Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 285

■ EXAMPLE 11.44
Problem: A No. 12 wire has a diameter of 80.81 mils. What are (1) its area in circular mils and (2)
its area in square mils?

Solution:

1. A = D 2 = (80.81) 2 = 6530 circular mils

2. A = 0.785 × 6530 = 5126 square mils

■ EXAMPLE 11.45
Problem: A rectangular conductor is 1.5 inches wide and 0.25 inch thick. (1) What is its area in
square mils? (2) What size of round conductor in circular mils is necessary to carry the same current
as the rectangular bar?

Solution:

1. 1.5 in. = 1.5 × 1000 = 1500 mils, and 0.25 in. = 0.25 × 1000 = 250 mils; thus,

A = 1500 × 250 = 375,000 square mils

2. To carry the same current, the cross-sectional area of the rectangular bar and the cross-
sectional area of the round conductor must be equal. There are more circular mils than
square mils in this area; therefore,

375 000
0 785

,

A = = 477,700 circular mils

.

Note: Many electric cables are composed of stranded wires. The strands are usually single wires
twisted together in sufficient numbers to make up the necessary cross-sectional area of the
cable. The total area in circular mils is determined by multiplying the area of one strand in
circular mils by the number of strands in the cable.

11.7.9.4 Circular-Mil-Foot
As shown in Figure 11.52, a circular-mil-foot is actually a unit of volume. More specifically, it is
a unit conductor 1 foot in length and having a cross-sectional area of 1 circular mil. The circular-
mil-foot is useful in making comparisons between wires that are made of different metals because
it is considered a unit conductor; for example, a basis of comparison of the resistivity of various
substances may be the resistance of a circular-mil-foot of each of the substances.

Note: It is sometimes more convenient to employ a different unit of volume when working with
certain substances. Accordingly, unit volume may also be taken as the centimeter cube. The
inch cube may also be used. The unit of volume employed is given in tables of specific
resistances.

1 foot

0.001"

FIGURE 11.52 Circular-mil-foot.