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General Physics II
Capacitors and Dielectrics
The ideas of energy storage in Efields can be carried a step further by understanding the
concept of "Capacitance."
Consider a sphere with a total charge, Q, and a radius, R. From previous problems we know
that the potential at the surface is,
Q
Vk
R
=
Putting more charge on the sphere stores more energy, but the ratio of energy or potential to
charge depends only on R, not on Q or V. That is,
0
4
QR
R
πε
==
.
It's true for all charged objects that the ratio of potential to voltage depends only on the shape,
so this ratio is defined as the capacitance.
Gaziantep University Faculty of Engineering
Department of Engineering Physics
1
.
The units of capacitance are
1 coulomb
1 Farad
1 F.
volts
≡≡
Common values of capacitance are
microfarads,
µ
F (10
6
Farads) and picofarads, pF (10
12
Farads).
Q
C
V
≡
Consider two conductors connected to the terminals of a battery.
The battery will supply an
equal amount of charge, but of opposite sign, to each of the conductors. The question arising
at this point: what will be capacitance of the conductor system? Let us consider different
conductor systems:
Parallel plates
Two conducting parallel plates separated
by a distance d with charges +
Q
and 
Q
.
The potential difference between the
plates (from one plate to the other) is
s
ab
VVVE
d
oo
Qd
d
A
ρ
ε
=
⎛⎞
−== =
⎜⎟
⎝⎠
.
The capacitance is
Conducting concentric spheres
Two concentric spheres of radii
R
and
r
.
The potential difference between the spheres is
11
4
o
Q
VVV
R
r
−==
−
.
r
R
4
o
Q
C
V
R
r
−
0
A
Q
C
Vd
The capacitance is
Coaxial Cable
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View Full DocumentGeneral Physics II
Coaxial cable (two concentric conducting cylinders) of length
L
.
The inside conductor has a
radius
r
with charge
ρ
A
and the inside surface of
the outside conductor is
R
with charge 
A
.
ln
ab
ln
22
oo
R
QR
rL
r
VVV
λ
πε
−==
3
=
r
R
2
ln
o
L
Q
C
R
V
r
==
L
The capacitance is
Exercise
There are electrical devices that are designed to store energy in this fashion.
These devices
are referred to a "capacitors."
To get an idea of the magnitude of the unit Farad, find how
large a parallel plate capacitor must be in order to have a capacitance of one Farad.
Take the
distance between the plates to be 0.1 mm.
Capacitors in Electrical Circuits
Gaziantep University Faculty of Engineering
Department of Engineering Physics
2
The circuit diagram of a capacitor
You can "charge" a capacitor by connecting the capacitor to
a battery (power supply).
(Remember that in the electrostatic
situation the wires (conductors) are equipotentials.)
Combinations of Capacitors  this is necessary because capacitors
with only certain values are available.
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 Fall '08
 RABE
 Physics, Capacitance, Charge, Energy

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