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Capacitors Part I. Capacitor. Composed of two metal plates. Each plate is charged one positive one negative Stores Charge. SYMBOL. A simple Capacitor. TWO PLATES. WIRES. Battery. INSIDE THE DEVICE. d. Air or Vacuum. E. - Q +Q. Symbol. Area A. - PowerPoint PPT Presentation
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Capacitors Part I
Capacitor
Composed of two metal plates. Each plate is charged
one positive one negative
Stores Charge
SYMBOL
A simple Capacitor
TWO PLATES
Battery
WIRES
INSIDE THE DEVICE
Two Charged Plates(Neglect Fringing Fields)
d
Air or Vacuum
Area A
- Q +QE
V=Potential Difference
Symbol
ADDED CHARGE
Where is the charge?
d
Air or Vacuum
Area A
- Q +QE
V=Potential Difference
------
++++++
AREA=A
=Q/A
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.
Capacitor
More on Capacitorsd
Air or Vacuum
Area A
- Q +QE
V=Potential Difference
GaussianSurface
000
0
0
0
)/(
0
AQ
A
QE
EAQ
QEAAEA
qd
Gauss
AE
Same result from other plate!
DEFINITION The Potential Difference is
APPLIED by a battery or a circuit.
The charge q on the capacitor is found to be proportional to the applied voltage.
The proportionality constant is C and is referred to as the CAPACITANCE of the device.
CVq
orV
qC
NOTE
Work to move a charge from one side of a capacitor to the other is qEd.
Work to move a charge from one side of a capacitor to the other is qV
Thus qV=qEd E=V/d (Hold this thought.)
UNITSUNITS A capacitor which
acquires a charge of 1 coulomb on each plate with the application of one volt is defined to have a capacitance of 1 FARAD
One Farad is one Coulomb/Volt
CVq
orV
qC
Continuing…
d
AC
sod
AVEAAq
V
qC
0
00
The capacitance of a parallel plate capacitor depends only on the Area and separation between the plates.
C is dependent only on the geometry of the device!
Units of 0
mpFmF
andm
Farad
Voltm
CoulombVoltCoulombm
Coulomb
Joulem
Coulomb
Nm
Coulomb
/85.8/1085.8 120
2
2
2
2
0
pico
Simple Capacitor Circuits Batteries
Apply potential differences Capacitors Wires
Wires are METALS. Continuous strands of wire are all at the same
potential. Separate strands of wire connected to circuit
elements may be at DIFFERENT potentials.
Size Matters! A Random Access Memory stores
information on small capacitors which are either charged (bit=1) or uncharged (bit=0).
Voltage across one of these capacitors ie either zero or the power source voltage (5.3 volts in this example).
Typical capacitance is 55 fF (femto=10-15) Question: How many electrons are stored
on one of these capacitors in the +1 state?
Small is better in the IC world!
electronsC
VF
e
CV
e
qn 6
19
15
108.1106.1
)3.5)(1055(
TWO Types of Connections
SERIES
PARALLEL
Parallel Connection
VCEquivalent=CE
321
321
321
33
22
1111
)(
CCCC
therefore
CCCVQ
qqqQ
VCq
VCq
VCVCq
E
E
E
Series Connection
V C1 C2
q -q q -q
The charge on eachcapacitor is the same !
Series Connection Continued
21
21
21
111
CCC
or
C
q
C
q
C
q
VVV
V C1 C2
q -q q -q
More General
ii
i i
CC
Parallel
CC
Series
11
Example
C1 C2
V
C3
C1=12.0 fC2= 5.3 fC3= 4.5 d
(12+5.3)pf
series
(12+5.3)pf
More on the Big C We move a charge
dq from the (-) plate to the (+) one.
The (-) plate becomes more (-)
The (+) plate becomes more (+).
dW=Fd=dq x E x d+q -q
E=0A/d
+dq
So….
2222
0
2
0
2
0 0
0
00
2
1
22
)(
1
22
1
1
CVC
VC
C
QU
ord
Aq
A
dqqdq
A
dUW
dqdA
qdW
A
qE
Gauss
EddqdW
Q
Not All Capacitors are Created Equal
Parallel Plate
Cylindrical Spherical
Spherical Capacitor
???
4)(
4
02
0
2
0
surprise
r
qrE
qEr
qd
Gauss
AE
Calculate Potential Difference V
drr
qV
EdsV
a
b
platepositive
platenegative
20
.
.
1
4
(-) sign because E and ds are in OPPOSITE directions.
Continuing…
ab
ab
V
qC
ab
abq
ba
qV
r
q
r
drqV
b
a
0
00
02
0
4
4
11
4
)1
(44
Lost (-) sign due to switch of limits.
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