farad:
The unit of C is farad:
V
C
V
C
F
1
1
1
1
= Circuit symbol for a capacitor:
Circuit symbol for a capacitor:
Recap
Recap
Circuit symbol for a battery:
Circuit symbol for a battery:
+
+
_
_
Battery
Battery Physics 122A
:
Lecture 13, Pg 3
d
A
C
0 =
Parallel plate capacitor
Parallel plate capacitor
Spherical Capacitor
Spherical Capacitor
Recap
Recap
2
1
1
2
C
C
2
2
Q
U
C V
C
=
= Energy stored in a capacitor:
Energy stored in a capacitor:
1
1 2
0
0
1
2
2
1
1
1
4
4
C
R R
Q
C
V
R
R
R
R =
= =
Parallel Plate Capacitor
Parallel Plate Capacitor Physics 122A
:
Lecture 13, Pg 4
Combining Capacitors
Combining Capacitors
In Parallel:
In Parallel:
Same
Same
D
D
V
V
, but different
, but different
Q
Q
s
s.
1
2
3
parallel
C
C
1
2
3
Q
Q
Q
Q
C
V
V
C
C
C
+
+
+
=
=
=
+
+
+
L
L
Q
Q
1
1
Q
Q
2
2
Q
Q
3
3
In Series:
In Series:
Same
Same
Q
Q
, but different
, but different
D
D
V
V
s
s
.
-
-
Q
Q
-
-
Q
Q
-
-
Q
Q
+
+
Q
Q
+
+
Q
Q
+
+
Q
Q
Recap
Recap
1
3
2
1
....
1
1
1



+
+
+
=
C
C
C
C
series Physics 122A
:
Lecture 13, Pg 5
Example: two Capacitors
Example: two Capacitors
A capacitor is charged to a voltage difference of
A capacitor is charged to a voltage difference of
D
D
V (S
V (S
1
1
closed).
closed).
The battery is removed (S
The battery is removed (S
1
1
opened) and an uncharged capacitor is
opened) and an uncharged capacitor is
attached in parallel (S
attached in parallel (S
2
2
closed).
closed).
What is the final
What is the final
potential difference of
potential difference of
the combination?
the combination?
2
1
0
q
q
q
+
=
V
C
q
=
V
C
V
C
V
C
2
1
0
1
+
=
2
1
1
0
C
C
C
V
V
+
= What is the final energy?
What is the final energy?
(
)
0
2
1
1
2
2
1
0
1
2
1
2
1
2
2
2
1
2
1
2
1
U
C
C
C
C
C
V
C
C
C
V
C
V
C
U
+
=




+
+
=
+
=
The final energy in the two capacitors is less than the initial
The final energy in the two capacitors is less than the initial
energy!
energy!
(something got must have gotten hot!)
(something got must have gotten hot!)
0
V
2
1
C
C
2
1
S
S Physics 122A
:
Lecture 13, Pg 6
Clicker Question 1
Clicker Question 1
7
7
m
m
F
F
3
3
m
m
F
F
4
4
m
m
F
F
1
1
m
m
F
F
2
2
m
m
F
F
5
5
m
m
F
F
6
6
m
m
F
F
Which capacitor has the highest Voltage
Which capacitor has the highest Voltage
difference across it?
difference across it?
V
V
A.
A.
The 1
The 1
m
m
F capacitor
F capacitor
B.
B.
The 2
The 2
m
m
F capacitor
F capacitor
C.
C.
The 4
The 4
m
m
F capacitor
F capacitor
D.
D.
The 5
The 5
m
m
F capacitor
F capacitor
E.
E.
The 6
The 6
m
m
F capacitor
F capacitor Physics 122A
:
Lecture 13, Pg 7
Clicker Question 1
Clicker Question 1
7
7
m
m
F
F
3
3
m
m
F
F
4
4
m
m
F
F
1
1
m
m
F
F
2
2
m
m
F
F
5
5
m
m
F
F
6
6
m
m
F
F
Which capacitor has the highest Voltage?
Which capacitor has the highest Voltage?
V
V
9
9
m
m
F
F
5.875
5.875
m
m
F
F
6
6
m
m
F
F
V
V
A.
A.
The 1
The 1
m
m
F capacitor
F capacitor
B.
B.
The 2
The 2
m
m
F capacitor
F capacitor
C.
C.
The 4
The 4
m
m
F capacitor
F capacitor
D.
D.
The 5
The 5
m
m
F capacitor
F capacitor
E.
E.
The 6
The 6
m
m
F capacitor
F capacitor
D
D
V =Q/ C
V =Q/ C
All these three
All these three
capacitors have
capacitors have
the same Q
the same Q
0.875
0.875
m
m
F
F Physics 122A
:
Lecture 13, Pg 8
Clicker Question 2
Clicker Question 2
Which capacitor has the smallest charge on it?
Which capacitor has the smallest charge on it?
A.
A.
The 1
The 1
m
m
F capacitor
F capacitor
B.
B.
The 2
The 2
m
m
F capacitor
F capacitor
C.
C.
The 4
The 4
m
m
F capacitor
F capacitor
D.
D.
The 5
The 5
m
m
F capacitor
F capacitor
E.
E.
The 6
The 6
m
m
F capacitor
F capacitor
7
7
m
m
F
F
3
3
m
m
F
F
1
1
m
m
F
F
2
2
m
m
F
F
4
4
m
m
F
F
6
6
m
m
F
F
V
V
5
5
m
m
F
F Physics 122A
:
Lecture 13, Pg 9
Clicker Question 2
Clicker Question 2
Which capacitor has the smallest charge on it?
Which capacitor has the smallest charge on it?
A.
A.
The 1
The 1
m
m
F capacitor
F capacitor
B.
B.
The 2
The 2
m
m
F capacitor
F capacitor
C.
C.
The 4
The 4
m
m
F capacitor
F capacitor
D.
D.
The 5
The 5
m
m
F capacitor
F capacitor
E.
E.
The 6
The 6
m
m
F capacitor
F capacitor
7
7
m
m
F
F
3
3
m
m
F
F
1
1
m
m
F
F
2
2
m
m
F
F
4
4
m
m
F
F
6
6
m
m
F
F
V
V
5
5
m
m
F
F
Q
Q
875
.
5
875
.
0
Q
875
.
5
5
Q
9
2
Q
9
4
Q
9
3
The 7
The 7
m
m
F and the
F and the
1
1
m
m
F have
F have
the same amount of charge. It
the same amount of charge. It
is the smallest amount of
is the smallest amount of
charge.
charge. Physics 122A
:
Lecture 13, Pg 10
The Electron Current
The Electron Current
While the discharge is taking place,
While the discharge is taking place,
the wire gets warm, a light bulb can
the wire gets warm, a light bulb can
be made to glow, and a compass
be made to glow, and a compass
needle can be deflected. These are
needle can be deflected. These are
indicators
indicators
of
of
current flow
current flow
in the
in the
wire.
wire.
The electrons quickly
The electrons quickly
move from one side to
move from one side to
the other.*
the other.*
The capacitor plates
The capacitor plates
become neutral.
become neutral.
nano
nano
-
-
seconds
seconds
* We will shortly make this

* We will shortly make this

statement more accurate.
statement more accurate. Physics 122A
:
Lecture 13, Pg 11
Are electrons really the charge carriers?
Are electrons really the charge carriers?
The
The
Tolman
Tolman
-
-
Stewart experiment (1916)
Stewart experiment (1916)
We modeled a metallic
We modeled a metallic
conductor as a rigid
conductor as a rigid
lattice of positive charges
lattice of positive charges
pervaded by a sea of
pervaded by a sea of
conduction electrons, 1
conduction electrons, 1
per atom, that move
per atom, that move
freely in the material.
freely in the material.
Accelerate a piece of metallic conductor:
Accelerate a piece of metallic conductor:
This polarization is
This polarization is
observed
observed
ï
ï
electrons are the
electrons are the
charge carriers in
charge carriers in
metals.
metals. Physics 122A
:
Lecture 13, Pg 12
Modern repeat of the
Modern repeat of the
Tolman
Tolman
-
-
Steward
Steward
Experiment
Experiment Physics 122A
:
Lecture 13, Pg 13
In a metallic conductor in
In a metallic conductor in
electrostatic
electrostatic
equilibrium
equilibrium
, the conduction electrons
, the conduction electrons
move around quite rapidly (random
move around quite rapidly (random
thermal motion). There is practically no
thermal motion). There is practically no
net movement of charge.
net movement of charge.
We define the electron
We define the electron
current
current
i
i
as the number of
as the number of
electrons
electrons
N
N
e
e
that pass
that pass
through a cross section of
through a cross section of
wire or other conductor in a
wire or other conductor in a
time interval
time interval
D
D
t.
t.
In other
In other
words:
words:
N
N
e
e
=i
=i
D
D
t
t
.
.
The Electron Current
The Electron Current
With an electric field applied (voltage
With an electric field applied (voltage
difference), the entire sea of electrons
difference), the entire sea of electrons
can move in a particular direction, like a
can move in a particular direction, like a
liquid flowing through a pipe.
liquid flowing through a pipe.
The net motion, the drift speed
The net motion, the drift speed
v
v
d
d
, is
, is
superimposed on the random thermal
superimposed on the random thermal
motions.
motions.
v
v
d
d
is typically surprisingly small:
is typically surprisingly small:
è
è
10
10
-
-
4
4
m/s.
m/s. Physics 122A
:
Lecture 13, Pg 14
Current and Drift Velocity
Current and Drift Velocity
In a time
In a time
D
D
t
t
the electrons have traveled the
the electrons have traveled the
distance
distance
D
D
x=
x=
v
v
d
d
D
D
t
t
.
.
The volume of electrons that moved is
The volume of electrons that moved is
D
D
xA
xA
.
.
(
(
A
A
= Cross sectional area of the wire)
= Cross sectional area of the wire)
The number of electrons in this volume is
The number of electrons in this volume is
n
n
D
D
x A
x A
,
,
n
n
= conduction electron density.
= conduction electron density.
d
i nAv
=
ï
ï
i
i
is a rate. Its units is 1/s
is a rate. Its units is 1/s
.
.
This is about one free
This is about one free
electron per atom
electron per atom Physics 122A
:
Lecture 13, Pg 15
Clicker Question 3
Clicker Question 3
Which wire has the largest electron current?
Which wire has the largest electron current? Physics 122A
:
Lecture 13, Pg 16
Question:
Question:
An electron current
An electron current
i
i
A
A
flows to the
flows to the
light bulb, passing point A, where it delivers
light bulb, passing point A, where it delivers
some energy and makes the bulb glow. How
some energy and makes the bulb glow. How
much electron current
much electron current
i
i
B
B
then passes point
then passes point
B
B
?
?
Answer:
Answer:
All of it!
All of it!
i
i
A
A
=
=
i
i
B
B
. Reason: the
. Reason: the
electrons dont have anywhere else to go.
electrons dont have anywhere else to go.
What goes to the bulb must return from the
What goes to the bulb must return from the
bulb. The bulb cannot use up the electrons.
bulb. The bulb cannot use up the electrons.
Plumbers Analogy:
Plumbers Analogy:
If water flows into a
If water flows into a
constant diameter pipe at 1gallon/minute, it
constant diameter pipe at 1gallon/min