General Description
A capacitor is a component which is capable of storing
electrical energy. It consists of two conductive plates (elec-
trodes) separated by insulating material which is called the
dielectric. A typical formula for determining capacitance is:
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:
C = Capacitance
L = Inductance
Rs = Series Resistance
Rp = Parallel Resistance
.224 KA
C =
t
RP
C = capacitance (picofarads)
K = dielectric constant (Vacuum = 1)
A = area in square inches
t = separation between the plates in inches
(thickness of dielectric)
L
R S
.224 = conversion constant
C
(.0884 for metric system in cm)
Reactance – Since the insulation resistance (Rp) is
normally very high, the total impedance of a capacitor is:
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
2
2
Z = RS + (XC - XL)
-6
ꢀ
and most capacitors have values in the micro (10 ), nano
where
-9
-12
(10 ) or pico (10 ) farad level.
Dielectric Constant – In the formula for capacitance given
above the dielectric constant of a vacuum is arbitrarily cho-
sen as the number 1. Dielectric constants of other materials
are then compared to the dielectric constant of a vacuum.
Z = Total Impedance
Rs = Series Resistance
XC = Capacitive Reactance =
1
2 π fC
Dielectric Thickness – Capacitance is indirectly propor-
tional to the separation between electrodes. Lower voltage
requirements mean thinner dielectrics and greater capaci-
tance per volume.
XL = 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 iden-
tical in value. In a “perfect” capacitor the current in the
capacitor will lead the voltage by 90°.
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 capacitance within
a material group.
Energy Stored – The energy which can be stored in a
capacitor is given by the formula:
I (Ideal)
I (Actual)
E = 1⁄ CV2
2
Loss
Phase
Angle
Angle
ꢂ
E = energy in joules (watts-sec)
V = applied voltage
C = capacitance in farads
f
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:
V
In practice the current leads the voltage by some other
phase angle due to the series resistance RS. The comple-
ment of this angle is called the loss angle and:
dV
dt
Iideal
=
C
where
Power Factor (P.F.) = Cos or Sine ꢂ
Dissipation Factor (D.F.) = tan ꢂ
I = Current
C = Capacitance
f
dV/dt = Slope of voltage transition across capacitor
for small values of ꢂ the tan and sine are essentially equal
which has led to the common interchangeability of the two
terms in the industry.
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.
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