Download Capacitance

C
Capacitance
Chapter 18 – Part II
Two parallel flat plates
that store CHARGE is
called a capacitor.
The plates have
dimensions >>d, the plate
separation.
The electric field in a
parallel plate capacitor
is normal to the plates.
The “fringing fields”
can be neglected.
Actually ANY physical
object that can store charge
is a capacitor.
V
A Capacitor Stores
CHARGE
Apply a Potential Difference V
And a charge
plates
Q
Q is found on the
charge
Q
C

Potential V
Q  CV
Unit of Capacitance = F
Volt
1
 1Farad
C
microfarad  F
millifarad  mF
nanofarad  nF
Thin Film Structure
Variable Capacitor and 1940’s Radio
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.
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
TWO Types of Connections
SERIES
PARALLEL
Parallel Connection
q1  C1V1  C1V
q2  C2V
q3  C3V
QE  q1  q2  q3
V
CEquivalent=CE
QE  V (C1  C2  C3 )
therefore
C E  C1  C2  C3
Series Connection
q
V
-q
C1
q
-q
C2
The charge on each
capacitor is the same !
Series Connection Continued
V  V1  V2
q
V
C1
-q
q
-q
C2
q
q
q


C C1 C 2
or
1
1
1


C C1 C 2
More General
Series
1
1

C
i Ci
Parallel
C   Ci
i
Example
C1
C1=12.0 uf
C2= 5.3 uf
C3= 4.5 ud
C2
(12+5.3)pf
V
C3
A Thunker
Find the equivalent capacitance between points a and b in the
combination of capacitors shown in the figure.
V(ab) same across each
V
Remember : E 
d
Q A A A
A
A
C




 0
V
V
V
Ed   d
d
  
0

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.
Stored Energy


Charge the Capacitor by moving Dq
charge from + to – side.
Work = Dq Ed= Dq(V/d)d=DqV
DW=DqV=Sum of strips
V0
DV
Dq
Q0
1
W   DqV  Q0V0
2
Q0  CV0
1
W  CV02
2
Energy Density
1
1  0 A  2 2
2
W  CV  
E d
2
2 d 
1
1
2
W   0 AE d   0 E 2 (Vol )
2
2
W
1
EnergyDens ity 
 0E2
Vol 2


DIELECTRIC
Stick a new material between the plates.
We can measure the C of a capacitor
(later)
C0 = Vacuum or air Value
C = With dielectric in place
C
K
C0
C=kC0
V
V
V0
Dielectric Breakdown!
Messing with
Capacitors
The battery means that the
potential difference across
the capacitor remains constant.
+
+
V
-
-
For this case, we insert the
dielectric but hold the voltage
constant,
+
+
q=CV
V
Remember – We hold V
constant with the battery.
-
since C  kC0
qk kC0V
THE EXTRA CHARGE
COMES FROM THE
BATTERY!
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.
No Battery
q0 =C0Vo
+
q0
V0
-
When the dielectric is inserted, no charge
is added so the charge must be the same.
qk  kC0V
+
q0  C0V0  qk  kC0V
qk
V
-
or
V
V0
k
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.
A little sheet from the past..
-q’
+q’
- -q
-
+
q+
+
Esheet

q'


2 0 2 0 A
q'
0
2xEsheet
0
q'
Esheet / dialectric  2 

2 0 A  0 A
Some more sheet…
Edielectricch arg e
q
E 0
0 A
so
q  q'
E
0 A
 q'

0 A