The Capacitor
GENERAL INFORMATION
A capacitor is a component which is capable
of storing electrical energy. It consists of two conductive
plates (electrodes) separated by insulating material which is
called the dielectric. A typical formula for determining
capacitance is:
Potential Change –
A capacitor is a reactive
component which reacts against a change in potential
across it. This is shown by the equation for the linear
charge of a capacitor:
I
ideal
=
C dV
dt
where
I
= Current
C
= Capacitance
dV/dt
= Slope of voltage transition across capacitor
Thus an infinite current would be required to instantly
change the potential across a capacitor. The amount of
current a capacitor can “sink” is determined by the
above equation.
Equivalent Circuit –
A capacitor, as a practical device,
exhibits not only capacitance but also resistance and
inductance. A simplified schematic for the equivalent
circuit is:
R
P
C = .224 KA
t
C
= capacitance (picofarads)
K
= dielectric constant (Vacuum = 1)
A
= area in square inches
t
= separation between the plates in inches
(thickness of dielectric)
.224
= conversion constant
(.0884 for metric system in cm)
Capacitance –
The standard unit of capacitance
is the farad. A capacitor has a capacitance of 1 farad
when 1 coulomb charges it to 1 volt. One farad is a very
large unit and most capacitors have values in the micro
(10
-6
), nano (10
-9
) or pico (10
-12
) farad level.
Dielectric Constant –
In the formula for capacitance
given above the dielectric constant of a vacuum is
arbitrarily chosen as the number 1. Dielectric constants
of other materials are then compared to the dielectric
constant of a vacuum.
Dielectric Thickness –
Capacitance is indirectly propor-
tional to the separation between electrodes. Lower volt-
age requirements mean thinner dielectrics and greater
capacitance per volume.
Area –
Capacitance is directly proportional to the area of
the electrodes. Since the other variables in the equation
are usually set by the performance desired, area is the
easiest parameter to modify to obtain a specific capaci-
tance within a material group.
Energy Stored –
The energy which can be stored in a
capacitor is given by the formula:
L
R
S
C
C
= Capacitance
R
s
= Series Resistance
L
= Inductance
R
p
= Parallel Resistance
Reactance –
Since the insulation resistance (R
p
)
is normally very high, the total impedance of a capacitor
is:
Z=
where
R
S
+ (X
C
- X
L
)
2
2
Z
= Total Impedance
R
s
= Series Resistance
X
C
= Capacitive Reactance =
E
=
1
⁄
2
CV
2
1
2
π
fC
X
L
= Inductive Reactance = 2
π
fL
The variation of a capacitor’s impedance with frequency
determines its effectiveness in many applications.
Phase Angle –
Power Factor and Dissipation Factor are
often confused since they are both measures of the loss
in a capacitor under AC application and are often almost
identical in value. In a “perfect” capacitor the current in
the capacitor will lead the voltage by 90°.
E
= energy in joules (watts-sec)
V
= applied voltage
C
= capacitance in farads
2
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