capacitance chapter 18 – part ii c two parallel flat plates that store charge is called a...
TRANSCRIPT
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Capacitance
Chapter 18 – Part II
C
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Two parallel flat platesthat store CHARGE is called a capacitor.
The plates have dimensions >>d, the plateseparation.
The electric field in aparallel plate capacitoris normal to the plates.
The “fringing fields”can be neglected.
Actually ANY physicalobject that can store chargeis a capacitor.
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A Capacitor Stores
CHARGE
V
Apply a Potential Difference V
And a charge Q is found on theplates
CVQV
Q
PotentialC
chargeQ
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Unit of Capacitance = F
nFnanofarad
mFmillifarad
Fmicrofarad
Farad11
C
Volt
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Thin Film Structure
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Variable Capacitor and 1940’s Radio
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One Way to Charge:
Start with two isolated uncharged plates. Take electrons and move them from the + to
the – plate through the region between. As the charge builds up, an electric field
forms between the plates. You therefore have to do work against the
field as you continue to move charge from one plate to another.
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The two metal objects in the figure have net charges of +79 pC and -79 pC, which result in a 10 V potential difference between them.
(a) What is the capacitance of the system? [7.9] pF(b) If the charges are changed to +222 pC and -222 pC, what does the capacitance become? [7.9] pF(c) What does the potential difference become?[28.1] V
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TWO Types of Connections
SERIES
PARALLEL
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Parallel Connection
VCEquivalent=CE
321
321
321
33
22
1111
)(
CCCC
therefore
CCCVQ
qqqQ
VCq
VCq
VCVCq
E
E
E
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Series Connection
V C1 C2
q -q q -q
The charge on eachcapacitor is the same !
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Series Connection Continued
21
21
21
111
CCC
or
C
q
C
q
C
q
VVV
V C1 C2
q -q q -q
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More General
ii
i i
CC
Parallel
CC
Series
11
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Example
C1 C2
V
C3
C1=12.0 fC2= 5.3 fC3= 4.5 d
(12+5.3)pf
series
(12+5.3)pf
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A Thunker
Find the equivalent capacitance between points a and b in the combination of capacitors shown in the figure.
V(ab) same across each
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d
A
d
A
Ed
A
V
A
V
A
V
QC 0
0
d
VE :Remember
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A capacitor is charged by being connected to a battery and is then disconnected from the battery. The plates are then pulled apart a little. How does each of the following quantities change as all this goes on? (a) the electric field between the plates, (b) the charge on the plates, (c) the potential difference across the plates, (d) the total energy stored in the capacitor.
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Stored Energy
Charge the Capacitor by moving q charge from + to – side.
Work = q Ed=q(V/d)d=qV
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W=qV=Sum of strips
0V
0Qq
V
20
00
00
2
1
2
1
CVW
CVQ
VQqVW
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20
20
20
2202
2
1
)(2
1
2
1
2
1
2
1
EVol
WityEnergyDens
VolEdAEW
dEd
ACVW
Energy Density
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DIELECTRIC
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Stick a new material between the plates.
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We can measure the C of a capacitor (later)
C0 = Vacuum or air Value
C = With dielectric in place
C=C0 0
0
V
VV
C
CK
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Dielectric Breakdown!
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Messing with Capacitors
+
V-
+
V-
+
-
+
-
The battery means that thepotential difference acrossthe capacitor remains constant.
For this case, we insert the dielectric but hold the voltage constant,
q=CV
since C C0
qC0V
THE EXTRA CHARGE COMES FROM THE BATTERY!
Remember – We hold V constant with the battery.
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Another Case We charge the capacitor to a voltage V0.
We disconnect the battery. We slip a dielectric in between the two plates. We look at the voltage across the capacitor to
see what happens.
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No Battery
+
-
+
-
q0
q
q0 =C0Vo
When the dielectric is inserted, no chargeis added so the charge must be the same.
0
0000
0
VV
or
VCqVCq
VCq
V0
V
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Another Way to Think About This
There is an original charge q on the capacitor.
If you slide the dielectric into the capacitor, you are adding no additional STORED charge. Just moving some charge around in the dielectric material.
If you short the capacitors with your fingers, only the original charge on the capacitor can burn your fingers to a crisp!
The charge in q=CV must therefore be the free charge on the metal plates of the capacitor.
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A little sheet from the past..
+++
---q-q
-q’ +q’
A
q
A
qE
A
qE
dialectricsheet
sheet
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2
'2
2
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2
0 2xEsheet 0
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Some more sheet…
A
qqE
so
A
qE
A
qE echdielectric
0
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