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# Resistance of Conductor

Author: E.E. Kimberly

Commercial copper wire for electrical use may be had in many sizes and cross-sectional shapes. Round wire is usually used in winding small magnet coils, motors, and generators. Wire of rectangular section is more economical in space and is used in large equipment. Conductors that may be bent frequently are usually built up of a number of small wires and are called stranded conductors.

As may be shown by test and demonstrated by Ohm's Law, the resistance of a conductor of uniform cross-section is directly proportional to its length and inversely proportional to its cross-sectional area. This statement may be expressed by the formula

in which

R = resistance of a conductor, in ohms;
l = length of the conductor, in feet;
A = cross-sectional area of the conductor, in circular mils;
ρ = a constant depending on the resistive properties of the substance of the conductor.

For any conducting substance, p may conveniently be taken as the resistance of a round bar of that substance 1 foot long and 0.001 inch or 1 mil in diameter. The cross-sectional area of such a bar is called 1 circular mil and the bar is said to be one circular mil-foot in size. The resistance of 1 circular mil-foot of a substance is called the resistivity of the substance. The resistivity of a substance is the reciprocal of its conductivity. At 25 C the resistivity p of annealed copper of 100 per cent conductivity is 10.6 ohms. The resistivity of aluminum is about 2 times that of copper, and the resistivity of iron is about 7 times that of copper.

The areas of similar plane figures are proportional to the squares of their like dimensions; so a circle with a diameter of M mils has an area A of M2 circular mils, or A = M2.

Example 6-1. - A two-wire line whose copper wires have diameters of 0.25 in. is 1 mile long. Find the resistance of the line at 25 C.

Solution. - The diameter of the wire is 250 mils. Then, the resistance of the line is

Last Update: 2010-10-06