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Lecture 22
Oscillating emf, transformers, and
simple AC circuits
Today: begin Ch 31 on AC circuits
Tuesday:
I, P, and resonance in driven LCR
Thursday: EM waves, (
and exam #3)
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View Full Document The LCR circuit
0
1
0
0
2
2
2
2
=
+
+
=
+
+

=
=


+
Q
LC
dt
dQ
L
R
dt
Q
d
or
dt
Q
d
L
dt
dQ
R
C
Q
dt
dQ
i
and
dt
di
L
iR
C
Q
L
+Q
Q
i
→
Take a CCW walk around Kirchhoff’s loop:
R
Add in just a little R (underdamped):
The oscillations get gradually smaller
2
2
2
0
4
1
'
),
'
cos(
)
(
L
R
LC
t
e
Q
t
q
t
L
R

=
+
=

ϖ
ϕ
“ring down effect”
Highly Damped LCR
No oscillations
when
LC
L
R
1
2
≥
But we can
force
the LCR circuit to oscillate by driving the circuit with a oscillating emf.
Our primary goal in ch 31 is to understand the (series) LCR driven by a sinusoidal emf.
Like a pendulum in
thick molasses
Like a car with
new shock
absorbers
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View Full Document Oscillating emf,
an AC power source
ξ(t) = ξ
max
cos(ωt)
or
ξ
max
sin(ωt)
or
ξ
max
cos(ωt + φ)
You control the amplitude and frequency
2
)
(
2
)
(
0
)
(
)
cos(
)
(
2
2
m
ave
m
ave
rec
ave
m
t
t
t
t
t
ξ
π
ϖ
=
<
=
<
=
<
=
V
ξ
m
ξ
m
cos(ωt)
Phasor
representation
rectified
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This note was uploaded on 04/04/2008 for the course PHYSICS 240 taught by Professor Davewinn during the Spring '08 term at University of Michigan.
 Spring '08
 DaveWinn

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