EECE251 Circuit Analysis I Set 4: Capacitors, Inductors, and First ...
Capacitors Part I
description
Transcript of Capacitors Part I
![Page 1: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/1.jpg)
Capacitors Part I
![Page 2: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/2.jpg)
Capacitor
Composed of two metal plates. Each plate is charged
one positive one negative
Stores Charge
SYMBOL
![Page 3: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/3.jpg)
A simple Capacitor
TWO PLATES
Battery
WIRES
![Page 4: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/4.jpg)
INSIDE THE DEVICE
![Page 5: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/5.jpg)
Two Charged Plates(Neglect Fringing Fields)
d
Air or Vacuum
Area A
- Q +QE
V=Potential Difference
Symbol
ADDED CHARGE
![Page 6: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/6.jpg)
Where is the charge?
d
Air or Vacuum
Area A
- Q +QE
V=Potential Difference
------
++++++
AREA=A
=Q/A
![Page 7: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/7.jpg)
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.
![Page 8: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/8.jpg)
Capacitor
![Page 9: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/9.jpg)
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!
![Page 10: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/10.jpg)
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
![Page 11: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/11.jpg)
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.)
![Page 12: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/12.jpg)
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
![Page 13: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/13.jpg)
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!
![Page 14: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/14.jpg)
Units of 0
mpFmF
andm
Farad
Voltm
CoulombVoltCoulombm
Coulomb
Joulem
Coulomb
Nm
Coulomb
/85.8/1085.8 120
2
2
2
2
0
pico
![Page 15: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/15.jpg)
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.
![Page 16: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/16.jpg)
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?
![Page 17: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/17.jpg)
Small is better in the IC world!
electronsC
VF
e
CV
e
qn 6
19
15
108.1106.1
)3.5)(1055(
![Page 18: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/18.jpg)
TWO Types of Connections
SERIES
PARALLEL
![Page 19: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/19.jpg)
Parallel Connection
VCEquivalent=CE
321
321
321
33
22
1111
)(
CCCC
therefore
CCCVQ
qqqQ
VCq
VCq
VCVCq
E
E
E
![Page 20: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/20.jpg)
Series Connection
V C1 C2
q -q q -q
The charge on eachcapacitor is the same !
![Page 21: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/21.jpg)
Series Connection Continued
21
21
21
111
CCC
or
C
q
C
q
C
q
VVV
V C1 C2
q -q q -q
![Page 22: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/22.jpg)
More General
ii
i i
CC
Parallel
CC
Series
11
![Page 23: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/23.jpg)
Example
C1 C2
V
C3
C1=12.0 fC2= 5.3 fC3= 4.5 d
(12+5.3)pf
series
(12+5.3)pf
![Page 24: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/24.jpg)
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
![Page 25: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/25.jpg)
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
![Page 26: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/26.jpg)
Not All Capacitors are Created Equal
Parallel Plate
Cylindrical Spherical
![Page 27: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/27.jpg)
Spherical Capacitor
???
4)(
4
02
0
2
0
surprise
r
qrE
qEr
qd
Gauss
AE
![Page 28: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/28.jpg)
Calculate Potential Difference V
drr
qV
EdsV
a
b
platepositive
platenegative
20
.
.
1
4
(-) sign because E and ds are in OPPOSITE directions.
![Page 29: Capacitors Part I](https://reader033.fdocuments.in/reader033/viewer/2022051001/56813b93550346895da4c589/html5/thumbnails/29.jpg)
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.