Inductors in AC Circuits
Previously, a procedure was discussed for working with circuits containing resistors and
capacitors driven by sinusoidal alternating current sources. Essentially, all circuit
elements were converted to
phasors
, math was carefully done on these complex values,
and the results were converted back to the
time domain
. Generically, voltages and
currents of the form
A
trig
(
ω
t +
φ
)
became
A
∠φ
where
A
was the amplitude,
φ
was the
phase shift, and
trig
was either
sin
or
cos
. A resistance simply became
!
R
=
R
!
0
°
. A
capacitance became a kind of
reactance
:
!
X
=
!
1
"
C
#
90
°
. Inductances also become
reactances. The value is given by
!
X
=
!
L
"
90
°
. Recall that phasors can be directly
added only if they have the same angle. The only significant difference between
capacitive and inductive reactances is that one kind is negative and the other is positive.
Capacitors act like
open circuits
when connected to DC. This is because there is no
physical connection between the plates. For AC, as the frequency
ω
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 Spring '11
 Tibbets
 Current, Work, Highpass filter, Bandpass filter, Lowpass filter, lowpass filters, highpass filters

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