#### Inductive Reactance

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Transcript Inductive Reactance

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 2fL
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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