Physics
ys cs 132:
3 Lecture
ectu e 14
Elements of Physics II
A
Agenda
d for
f T
Today
d





Capacitors
 Parallel-plate
Charging of capacitors
C
Combinations
off capacitors
Energy stored in a capacitor
Dielectrics in capacitors
Physics 201: Lecture 1, Pg 1
Clicker Question 1:
Metal wires are attached to the terminals of a 3 V battery.
What is the potential difference between points 1 and 2?
A.
6 V.
B.
3 V.
C. 0 V.
D. Undefined.
E.
Not enough
g information to tell.
Physics 201: Lecture 1, Pg 2
How Capacitor works


When a voltage is applied over a capacitor it will
become charged
charged.
Circuit is open, and there is no charge on
capacitor
-
+
Battery
y
Physics 201: Lecture 1, Pg 3
How Capacitor works

When circuit is close and a voltage is applied
over a capacitor it quickly becomes charged.
VC = 12 V
-
-Q
+
+
+
+Q
-
Potential difference is same
as battery!!
+
Battery
y
Electrons travel from one
plate to the other plate!
VB = 12 V
Physics 201: Lecture 1, Pg 4
How Capacitor works


What happens after capacitor is fully charged?
No more charges flowing!!!!
Charge is ready to be
used
-Q
-
+
+
+
+Q
-
+
Battery
y
Physics 201: Lecture 1, Pg 5
How Capacitor works
-Q
-
+
+
+
-
+Q
+
Battery
y
Physics 201: Lecture 1, Pg 6
Definition of Capacitance

Capacitance: The ratio of the charge on one
conductor to the potential difference between
conductors
Q
C 
V

Units: Farad (F)

The larger the capacitance, the more charge can
be stored with a certain potential difference.
Physics 201: Lecture 1, Pg 7
Parallel Plate Capacitor

Capacitance of PP can be found:
ε 0  8.85 10 12
C2
Nm 2
A is area of plate
0 is p
permittivity
y of free space
p
d is distance of separation
Closer plates have bigger C!!
A
C  ε0
d
Physics 201: Lecture 1, Pg 8
How Capacitor works
-Q
-
+
+
+
+Q
-
+
Battery
y
Physics 201: Lecture 1, Pg 9
How Capacitor works
-Q
-
+
+
+
+
+
+Q
-
+
Battery
y
Physics 201: Lecture 1, Pg 10
Clicker Question 2:
A parallel-plate capacitor initially has a voltage of 400 V
and stays
y connected to the battery.
y If the p
plate spacing
p
g is
now doubled, what happens?
a) the voltage decreases
b) the voltage increases
c) the charge decreases
d) the charge increases
400V
C
e) both voltage and charge change
Physics 201: Lecture 1, Pg 11
Clicker Question 3:
A parallel-plate capacitor initially has a potential
difference of 400 V and is then disconnected from the
charging battery. If the plate spacing is now doubled,
what is the new value of the voltage?
a) 100 V
b) 200 V
400V
C
c) 400 V
d) 800 V
e)) 1600 V
Physics 201: Lecture 1, Pg 12
Dielectrics in Capacitors



Insulating sheets called
dielectrics are sometimes
placed between the plates of a
capacitor
This allows for the plates to be
closer together thus having a
l
larger
capacitance
it
((without
ith t
electrons flowing between)
So we
e ge
get a new
e relation
e a o for
o the
e
capacitance of PP when a
dielectric is between the plates:
A
C  κε0
d
 is dielectric constant
Physics 201: Lecture 1, Pg 13
Dielectrics in Capacitors


Electric field when
capacitor is charged
When a dielectric is
added it polarizes

This makes
Thi
k an E
E-field
fi ld
that partially cancels the
original E-field.

Allows more charge to be
held on the capacitor, thus
capacitance is increased
+
+
+
+
+
+
Physics 201: Lecture 1, Pg 14
Capacitors in Series and Parallel
Physics 201: Lecture 1, Pg 15
Capacitors in Parallel
-Q2
-
-Q1
--
-
+Q2
Total charge is increased!
+
+
+ Potential difference is same
+
for both!
+
+
+
+
+
+Q1
+
Battery
y
Two capacitors don’t
effect each other
Physics 201: Lecture 1, Pg 16
Capacitors in Parallel

Consider two capacitors C1 and
C2 connected in parallel.

The total charge drawn from the
battery is Q = Q1 + Q2.

In figure (b) we have replaced
the capacitors with a single
“equivalent” capacitor:
Ceq = C1 + C2
Physics 201: Lecture 1, Pg 17
Capacitors in Series

This time the capacitors will effect each other
Potential difference of capacitors adds up to that of battery
-Q
-
+
+
+
-
+Q -Q
-
+ +Q
+
+
+
Battery
y
Charge must be equal
Physics 201: Lecture 1, Pg 18
Capacitors in Series
V  V1  V2
Q
Q Q


Ceq C1 C2
1
1
1


Ceq C1 C2

The equivalent
capacitance
i
off a series
i
combination is always
less than any individual
capacitor in the
combination
Physics 201: Lecture 1, Pg 19
Summary: Capacitors in Series and Parallel
Ceq
Series
Parallel
V
Q
Veq = V1 + V2
Ceq = C1 + C2
V1 = V2
Q1 = Q2
Qeq = Q1 + Q2
Physics 201: Lecture 1, Pg 20
Example:
What is the equivalent capacitance of the capacitors the below?

20 F
60 F
10 F
Physics 201: Lecture 1, Pg 21
Clicker Question 4:
Find the equivalent capacitance of these capacitors
capacitors.
(a) 10.4 F
(b) 7 F
(c) 4.44 F
(d) 6 F
(e) 12.4 F
Physics 201: Lecture 1, Pg 22
Clicker Question 4:
Find the equivalent capacitance of these capacitors.
Physics 201: Lecture 1, Pg 23
Clicker Question 5/Example:
What is the voltage across the 6 μF capacitor?
(a)
(b)
(c)
(d)
(e)
10 V
12 V
18 V
20 V
30 V
Physics 201: Lecture 1, Pg 24
Clicker Question 10/Example:
What is the voltage across the 6 μF capacitor?
C (F)
Q (C)
V (V)
Physics 201: Lecture 1, Pg 25
Clicker Question 10/Example:
What is the voltage across the 6 μF capacitor?
C (F)
Q (C)
V (V)
Physics 201: Lecture 1, Pg 26
Stored energy in a capacitor
First electron: W = q V = q (0)
PE  QV
Last electron: W = q V  q V
Average: W = 1/2 q V
-Q
--
+
+
+
+
+
-
1
2
Using Q = CV
PE = ½QV = ½CV2 = ½Q2/C
+Q
+
Battery
y
Physics 201: Lecture 1, Pg 27