Inductive ReactanceInductive Reactance

Inertial MassInertial Mass Acceleration of water in a pipe Acceleration of water in a pipe

requires force to move a mass.requires force to move a mass.

An inductor creates an emf An inductor creates an emf proportional to a change in proportional to a change in current. current. • Magnetic field in the coilMagnetic field in the coil

The field acts as a mass that The field acts as a mass that reduces change in the current. reduces change in the current.

A)v

i

L

t

vmtF

)(

t

tILtV

)(

)(

Inductor AloneInductor Alone An AC source provides a An AC source provides a

sinusoidal voltage.sinusoidal voltage.• Inductor matchesInductor matches

• One loop circuitOne loop circuit

The inductor voltage varies The inductor voltage varies with the current.with the current.

The voltage is related to the The voltage is related to the rate of change of the current.rate of change of the current.

Lv

tVvL sin0

tVL

i

cos1

0

t

iLtV

sin0

Phase ShiftPhase Shift

Voltage and current are not in phase through an Voltage and current are not in phase through an inductor.inductor.• Voltage leads current: ELI the ICE manVoltage leads current: ELI the ICE man

Ohm for InductorsOhm for Inductors The amplitude of voltage and The amplitude of voltage and

current through an inductor are current through an inductor are related.related.

The ratio gives an expression The ratio gives an expression like Ohm’s law.like Ohm’s law.

This is the This is the inductive reactanceinductive reactance..• Measured in ohmsMeasured in ohms

L

LLV

V

i

vX LL

0

0

v

00 sin VtVvL

L

Vt

L

Vi

00 cos

Frequency DependentFrequency Dependent Inductive reactance depends Inductive reactance depends

linearly on frequency.linearly on frequency.• Low reactance at low Low reactance at low

frequencyfrequency

• High reactance at high High reactance at high frequencyfrequency

DC has no inductive DC has no inductive reactance.reactance.• Equal to zero frequencyEqual to zero frequencyf

XL

fLX L 2

Different ResponseDifferent Response Inductors and capacitors react Inductors and capacitors react

differently with changes to differently with changes to frequency.frequency.• Resistors stay the sameResistors stay the same

Consider reactances that are Consider reactances that are equal at a frequency equal at a frequency ωω00..

• Capacitive reactance higher Capacitive reactance higher for low frequencyfor low frequency

• Inductive reactance higher for Inductive reactance higher for high freqencyhigh freqency

Resistance vs ReactanceResistance vs Reactance Resistance is measured in Resistance is measured in

ohms.ohms.

Resistance doesn’t depend on Resistance doesn’t depend on frequency.frequency.

Resistance doesn’t affect the Resistance doesn’t affect the phase.phase.

Reactance is measured in Reactance is measured in ohms.ohms.

Reactance depends on Reactance depends on frequency.frequency.• 1/1/CC or or LL

Reactance shifts the phase.Reactance shifts the phase.• ELI the ICE manELI the ICE man

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