Chapter 13

Inductance and Inductors

Inductors

Common form of an inductor is a coil of wire

Used in radio tuning circuits

In fluorescent lights

Part of ballast circuit

Inductors

On power systems

Part of the protection circuitry used to control short-circuit currents during faults

Electromagnetic Induction

Voltage is induced

When a magnet moves through a coil of wire

When a conductor moves through a magnetic field

Electromagnetic Induction

Change in current in one coil can induce a voltage in a second coil

Change in current in a coil can induce a voltage in that coil

Electromagnetic Induction

Faraday’s Law

Voltage is induced in a circuit whenever the flux linking the circuit is changing

Magnitude of voltage is proportional to rate of change of the flux linkages with respect to time

Electromagnetic Induction

Lenz’s Law

Polarity of the induced voltage opposes the cause producing it

Induced Voltage and Induction

If a constant current is applied

No voltage is induced

If current is increased

Inductor will develop a voltage with a polarity to oppose increase

Induced Voltage and Induction

If current is decreased

Voltage is formed with a polarity that opposes decrease

Iron-Core Inductors

Have flux almost entirely confined to their cores

Flux lines pass through the windings

Flux linkage as product

Flux times number of turns

Iron-Core Inductors

By Faraday’s law

Induced voltage is equal to rate of change of NF

Air-Core Inductors

All flux lines do not pass through all of the windings

Flux is directly proportional to current

Induced voltage directly proportional to rate of change of current

Self-Inductance

Voltage induced in a coil is proportional to rate of change of the current

Proportionality constant is L

Self-inductance of the coil-units are Henrys (H)

Self-Inductance

Inductance of a coil is one Henry

If the voltage created by its changing current is one volt

When its current changes at rate of one amp per second

Inductance Formulas

Inductance of a coil is given by

l is the length of coil in meters

A is cross-sectional area in square meters

N is number of turns

µ is permeability of core

Inductance Formulas

If air gap is used, formula for inductance is

Where µ_o is permeability of air

A_g is area of air gap

l_g is length of gap

Computing Induced Voltage

When using equation

If current is increasing, voltage is positive

If current is decreasing, voltage is negative

Di/Dt is slope for currents described with straight lines

Inductances in Series

For inductors in series

Total inductance is sum of individual inductors (similar to resistors in series)

Inductances in Parallel

Inductors in parallel add as resistors do in parallel

Core Types

Type of core depends on intended use and frequency range

For audio or power supply applications

Inductors with iron cores are generally used

Core Types

Iron-core inductors

Large inductance values but have large power losses at high frequencies

For high-frequency applications

Ferrite-core inductors are used

Variable Inductors

Used in tuning circuits

Inductance may be varied by changing the coil spacing

Inductance may be changed by moving a core in or out

Circuit Symbols

Stray Capacitance

Turns of inductors are separated by insulation

May cause stray or parasitic capacitance

At low frequencies, it can be ignored

At high frequencies, it must be taken into account

Some coils are wound in multiple sections to reduce stray capacitance

Stray Inductance

Current-carrying components have some stray inductance

Due to magnetic effects of current

Leads of resistors, capacitors, etc. have inductance

These leads are often cut short to reduce stray inductance

Inductance and Steady State DC

Voltage across an inductance with constant dc current is zero

Since it has current but no voltage, it looks like a short circuit at steady state

For non-ideal inductors

Resistance of windings must be considered

Energy Stored by an Inductance

When energy flows into an inductor

Energy is stored in its magnetic field

When the field collapses

Energy returns to the circuit

Energy Stored by an Inductance

No power is dissipated, so there is no power loss

Energy stored is given by

Troubleshooting Hints

Use ohmmeter

Open coil will have infinite resistance

Coil can develop shorts between its windings causing excessive current

Checking with an ohmmeter may indicate lower resistance


	Common form of an inductor is a coil of wire
		Used in radio tuning circuits
	In fluorescent lights
		Part of ballast circuit


	On power systems
		Part of the protection circuitry used to control short-circuit currents during faults


	Voltage is induced
		When a magnet moves through a coil of wire
		When a conductor moves through a magnetic field


	Change in current in one coil can induce a voltage in a second coil
	Change in current in a coil can induce a voltage in that coil


	Faraday’s Law
		Voltage is induced in a circuit whenever the flux linking the circuit is changing
		Magnitude of voltage is proportional to rate of change of the flux linkages with respect to time


	Lenz’s Law
		Polarity of the induced voltage opposes the cause producing it


	If a constant current is applied
		No voltage is induced
	If current is increased
		Inductor will develop a voltage with a polarity to oppose increase


	If current is decreased
		Voltage is formed with a polarity that opposes decrease


	Have flux almost entirely confined to their cores
	Flux lines pass through the windings
	Flux linkage as product
		Flux times number of turns


	By Faraday’s law
		Induced voltage is equal to rate of change of NF


	All flux lines do not pass through all of the windings
	Flux is directly proportional to current
	Induced voltage directly proportional to rate of change of current


	Voltage induced in a coil is proportional to rate of change of the current
	Proportionality constant is L
		Self-inductance of the coil-units are Henrys (H)


	Inductance of a coil is one Henry
		If the voltage created by its changing current is one volt
		When its current changes at rate of one amp per second


	Inductance of a coil is given by


	l is the length of coil in meters
	A is cross-sectional area in square meters
	N is number of turns
	µ is permeability of core


	If air gap is used, formula for inductance is

	Where µ_o is permeability of air
	A_g is area of air gap
	l_g is length of gap


	When using equation


		If current is increasing, voltage is positive
		If current is decreasing, voltage is negative
		Di/Dt is slope for currents described with straight lines


	For inductors in series
		Total inductance is sum of individual inductors (similar to resistors in series)


	Type of core depends on intended use and frequency range
	For audio or power supply applications
		Inductors with iron cores are generally used


	Iron-core inductors
		Large inductance values but have large power losses at high frequencies
	For high-frequency applications
		Ferrite-core inductors are used


	Used in tuning circuits
	Inductance may be varied by changing the coil spacing
	Inductance may be changed by moving a core in or out


	Turns of inductors are separated by insulation
		May cause stray or parasitic capacitance
	At low frequencies, it can be ignored
		At high frequencies, it must be taken into account
	Some coils are wound in multiple sections to reduce stray capacitance


	Current-carrying components have some stray inductance
		Due to magnetic effects of current
	Leads of resistors, capacitors, etc. have inductance
		These leads are often cut short to reduce stray inductance


	Voltage across an inductance with constant dc current is zero
	Since it has current but no voltage, it looks like a short circuit at steady state
	For non-ideal inductors
		Resistance of windings must be considered


	When energy flows into an inductor
		Energy is stored in its magnetic field
	When the field collapses
		Energy returns to the circuit


	No power is dissipated, so there is no power loss
	Energy stored is given by


	Use ohmmeter
	Open coil will have infinite resistance
	Coil can develop shorts between its windings causing excessive current
		Checking with an ohmmeter may indicate lower resistance