Wire Gages

Although it is convenient to express all wire sizes in circular mils, round wires are frequently specified by American Wire Gage numbers.¹ By remembering the progressive law followed in the table, it is easy to convert gage numbers to circular mils or vice versa. A No. 10 copper wire has a diameter of approximately 100 mils and a resistance of 1 ohm per 1000 feet at 25 C.

As the gage number of the wire decreases, the cross-sectional area doubles at every three numbers and the diameter doubles at every six numbers. As the gage number increases, the cross-sectional area is halved at every three numbers and the diameter is halved at every six numbers. The area of any round wire is therefore

times as great as that of the next smaller integral size. Sizes of conductors larger than 0000 are specified in circular mils instead of by numbers.

Change in Resistance With Change in Temperature. - Almost all metals and alloys show an increase in resistance with an increase in temperature. Some alloys properly proportioned show practically no such change in resistance with change in .temperature. When the temperature of a pure copper wire above 0 C increases by 1 deg C, its resistance rises 0.427 per cent of its resistance at 0 C. This law is expressed by the formula

in which R_t = resistance at temperature t; R₀ = resistance at 0 C; A₀ = 0.00427, for 0 C as reference; t = temperature of conductor, in deg C.

It is only when 0 C is used as the base temperature that α₀ = 0.00427. For every other base temperature, there is another coefficient. To avoid the need of a table of coefficients, it is best to remember only α₀, which is 0.00427.

Example 6-2. At 75 C a conductor has a resistance of 400 ohms. What is its resistance at 55 C?

First Solution. - First, find the resistance of the conductor at 0 C. Thus,

and

Then, the desired resistance at 35 C is

Second Solution. - In the temperature range from 0 C to 100 C, in which copper conductors are usually used, the resistance of pure copper varies linearly with the temperature. If this linear relationship continued in the lower temperatures, the resistance of pure copper would be zero at -234.5 C.

It is therefore permissible to say that the resistance of pure copper is directly proportional to the temperature above - 234.5 C. The variation for this example is represented in Fig. 6-1. The resistance at 35 C may then be found as follows:

Fig. 6-1. Variation of Resistance With Temperature