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PHYS
142
Poling cards
Materials for Lecture
CH 26
TESTING
Demos:
http://www.physics.umd.edu/deptinfo/facilities/lecdem/lecdem.htm
J4-01
J4-22
J4-51
Animations courtesy of:
http://webphysics.davidson.edu/Applets/Applets.html
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CH 26
Capacitors
Fields near point charges is all well and good, but let’s do
something practical!
Capacitors are found in all electric circuits.
Capacitor
Industries, Inc
Chicago, IL
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Capacitors
CH 26
A capacitor is a way of storing charge.
The symbol for a capacitor in a
schematic for an electrical circuit
shows basically what it is: two plates
with a gap.
The charges are held together on the
plates by their attraction.
(often want to store charge so that it can provide
current)
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Storing Charge
CH 26
Let’s think about storing charge…
Often, you want to store as much charge as possible, while
avoiding large (dangerous) voltages
V  Ed

Q
E 
 0 A 0
VA 0
Q
d
For a fixed voltage, you can increase the charged stored by
increasing A or decreasing d
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Capacitance
CH 26
VA 0
Q A 0
Q
 
d
V
d
Or the charge you can store per
volt is related to the geometry of
the plates and the gap
Capacitance is the amount of charge you can store per volt, or Q/V.
Farad=coulomb/volt
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Increasing Area
Sarah Eno
CH 26
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Test Yourself
CH 26
Demo j4-01
I’m going to charge these plates to 1000 V. I’m going to remove
the charger, then I’m going to move them apart. As I move
them, will the voltage
1) Increase
2) Decrease
3) Stay the same
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Example
CH 26
What would be the area of a capacitor with a gap of ½ mm to have
a capacitance of 1 farad?
A
C  0
d
A
8.85 x10
1
0.0005
6
2
A  56 x10 m
12
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Example
CH 26
Air breaks down and conducts for an electric field strength of
3x106 V/m. How many volts can it hold if it has a gap of 1mm?
V  Ed  3x10  0.001  3000V
6
Capacitors come with voltage ratings. Cheap capacitors can
typically hold 50 V.
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The Gap
CH 26
What if I stick something inside the gap?
Maybe something made of molecules that are electric dipoles…
• ceramics
• mica
• polyvinyl chloride
• polystyrene
• glass
• porcelain
• rubber
• electrolyte (glyco-ammonium borate, glycerol-ammonium
borate, ammonium lactates, etc dissolved in goo or paste)
Dielectric material
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Inside: Dipoles
CH 26
Electric Dipole moments
in random directions
Put a charge on the
plates. The charge
creates an electric field.
Dipole moments try to
align with the field.
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CH 26
Capacitors
2
3
1
5
4
7
8
9
6
11
10
12
1)
365 pf, 200V, air variable
2)
0.25 mF, 3000V, mineral oil
3)
21000 mF, 25 V, electrolytic
4)
20 pF, 100 V, air variable
5)
2 mF, 400 V, polystyrene
6)
100 mF, 12 V, electrolytic
7)
10 pf, 200 V, glass/air
8)
0.1 mF, 10 V, ceramic
9)
0.1 mF, 1 kV, ceramic
10) 0.33 mF, 400 V, mylar
1) Tune radios, 2) filter HV, 3) power supply filter, 4) tune rf, 11) 100 pF, 2kV, ceramic
5) audio 6) audio, 7) vhf/uhf, 8) audio, 9) audio, 10) audio,
12) 1000 pF, 200V, silver mica
11) high power rf, 12) precision rf
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Test Yourself
CH 26
Will the field between (and thus
the voltage between) the
plates be
1) Larger
2) Smaller
3) The same
As without the dielectric?
Do j4-22
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CH 26
Inside: Fields
The field goes down. So, the
amount of charge you can put on
for 1 volt is larger. So, the
capacitance goes up.
A certain fraction of the field is
“canceled”. E=E0/k. V=V0/k.
C=kC0
C
k 0 A
d

A
d
  k 0
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Dielectrics
Material
CH 26
k
Breakdown field
(106 V/m)
--------------------------------------------------------------Air
1.00059
3
Paper
3.7
16
Glass
4-6
9
Paraffin
2.3
11
Rubber
2-3.5
30
Mica
6
150
Water
80
0
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Example
CH 26
What area would a capacitor with a 0.5 mm gap have to for a
capacitance of 1 farad if it had a dielectric constant (k) of
10?
Found earlier that without dielectric, need an area of 56x106
m2. So, reduce this by 10 to 56x105 m2
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Example
CH 26
A typical capacitor has a capacitance of 10 mF, a gap of 0.1
mm, and is filled with a dielectric with a dielectric strength of
10. What is the area?
k 0 A
6
10 x10  0.0001
2
C
; A=

 11m
12
d
k 0 10  8.85 x10
Cd
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Energy Stored
CH 26
How much work to move some this
charge onto the capacitor?
Q
W  qV  q
C
Amount of work to charge from
scratch. Sum (integral) up the
contributions to bring each charge
Q
Q
1 Q2
W   dQ 
C
2 C
0
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Energy Stored
CH 26
But, Q is hard to measure 
2
2
2
1Q
1CV
1
2
W

 CV
2 C 2 C
2
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Simple Circuits
CH 26
Let’s try our first simple circuit
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Capacitors with a Battery
CH 26
An “ideal” battery is a source of
constant voltage. Though it is done
using properties of metal, ions, etc,
you should think of it as containing a
fixed E field.
Charge on one
side is at a
higher potential
than the other
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Batteries
CH 26
Students have many misconceptions about batteries, which lead to
serious difficulties in making predictions about circuits.
Batteries are not charged. They do not contain a bunch of
electrons, ready to “spit out”
Batteries are not current sources. They don’t put out a
constant current.
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Ground
CH 26
Zero volt point. Reservoir of electrons. Can take and give electrons
easily.
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Circuits
CH 26
Remember: it takes no work to move an charge through a
conductor. The potential does not change! (for an ideal
conductor… since only a “superconductor” is an ideal
conductor, this is only mostly true for copper, gold, etc)
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Test Yourself
CH 26
When I close the switch will the voltage across the battery
1) Go down because charge leaves the battery to go to the
capacitor
2) Go up because the battery will get additional charge from
the capacitor
3) Stay the same because the voltage across a battery always
stays the same
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Battery + Capacitor
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CH 26
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Example
CH 26
What is the charge on a 1 mF capacitor attached to a 1.5 V battery?
Q
C
Q=CV=1x10-6 1.5  1.5m F
V
How many electrons is that?
6
1.5 x10
13
n

10
1.6 x1019
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Capacitor Circuits
CH 26
If you have more than 1 capacitor in a circuit, two basic
ways to arrange them
• parallel
• series
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CH 26
Parallel Circuits
Connected
in Parallel
How will the voltage across them compare?
1) It will half. The voltage from the battery will be divided
between the two
2) It will double. Because there will be two capacitors
charged
3) It will be the same. The voltage is always the same.
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Parallel Circuits
CH 26
How does the charge compare?
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Parallel
CH 26
Twice the charge
for the same
voltage.
Effectively
increasing the area
of the capacitor
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Parallel
CH 26
If you replaced the 2 capacitors with 1 capacitor, what
capacitance would it have to have in order to have the same
voltage and the same charge -> effective capacitance of the
system
Ceff  C1  C2
Q A 0
C 
V
d
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Series
CH 26
How will the voltage across
them compare?
1) It will half. The voltage from
the battery will be divided
between the two
The voltage across each is
1/2. That means the
charge on each is ½
compared to 1 capacitor
circuit.
2) It will double. Because there
will be two capacitors
charged
3) It will be the same. The
voltage is always the same.
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Series
CH 26
Its like you
have twice the
gap. The
effective
capacitance
goes down.
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Series in General
CH 26
V1  V2  V
Q1
Q2
V1  ; V2 
C1
C2
Q1  Q2
Q Q

V
C1 C2
Q
V
(1/ C1  1/ C2 )
1
1
1
 
Ceff C1 C2
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Check
CH 26
1
1
1
 
C eff C1 C2
if C1  C2  Ceff
1
 C
2
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Hints for Capacitors
CH 26
• remember the voltage across a battery is fixed
• remember voltage does not change along a wire
• look for parallel and series combinations, and calculate the
equivalent capacitance.
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Example
CH 26
What is the charge on each
cap? What is the voltage
across each cap?
1) Look for series and parallel
combinations. Calculate
equivalent capacitance.
Replace. Repeat until have
1 cap.
1 1 1
 
1.2 2 3
2) Then work backwards
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Example
CH 26
Q
 Q  13.2 x106 C
6V
Q
6
1x10 F 
 Q  6 x106 C
6V
6
Q
6
1.2 x10 F 
 Q  7.2 x10 C
6V
6 x106  7.2 x106  13.2 x106 C
2.2 x106 F 
6
7.2
x
10
C
6
2 x10 F 
 V  3.6V
V
6
7.2
x
10
C
3x106 F 
 V  2.4V
V
3.6  2.4  6V
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Example
CH 26
Before the dielectric is added, the
capacitance is C0. What is the
capacitance afterwards?
Picture it as two caps in series,
each with a gap d/2 and therefore
capacitance 2C0.
When add dielectric, each
capacitance goes up a factor k
k k
1
1
1
1 1 1



(  ) 1 2
Ceff k 1 2C0 k 2 2C0 2C0 k 1 k 2
2C0k 1k 2
Ceff 
2k 1k 2
C0
k1  k 2
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Test Yourself
CH 26
Which capacitor has
the biggest
charge?
1) 1mF
2) 0.2 mF
3) 0.6 mF
4) They all have the
same charge
5) None of the
above
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CH 26
Example
What is the
equivalent
capacitance?
.6 and .2 are in parallel.
Add them to get .8
The 1 and the “.8” are in
series.
1
1 1
   Ceff  0.44m F
Ceff 1 .8
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Fun
CH 26
Another use for capacitance
Do j4-51
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Hints for Capacitor Problems
Sarah Eno
CH 26
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