Resistors, Capacitors, and Inductors 253The dielectric constant of materials is generally
affected by both temperature and frequency, except for
quartz, Styrofoam, and Teflon, whose dielectric
constants remain essentially constant. Small differences
in the composition of a given material will also affect
the dielectric constant.
Force. The equation for calculating the force of attrac-
tion between the two plates is
(10-20)where,
F is the attractive force in dynes,
A is the area of one plate in square centimeters,
V is the potential energy difference in volts,
K is the dielectric constant,
S is the separation between the plates in centimeters.
10.2.1 Time Constants
When a dc voltage is impressed across a capacitor, a
time (t) is required to charge the capacitor to a voltage.
This is determined with the equation:
(10-21)where,
t is the time in seconds,
R is the resistance in ohms,
C is the capacitance in farads.
In a circuit consisting of only resistance and capaci-
tance, the time constant t is defined as the time it takes
to charge the capacitor to 63.2% of the maximum
voltage. During the next time constant, the capacitor is
charged or the current builds up to 63.2% of the
remaining difference of full value, or to 86.5% of the
full value. Theoretically, the charge on a capacitor or the
current through a coil can never actually reach 100%
but is considered to be 100% after five time constants
have passed. When the voltage is removed, the capac-
itor discharges and the current decays 63.2% per time
constant to zero.
These two factors are shown graphically in Fig.
10-14. Curve A shows the voltage across a capacitor
when charging. Curve B shows the capacitor voltage
when discharging. It is also the voltage across the
resistor on charge or discharge.10.2.2 Network Transfer FunctionNetwork transfer functions are the ratio of the output to
input voltage (generally a complex number) for a given
type of network containing resistive and reactive
elements. The transfer functions for networks consisting
of resistance and capacitance are given in Fig. 10-15.
The expressions for the transfer functions of the
networks are:A is jZ or j2Sf,
B is RC,
C is R 1 C 1 ,
D is R 2 C 2 ,
n is a positive multiplier,
f is the frequency in hertz,
C is in farads,
R is in ohms.10.2.3 Characteristics of CapacitorsThe operating characteristics of a capacitor determine
what it was designed for and therefore where it is best
used.Capacitance (C). The capacitance of a capacitor is
normally expressed in microfarads (μF or 10^6 farads)Quartz 3.8–4.4
Glass 4.8–8.0
Porcelain 5.1–5.9
Mica 5.4–8.7
Aluminum oxide 8.4
Tantalum pentoxide 26.0
Ceramic 12.0–400,000Table 10-2. Comparison of Capacitor Dielectric
Constants (Continued)
Dielectric K (Dielectric Constant)F AV2K 1504 S=-------------------------- 2 -tRC=Figure 10-14. Universal time graph.Percent of voltage or current100806040200
0 1 2 3 4 5 6ABTime—RC or L/R
A. Voltage across C when charging.
B. Voltage across C when discharging.