252 Chapter 10
VA is the applied voltage in volts,
CX is the capacitance of the individual capacitor under
consideration in farads,
CT is the sum of all of the capacitors in series.
When used in an ac circuit, the capacitive reactance,
or the impedance the capacitor injects into the circuit, is
important to know and is found with the equation:
(10-15)where,
XC is the capacitive reactance in ohms,
f is the frequency in hertz,
C is the capacitance in farads.
To determine the impedance of circuits with resis-
tance, capacitance, and inductance, see Section 10.4.
Capacitance is the concept of energy storage in an
electric field. If a potential difference is found between
two points, an electric field exists. The electric field is
the result of the separation of unlike charges, therefore,
the strength of the field will depend on the amounts of
the charges and their separator. The amount of work
necessary to move an additional charge from one point
to the other will depend on the force required and there-
fore upon the amount of charge previously moved. In a
capacitor, the charge is restricted to the area, shape, and
spacing of the capacitor electrodes, sometimes known
as plates, as well as the property of the material sepa-
rating the plates.
When electrical current flows into a capacitor, a force
is established between two parallel plates separated by a
dielectric. This energy is stored and remains even after
the input current flow ceases. Connecting a conductor
across the capacitor provides a plate-to-plate path by
which the charged capacitor can regain electron balance,
that is, discharge its stored energy. This conductor can
be a resistor, hard wire, or even air. The value of a
parallel plate capacitor can be found with the equation
(10-16)where,
C is the capacitance in farads,
x is 0.0885 when A and d are in cm, and 0.225 when A
and d are in inches,
H is the dielectric constant of the insulation,
N is the number of plates,
A is the area of the plates,
d is the spacing between the plates.
The work necessary to transport a unit charge from
one plate to the other is(10-17)
where,
e is the volts expressing energy per unit charge,
k is the proportionality factor between the work neces-
sary to carry a unit charge between the two plates and
the charge already transported and is equal to 1/C
where C is the capacitance in farads,
g is the coulombs of charge already transported.The value of a capacitor can now be calculated from
the equation(10-18)where,
q is the charge in coulombs,
e is found with Eq. 10-17.The energy stored in a capacitor is found with the
equation(10-19)where,
W is the energy in joules,
C is the capacitance in farads,
V is the applied voltage in volts.Dielectric Constant (K). The dielectric constant is the
property of a given material that determines the amount
of electrostatic energy that may be stored in that material
per unit volume for a given voltage. The value of K
expresses the ratio of a capacitor in a vacuum to one
using a given dielectric. The K of air is 1 and is the refer-
ence unit employed for expressing K of other materials.
If K of the capacitor is increased or decreased, the capac-
itance will increase or decrease respectively if other
quantities and physical dimensions are kept constant.
Table 10-2 is a listing of K for various materials.XC^1
2 SfC-------------=C xH>@^ N 1– A
d--------------------------------
u 10 –^13
=
Table 10-2. Comparison of Capacitor Dielectric
Constants
Dielectric K (Dielectric Constant)
Air or vacuum 1.0
Paper 2.0–6.0
Plastic 2.1–6.0
Mineral oil 2.2–2.3
Silicone oil 2.7–2.8ekg=Cq
e---=W CV22----------=