THE MAGNETIC CIRCUIT ELECTROMAGNETS 37 



resistance follow a straight-line law, all as indicated in Fig 14. 

 Thus, if R t and RQ stand respectively for the resistances at 

 temperatures of t degrees and zero degrees, the relation is, 



R t = JRoU + at) (23) 



If it is desired to calculate the 

 change in resistance which occurs 

 when the temperature is raised 

 from ti to tz degrees, we have, 



Dividing the first equation by 

 the second, in order to eliminate 

 #o, we get, 



(1 + at,) r 





(24) ~ 238 C -^("Inferred" Absolute Zero) 



FIG. 14. Diagram illustrating 

 by which the resistance # 2 at the variation of resistance with temper- 



temperature tz can be calculated 



when the resistance Ri at the temperature ti is known. 



The coefficient a = 0.004 if the temperatures are expressed in 

 degrees Centigrade. If temperatures are read on the Fahrenheit 

 scale, a = 0.0024. 



Numerical Example Change of Resistance with Temperature. 

 The resistance of copper per circular mil per foot is 12 ohms at 

 60C. Calculate the temperature at which the resistance will 

 be 10 ohms per circular mil per foot. 



# 60 = # (1 + 60a) 

 Rt = # (1 + ta) 



Divide the first equation by the second, and solve for t, the value 

 of which is found to be, 



_ R t (l + 60a) - #60 

 #60 X a 



Substitute the numerical values, # 6 o = 12; R t = 10; and a = 

 0.004 which will give the answer 8.33C. 



Insulating Materials. The covering on the copper wires may 

 consist of one, two, or three layers of cotton or silk. Silk cover- 

 ings are used only on the smaller sizes, especially when it is 

 important to economize space, that is to say, where the space 



