the lines of force of one coil link with the windings of the second coil called?

Coupling


Inductance in AC Circuits

• Inductance produces counter emf to oppose source voltage

• Reactance (X)

• Inductive reactance (XL)


Induced Current and Voltage

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

• XL = 2fL


Induced Current and Voltage (Cont.)

• As frequency or inductance increases, inductive reactance increases


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


Power Factor (PF)

• True power = Apparent power × cos • True power = Eeff × Ieff × cos

powerApparent

power True cos factor Power θ


Power Factor Example

0 VA 1000

W 0 cos PF


A Purely Resistive Circuit


Resistance and Inductance in an AC Circuit

• Different traits for added inductor


Resistance and Inductance in an AC Circuit (Cont.)

• Impedance (Z)• Pythagorean theorem

• Finding impedance

• Phase angle ()• cos = PF

22 bac

22 LXRZ


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

A 0.2 500

V 100

Z

EI


Ohm’s Law for AC Circuits

• E = I × Z

Z

EI

I

EZ


Ohm’s Law Example

• Reactance of L– XL = 2 × 3.14 × 60 Hz × 8 H

– XL = 3014 Ω

• Impedance

– Z = 5000 Ω

22 ) (3000 ) (4000 Z


Ohm’s Law Example (Cont.)

• Current

– I = 0.04 A

• Voltage drops– ER = 0.04 A × 4000 Ω = 160 V

• Source voltage

5000

V 200 I

V 120 3000 A 0.04 LXE

V 200 V) (120 V) (160 22 SE


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

0.8 5000

4000 cos

Θ

o37Θ


Parallel RL Circuits

• No phase difference among the elements

• Phase difference among total and branch currents


Parallel RL Circuits (Cont.)

T

S

I

EZ

22 LRT II I

R

L

I

Iarctan


Parallel RL Circuit Example

• Inductive reactance– XL = 6.28 × 100 Hz × 4 H = 2512 Ω

• Branch currentsA 0.067

1500

V 100

R

EI S

R

A 0.04 2512

V 100

L

SL X

EI


Parallel RL Circuit Example (Cont.)

• Phase angle

– arctan 0.597 = 30.8°

• Total circuit current

0.597arctan A 0.067

A 0.04arctan θ

A 0.078 A) (0.04 A) (0.067 22 TI


Parallel RL Circuit Example (Cont.)

• Impedance

1282 A 0.078

V 100 Z


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


Review

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

Reactance


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


Review

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

They are in direct proportion


Review

How is reactive power measured?

Volt-ampere-reactive (VAR)


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?

chapter 14 inductance and rl circuits © goodheart-willcox co., inc.permission granted to reproduce...

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