0195136047.pdf

1.2 LUMPED-CIRCUIT ELEMENTS 17

iab

vab

ab(Fixed)R

+−

iab

iab = vab/R = Gvab

vab

ab(Variable)R

+−

Figure 1.2.1Circuit symbols of fixed

and variable resistors and illustration of

Ohm’s law.

TABLE 1.2.1Resistivity of Some Materials

Type Material ρ(·m)

Conductors Silver 16 × 10 −^9
(at 20°C) Copper 17 × 10 −^9
Gold 24 × 10 −^9
Aluminum 28 × 10 −^9
Tungsten 55 × 10 −^9
Brass 67 × 10 −^9
Sodium 0. 04 × 10 −^6
Stainless steel 0. 91 × 10 −^6
Iron 0. 1 × 10 −^6
Nichrome 1 × 10 −^6
Carbon 35 × 10 −^6
Seawater 0. 25
Semiconductors Germanium 0. 46
(at 27°C or 300 K) Silicon 2. 3 × 103
Insulators Rubber 1 × 1012
Polystyrene 1 × 1015

conductors with zero resistance as a good approximation. Table 1.2.1 lists values ofρfor some
materials.
The resistivity of conductor metals varies linearly over normal operating temperatures
according to

ρT 2 =ρT 1

(

T 2 +T

T 1 +T

)

(1.2.3)

whereρT 2 andρT 1 are resistivities at temperaturesT 2 andT 1 , respectively, andTis a temperature
constant that depends on the conductor material. All temperatures are in degrees Celsius. The
conductor resistance also depends on other factors, such as spiraling, frequency (the skin effect
which causes the ac resistance to be slightly higher than the dc resistance), and current magnitude
in the case of magnetic conductors (e.g., steel conductors used for shield wires).
Practical resistors are manufactured in standard values, various resistance tolerances, several
power ratings (as will be explained shortly), and in a number of different forms of construction.
The three basic construction techniques arecompositiontype, which uses carbon or graphite and
is molded into a cylindrical shape,wire-woundtype, in which a length of enamel-coated wire
is wrapped around an insulating cylinder, andmetal-filmtype, in which a thin layer of metal is
vacuum deposited. Table 1.2.2 illustrates the standard color-coded bands used for evaluating
resistance and their interpretation for the common carbon composition type. Sometimes a fifth
band is also present to indicate reliability. Black is the least reliable color and orange is 1000
times more reliable than black.
For resistors ranging from 1 to 9.1, the standard resistance values are listed in Table 1.2.3.
Other available values can be obtained by multiplying the values shown in Table 1.2.3 by factors