Capacitance PHY 2049 Chapter 25 Chapter 25 Capacitance In this chapter we will cover the following...
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Transcript of Capacitance PHY 2049 Chapter 25 Chapter 25 Capacitance In this chapter we will cover the following...
Chapter 25 Capacitance
In this chapter we will cover the following topics:
-Capacitance C of a system of two isolated conductors. -Calculation of the capacitance for some simple geometries.
-Methods of connecting capacitors (in series , in parallel). -Equivalent capacitance. -Energy stored in a capacitor. -Behavior of an insulator (a.k.a. dielectric) when placed in the electric field created in the space between the plates of a capacitor.
-Gauss’ law in the presence of dielectrics.
(25 - 1)
Capacitor
Composed of two metal plates. Each plate is charged
one positive one negative
Stores energy
SYMBOL
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.
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 - Capacity 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
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!
S
P
N
n̂
The plates have area and are separated
by a distance . The upper plate has a
charge and the lower plate a charge -
A
d
q q
Capacitance of a parallel plate capacitor
We apply Gauss' law using the Gaussian surface S shown in the figure.
The electric flux cos 0 .
From Gauss' law we have:
The potential difference between the positive ano o o
EA EA
q q qEA E
A
V
d the negative plate is
given by: cos0
The capacitance /
o
o
o
qdV Eds E ds Ed
A
Aq qC
V qd A d
oA
Cd
(25 - 6)
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.
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 As before
Parallel Connection
VCEquivalent=CE
321
321
321
33
22
1111
)(
CCCC
therefore
CCCVQ
qqqQ
VCq
VCq
VCVCq
E
E
E
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
Calculate Potential Difference V
drr
qV
EdsV
a
b
platepositive
platenegative
20
.
.
1
4
(-) sign because E and ds are in OPPOSITE directions.