Inductive Reactance
Inertial Mass
 Acceleration of water in a pipe
(rA)v
v
F (t )  m
t
requires force to move a mass.
 An inductor creates an emf
proportional to a change in
current.
• Magnetic field in the coil
i
 The field acts as a mass that
L
V (t )  L
I (t )
t
reduces change in the current.
Inductor Alone
 An AC source provides a
sinusoidal voltage.
• Inductor matches
• One loop circuit
 The inductor voltage varies
with the current.
 The voltage is related to the
rate of change of the current.
v
L
vL  V0 sin t
V0 sin t  L
i
i
t
1
V0 cos t
L
Phase Shift
 Voltage and current are not in phase through an inductor.
• Voltage leads current: ELI the ICE man
Ohm for Inductors
 The amplitude of voltage and
current through an inductor are
related.
 The ratio gives an expression
like Ohm’s law.
 This is the inductive reactance.
• Measured in ohms
L
v
vL  V0 sin t  V0
i
V0
V
cos t  0
L
L
XL 
vL
i

V0
V0 L
 L
Frequency Dependent
 Inductive reactance depends
XL
X L  2fL
linearly on frequency.
• Low reactance at low
frequency
• High reactance at high
frequency
 DC has no inductive
reactance.
f
• Equal to zero frequency
Different Response
 Inductors and capacitors react
differently with changes to
frequency.
• Resistors stay the same
 Consider reactances that are
equal at a frequency ω0.
• Capacitive reactance higher
for low frequency
• Inductive reactance higher for
high freqency
Resistance vs Reactance
 Resistance is measured in
ohms.
 Resistance doesn’t depend on
frequency.
 Reactance is measured in
ohms.
 Reactance depends on
frequency.
• 1/C or L
 Resistance doesn’t affect the
phase.
 Reactance shifts the phase.
• ELI the ICE man
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