November 27, 2006 Physics 6C Lecture 25 1
Physics 6C
Physics 6C
Introduction to Physics III
Introduction to Physics III
Electricity and Magnetism
Electricity and Magnetism
Robert Johnson
Professor of Physics
rjohnson@scipp.ucsc.edu
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community
Ask the community for help and clear up your study doubts
University Rankings
Discover the best universities in your country according to Docsity users
Free resources
Our save-the-student-ebooks!
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Physics 6C Lecture 25: RC Circuit and AC Sources, Study notes of Physics
A portion of the lecture notes from physics 6c, introduction to physics iii, covering the topics of rc circuits and ac sources. It includes explanations of transient responses, kirchhoff's loop rule, and finding the resulting current and phase angle for an rc circuit with an ac source.
Typology: Study notes
Pre 2010
1 / 15
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Physics 6C Lecture 25: RC Circuit and AC Sources and more Study notes Physics in PDF only on Docsity!
November 27, 2006
Physics 6C Lecture 25
Physics 6C Physics 6C
Introduction to Physics IIIIntroduction to Physics III Electricity and MagnetismElectricity and Magnetism
Robert Johnson
Professor of Physics
rjohnson@scipp.ucsc.edu
November 27, 2006
Physics 6C Lecture 25
RC Circuit: Charging^ RC Circuit: Charging
0
1
2
3
4
5
6
0
1
Q t
( )
t
0
1
2
3
4
5
6
0
1
I t
( )
t
(
)
RC
t
e
CV
t
Q
ā
ā
ā
=
1
)
(
0
RC
t
e
I
t
I
ā
ā
=
0
)
(
This is an example of a ātransientāresponse. The current changeswith time after the switch closesand eventually reaches a constantvalue of zero.For AC circuits, we are notinterested in the transientresponse, but instead we consider only the behavior after the circuithas been on for a long time.
November 27, 2006
Physics 6C Lecture 25
RC Circuit^ RC Circuit
t
v
t
v
t
C
R
max
max
cos
cos(
cos
t C I t R I t ,
This equation can be solved for both
I
max
and
Ļ
by using trig identities, but it
is easier to do it graphically using phasors. The algebra then just looks likevector addition.
RC
V V
R
C
tan
As in a circuit with just a capacitor, thevoltage lags behind the current, but byless than 90 degrees.
I
max
V
R
V
C
max
C
R
I
V
V
C
R
Note
C
X
R
Z
Ļ
November 27, 2006
Physics 6C Lecture 25
Problem 35-^ Problem 35
-
36
a)
Evaluate V
R
at emf frequencies 100,
300, 1000, 3000, and 10,000 Hz
b)
Graph V
R
vs frequency.
V
in
V
out
This is an example of a āhigh passfilter.āNote that for
f=
0
(DC) the current must
be zero, and therefore V
out
is 0.
November 27, 2006
Physics 6C Lecture 25
Problem 35-36continued.This plot demonstratesfor one frequency(1500 Hz) how theresistor and capacitorvoltages add togetherat all times to yield thevoltage of the source.
R
C
6
ā
V
in
Ļ
Ļ ā
V t
V
in
cos
Ļ
t ā
(
)
I
max
V
in
R
2
Ļ
C
2
Ļ
atan
Ļ
R
C
Ļ
33.716 deg
I t
I
max
cos
Ļ
t ā
Ļ
(
)
V
R
t ( )
I
max
R
cos
Ļ
t ā
Ļ
(
)
V
C
t ( )
I
max
Ļ
C
cos
Ļ
t ā
Ļ
Ļ^2
0
2
.
10
4
4
.
10
4
6
.
10
4
8
.
10
4
10
0
10
V
R
t ( )
V
C
t ( )
V
R
t ( )
V
C
t
( )
V t
( )
t
November 27, 2006
Physics 6C Lecture 25
Problem 35-^ Problem 35
-
37
a)
Evaluate V
C
at emf frequencies 1, 3,
10, 30, and 100 kilo-Hertz
b)
Graph V
C
vs frequency.
V
in
V
out
This is an example of a ālow pass filter.āNote that for
f=
0
(DC) the current must
be zero, and therefore V
out
is V
in.
November 27, 2006
Physics 6C Lecture 25
f
atan
f
R
C
ļ£«ļ£¬ļ£
ļ£¶ ļ£ø
Ļ^2
3
4
5
Ļ
f
( ) Ļ
f
It is very common to plot frequency on a log scale. In that case, the samephase-angle plot looks as shown here.The point where the phase angle is
ā
45
Ā°
is called the cross-over
frequency. It occurs where
kHz
10
or
kHz
5
.
62
1
=
=
=
f
RC
c
Ļ
Problem 35-^ Problem 35
-
37
November 27, 2006
Physics 6C Lecture 25
AC Circuits: Inductance^ AC Circuits: Inductance
t
V
t
V
Ļ
cos
)
(
=
dt dI
L
V
=
ā«
=
dt
t
V
L
t
I
)
(
1
)
(
ā«
=
dt
t
L
V
t
I
cos
)
(
0
Ļ
)
cos(
)
(
2
0
Ļ
Ļ
Ļ
ā
ā
=
t
L
V
t
I
I
0
)
(
=
,
t
V
dt dI
L
ā
=
,
t
V
L
t
I
Ļ
Ļ
sin
1
)
(
0
=
Kirchhoffās rule:
Energy is stored, NOT dissipated!
November 27, 2006
Physics 6C Lecture 25
Reactance^ Reactance
t
R
V
t
I
Ļ
cos
)
(
0
=
)
cos(
1
)
(
2
0
Ļ
Ļ
Ļ
=
t
C
V
t
I
)
cos(
)
(
2
0
Ļ
Ļ
Ļ
ā
=
t
L
V
t
I
All 3 elements provide an āimpedanceā (
Z
) to the flow of current, but
one has to specify a phase difference between current and voltageas well as a change in amplitude.Assume that the voltage is given by
t
V
t
V
Ļ
cos
)
(
0
=
0
and
=
=
Ļ
R
Z
2
and
1
Ļ
Ļ
Ļ
=
=
=
C
X
Z
C
2
and
Ļ
Ļ
Ļ
ā
=
=
=
L
X
Z
L
Reactance:
I
and
V
in phase
I
leads
V
by 90
Ā°
I
lags
V
by 90
Ā°
(
)
Ļ
Ļ +
=
t
I
t
I
cos
)
(
max
November 27, 2006
Physics 6C Lecture 25
RL Circuit with AC Source^ RL Circuit with AC Source
Problem 35-47.
t
V
t
v
Ļ
cos
)
(
=
V
R
V
L
V
Ļ
I
max
)
cos(
)
(
max
Ļ
Ļ
=
t I t i Ļ 0 < Ļ
The current islagging behind thevoltage (negativephase).
(
)
2
2
max
2
2
0
L R I V V V
L
R
Ļ
=
=
R
L
V V
L R
Ļ
Ļ
1
1
tan
tan
ā
ā
ā
=
ā
=
2
2
:
Note
L
X
R
Z
=
R
L