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Chapter 14

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Chapter 14

Inductance and RL Circuits

- 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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- 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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- Coils of wire
- Inductors
- Reactors
- Chokes

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

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

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- 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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- 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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- Coil connected to dc voltage source

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

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- L coil shorted through switch 2

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- Graphs show charge and discharge circuits

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

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What is inductance?

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

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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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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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What kind of circuit contains resistance and inductance?

RL circuit

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- Two coils close together
- Coupling
- Unity coupling

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- LMis mutual inductance
- k is coefficient or percentage of coupling
- L1 and L2 are inductances of coils

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

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

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- Without mutual inductance
- With mutual inductance

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

Mutual inductance

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

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

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- As frequency or inductance increases, inductive reactance increases

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

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- Different traits for added inductor

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- Impedance (Z)
- Pythagorean theorem
- Finding impedance
- Phase angle ()
- cos = PF

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- 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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- E = I× Z

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- Reactance of L
- XL = 2 × 3.14 × 60 Hz × 8 H
- XL= 3014 Ω

- Impedance
- Z = 5000 Ω

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- Current
- I = 0.04 A

- Voltage drops
- ER = 0.04 A × 4000 Ω = 160 V

- Source voltage

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

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

- Branch currents

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- Phase angle
- arctan 0.597 = 30.8°

- Total circuit current

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- Impedance

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

Reactance

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

They are in direct proportion

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How is reactive power measured?

Volt-ampere-reactive (VAR)

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- 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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