36 PRINCIPLES OF ELECTRICAL DESIGN 



in diameter, and the number of circular mils in a given area 

 is therefore greater than the number of square mils. Thus, in 1 



sq. in. there are 1,000,000 square mils; but 10 6 X - = 1,273,237 



7T 



circular mils. The cross-section of a cylindrical wire in circular 

 mils is, 



(m) = (diameter in mils) 2 



true area in square mils 

 0.7854 



The area of any conductor expressed in circular mils is always 

 greater than the true area expressed in square mils; because the 

 unit area called the circular mil is smaller than the square mil. 



Simple Formulas for Resistance of Wires. A very convenient 

 and easily remembered rule is that the resistance of any copper 

 wire 1 is 1 ohm per circular mil per inch length, or 



at a temperature of about 60C. (or 140F.). This formula is 

 therefore applicable to the calculation of coil resistances under 

 operating conditions, when they are hot. 



The system on which the B. & S. (Brown and Sharp) gage is 

 based, exactly halves the cross-section with an increase of three 

 sizes. It will also be found that a No. 10 B. & S. copper wire 

 has a cross-section of about 10,000 circular mils (diameter = 0.1 

 in. approx.) and its resistance at normal temperatures (about 

 20C.) is 1 ohm per 1,000 ft. Thus, for approximate calculations, 

 sizes of wire on the B. & S. gage can be determined if necessary 

 without reference to tables. 



The weight of any size of round copper wire may be calculated 



by the formula: 



d 2 

 Weight in pounds per 1,000 ft. = 



where d = diameter in mils. 



Variation of Resistance with Temperature. If the resistance of 

 a wire is known for any given temperature it can be calculated 

 approximately for any other temperature by remembering that 

 the resistance of all pure metals tends to become zero at the abso- 

 lute zero of temperature, and by assuming that the variations in 



1 The specific resistance of commercial wires can be, and usually is, equal 

 to that of pure electrolytic copper of 100 per cent, conductivity by 

 Matthiesson's standard. 



