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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.

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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Inductance

- Coils of wire
- Inductors
- Reactors
- Chokes

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Inductance (Cont.)

- Lenz’s law
- Symbol is L, unit is henry (H)

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Inductance (Cont.)

- Strong and weak magnetic fields
- Self induction
- Transient responses

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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

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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

- Coil connected to dc voltage source

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Transient Responses (Cont.)

- Current builds up gradually when switch is closed
- Current decays gradually when switch opens

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RL Circuits

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RL Circuits (Cont.)

- L coil shorted through switch 2

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Transient Response Curves

- Graphs show charge and discharge circuits

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Transient Response Curves

- Time constant ()
- Inductance in henrys
- Resistance in ohms

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Review

What is inductance?

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

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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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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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Review

What kind of circuit contains resistance and inductance?

RL circuit

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Mutual Inductance

- Two coils close together
- Coupling
- Unity coupling

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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

- Without mutual inductance
- LT = L1 + L2 + L3 …+ LN

- With mutual inductance
- LT = L1 + L2± 2LM

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Phase Relationship in Parallel Inductance

- Without mutual inductance
- With mutual inductance

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Review

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

Mutual inductance

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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 produces counter emf to oppose source voltage
- Reactance (X)
- Inductive reactance (XL)

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Induced Current and Voltage

- Counter emf is 180° out of phase with source voltage
- XL = 2fL

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Induced Current and Voltage (Cont.)

- As frequency or inductance increases, inductive reactance increases

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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)

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

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Power Factor Example

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A Purely Resistive Circuit

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Resistance and Inductance in an AC Circuit

- Different traits for added inductor

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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

- 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 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.)

- 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 (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

- No phase difference among the elements
- Phase difference among total and branch currents

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Parallel RL Circuits (Cont.)

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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.)

- Phase angle
- arctan 0.597 = 30.8°

- Total circuit current

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Parallel RL Circuit Example (Cont.)

- Impedance

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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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Review

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

Reactance

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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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Review

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

They are in direct proportion

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Review

How is reactive power measured?

Volt-ampere-reactive (VAR)

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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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