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66 ⏐⏐⏐ RESISTANCE
A = 1 cm 2
l = 1 cm
FIG. 3.11
Defining r in ohm-centimeters.
TABLE 3.3
Resistivity (r) of various materials in
ohm-centimeters.
Silver 1.645 � 10 �6
Copper 1.723 � 10 �6
Gold 2.443 � 10 �6
Aluminum 2.825 � 10 �6
Tungsten 5.485 � 10 �6
Nickel 7.811 � 10 �6
Iron 12.299 � 10 �6
Tantalum 15.54 � 10 �6
Nichrome 99.72 � 10 �6
Tin oxide 250 � 10 �6
Carbon 3500 � 10 �6
0.3 cm
ρ
0.6 cm
FIG. 3.12
Thin-film resistor (note Fig. 3.22).
d
meters. However, the meter is generally too large a unit of measure for
most applications, and so the centimeter is usually employed. The
resulting dimensions for Eq. (3.1) are therefore
r: ohm-centimeters
l: centimeters
A: square centimeters
The units for r can be derived from
�⋅cm
r � � ��⋅cm
2
RA
� �
l cm
The resistivity of a material is actually the resistance of a sample
such as that appearing in Fig. 3.11. Table 3.3 provides a list of values of
r in ohm-centimeters. Note that the area now is expressed in square
centimeters, which can be determined using the basic equation A �
pd 2 /4, eliminating the need to work with circular mils, the special unit
of measure associated with circular wires.
EXAMPLE 3.7 Determine the resistance of 100 ft of #28 copper telephone
wire if the diameter is 0.0126 in.
Solution: Unit conversions:
12 in. 2.54 cm
l � 100 ft � � � �� � � 3048 cm
1 ft 1 in.
d � 0.0126 in. � ��0.032 cm
Therefore,
A � � �8.04 � 10 �4 cm 2
(1.723 � 10
R � r � � 6.5 �
Using the units for circular wires and Table 3.2 for the area of a #28
wire, we find
l (10.37 CM⋅�/ft)(100 ft)
R � r� ���� � 6.5 �
A 159.79 CM
�6 �⋅cm)(3048 cm)
����
8.04 � 10 �4 cm 2
(3.1416)(0.032 cm)
l
�
A
2
pd
���
4
2
2.54 cm
�
1 in.
�
4
EXAMPLE 3.8 Determine the resistance of the thin-film resistor of
Fig. 3.12 if the sheet resistance Rs (defined by Rs � r/d) is 100 �.
Solution: For deposited materials of the same thickness, the sheet
resistance factor is usually employed in the design of thin-film resistors.
Equation (3.1) can be written
l l r l l
R � r� � r� ����� � � � Rs� A dw d w w
where l is the length of the sample and w is the width. Substituting into
the above equation yields
l (100 �)(0.6 cm)
R � Rs� ��� �200 �
w 0.3 cm
as one might expect since l � 2w.
R
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