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Lecture 11: AC Power, Circuits
AC Circuits
– LCR Circuits
• Phasors, Impedance
• Resonance
– RC and RL Circuits
• Filters
– Motors
• AC and DC
October 11
Physics 104, Fal 2011
1
AC Power
• Voltage, current and power depend on time
October 11
Physics 104, Fal 2011
2
• We are interested in averages (
f
= 60Hz)
V
=
V
0
sin2
π
ft
I
=
I
0
sin2
ft
P
=
VI
=
V
0
I
0
sin
2
2
ft
I
rms
=
V
rms
R
P
ave
=
V
rms
I
rms
=
V
rms
2
R
=
I
rms
2
R
P
ave
=
1
2
V
0
I
0
V
rms
=
V
0
2
I
rms
=
I
0
2
Phasors
•
AC circuits can be analyzed
graphically
•
An arrow has a length V
max
•
The arrow’s tail is at the origin
•
The arrow makes an angle of
θ
with the horizontal
•
The angle varies with time
according to
θ
= 2
π
ƒt
•
The rotating arrow represents
the voltage in an AC circuit
•
The arrow is called a
phasor
•
A phasor is not a vector
•
Provides time dependence in
an AC circuit
Section 22.2
October 11
3
Physics 104, Fal 2011
Resistor Phasor Diagram
The current in an AC circuit can also be represented
by a phasor
The two phasors always make the same angle with
the horizontal axis as time passes
The current and voltage are in phase
For a circuit with only resistors
October 11
4
Physics 104, Fal 2011
Capacitor Phasor Diagram
• The current is out of phase with the voltage
• The angle
π
/2 is
phase angle,
Φ
, between V and I
• The current and voltage are out of phase by 90
o
– It takes time to build voltage across a capacitor
October 11
5
Physics 104, Fal 2011
Inductor Phasor Diagram
• The current is out of phase with the voltage
• For this circuit, the current and voltage are out of
phase by 90
o
– Remember, for a capacitor, the phase difference was +90
o
October 11
6
Physics 104, Fal 2011
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Impedance
October 11
Physics 104, Fal 2011
7
Impedance
frequency
Impedance in AC Circuits
•
R is independent of f
R
Impedance
October 11
Physics 104, Fal 2011
8
frequency
Impedance in AC Circuits
•
R
is independent of
f
•
X
L
increases with f
R
X
L
X
L
=
2
π
f L
Impedance
October 11
Physics 104, Fal 2011
9
frequency
Impedance of AC Circuits
•
X
C
decreases as 1/f
R
X
L
X
C
•R is independent of f
•X
L
increases with f
Impedance
X
L
=
2
f L
X
C
=
1
2
f C
Impedance
October 11
Physics 104, Fal 2011
10
frequency
Impedance of AC Circuits
•
R is independent of f
•
X
L
increases with f
•
X
C
decreases as 1/f
Z:
X
L
and X
C
subtract
R
X
L
X
C
Z
f
0
Impedance
X
L
=
2
f L
X
C
=
1
2
f C
Z
=
R
2
+
(
X
L
−
X
C
)
2
AC Circuits
Resistors:
V
R
=IR
V
R
and I in phase
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 Fall '11
 dasu/karle
 Physics, Current, Power

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