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Sarah Eno 1
PHYS142
CH 26Materials for Lecture
Poling cards
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
T E S T I N G
Sarah Eno 2
PHYS142
CH 26Capacitors
Fields near point charges is all well and good, but let’s do something practical!
Capacitors are found in all electric circuits.
Capacitor Industries, IncChicago, IL
Sarah Eno 3
PHYS142
CH 26Capacitors
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)
Sarah Eno 4
PHYS142
CH 26Storing ChargeLet’s think about storing charge…Often, you want to store as much charge as possible, while avoiding large (dangerous) voltages
0 0
0
V Ed
QE
A
VAQ
d
For a fixed voltage, you can increase the charged stored by increasing A or decreasing d
Sarah Eno 5
PHYS142
CH 26Capacitance
0 0VA AQQ
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
Sarah Eno 7
PHYS142
CH 26Test Yourself
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) Increase2) Decrease3) Stay the same
Demo j4-01
Sarah Eno 8
PHYS142
CH 26ExampleWhat would be the area of a capacitor with a gap of ½ mm to have a capacitance of 1 farad?
0
12
6 2
8.85 10 10.0005
56 10
AC
dA
x
A x m
Sarah Eno 9
PHYS142
CH 26Example
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?
63 10 0.001 3000V Ed x V
Capacitors come with voltage ratings. Cheap capacitors can typically hold 50 V.
Sarah Eno 10
PHYS142
CH 26The Gap
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
Sarah Eno 11
PHYS142
CH 26Inside: Dipoles
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.
Sarah Eno 12
PHYS142
CH 26Capacitors
1
2 3
45
6
7 8 9 1011
12
1) 365 pf, 200V, air variable
2) 0.25 F, 3000V, mineral oil
3) 21000 F, 25 V, electrolytic
4) 20 pF, 100 V, air variable
5) 2 F, 400 V, polystyrene
6) 100 F, 12 V, electrolytic
7) 10 pf, 200 V, glass/air
8) 0.1 F, 10 V, ceramic
9) 0.1 F, 1 kV, ceramic
10) 0.33 F, 400 V, mylar
11) 100 pF, 2kV, ceramic
12) 1000 pF, 200V, silver mica
1) Tune radios, 2) filter HV, 3) power supply filter, 4) tune rf, 5) audio 6) audio, 7) vhf/uhf, 8) audio, 9) audio, 10) audio, 11) high power rf, 12) precision rf
Sarah Eno 13
PHYS142
CH 26Test Yourself
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
Sarah Eno 14
PHYS142
CH 26Inside: 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/V=V0/. C=C0
0
0
A AC
d d
Sarah Eno 15
PHYS142
CH 26Dielectrics
Material Breakdown field (106 V/m)---------------------------------------------------------------Air 1.00059 3Paper 3.7 16Glass 4-6 9Paraffin 2.3 11Rubber 2-3.5 30Mica 6 150Water 80 0
Sarah Eno 16
PHYS142
CH 26Example
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 () of 10?
Found earlier that without dielectric, need an area of 56x106 m2. So, reduce this by 10 to 56x105 m2
Sarah Eno 17
PHYS142
CH 26Example
A typical capacitor has a capacitance of 10 F, a gap of 0.1 mm, and is filled with a dielectric with a dielectric strength of 10. What is the area?
620
120
Cd 10 10 0.0001; A= 11
10 8.85 10
A xC m
d x
Sarah Eno 18
PHYS142
CH 26Energy Stored
How much work to move some this charge onto the capacitor?
Amount of work to charge from scratch. Sum (integral) up the contributions to bring each charge
QW qV q
C
2
0
1
2
QQ Q
W dQC C
Sarah Eno 21
PHYS142
CH 26Capacitors with a Battery
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
Sarah Eno 22
PHYS142
CH 26Batteries
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.
Sarah Eno 23
PHYS142
CH 26Ground
Zero volt point. Reservoir of electrons. Can take and give electrons easily.
Sarah Eno 24
PHYS142
CH 26Circuits
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)
Sarah Eno 25
PHYS142
CH 26Test Yourself
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
Sarah Eno 27
PHYS142
CH 26Example
What is the charge on a 1 F capacitor attached to a 1.5 V battery?
-6 Q=CV=1x10 1.5 1.5Q
C FV
How many electrons is that?
613
19
1.5 1010
1.6 10
xn
x
Sarah Eno 28
PHYS142
CH 26Capacitor Circuits
If you have more than 1 capacitor in a circuit, two basic ways to arrange them
• parallel
• series
Sarah Eno 29
PHYS142
CH 26Parallel 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.
Sarah Eno 31
PHYS142
CH 26Parallel
Twice the charge for the same voltage.
Effectively increasing the area of the capacitor
Sarah Eno 32
PHYS142
CH 26Parallel
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
1 2effC C C 0AQC
V d
Sarah Eno 33
PHYS142
CH 26Series
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.
The voltage across each is 1/2. That means the charge on each is ½ compared to 1 capacitor circuit.
Sarah Eno 34
PHYS142
CH 26Series
Its like you have twice the gap. The effective capacitance goes down.
Sarah Eno 35
PHYS142
CH 26Series in General1 2
1 21 2
1 2
1 2
1 2
1 2
1 2
; V
(1/ 1/ )
1 1 1
eff
V V V
Q QV
C C
Q Q
Q QV
C C
QV
C C
C C C
Sarah Eno 37
PHYS142
CH 26Hints for Capacitors
• 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.
Sarah Eno 38
PHYS142
CH 26Example
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.
2) Then work backwards1 1 1
1.2 2 3
Sarah Eno 39
PHYS142
CH 26Example
6 62.2 10 13.2 106
Qx F Q x C
V
6
6 6
6
6 6 6
1 10 6 106
1.2 10 7.2 106
6 10 7.2 10 13.2 10
Qx F Q x C
VQ
x F Q x CV
x x x C
6
6
66
7.2 102 10 3.6
7.2 103 10 2.4
3.6 2.4 6
x Cx F V V
V
x Cx F V V
VV
Sarah Eno 40
PHYS142
CH 26ExampleBefore 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.
1 2
1 0 2 0 0 1 2 0 1 2
1 20
1 2
1 1 1 1 1 1( )
2 2 2 2
2
eff
eff
C C C C C
C C
When add dielectric, each capacitance goes up a factor
Sarah Eno 41
PHYS142
CH 26Test Yourself
Which capacitor has the biggest charge?
1) 1F2) 0.2 F3) 0.6F4) They all have the
same charge5) None of the
above
Sarah Eno 42
PHYS142
CH 26Example
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 10.44
1 .8 effeff
C FC