RESISTANCE AND ELECTROMOTIVE FORCE. 



33 



Temperature coefficient of resistance. The curves a, b and c 

 in Fig. 1 4 are approximately straight lines ; the same is true of the 

 temperature-resistance curves of all pure metals and of many 

 alloys. Therefore, the increase of resistance of a wire from a 

 standard temperature, say, o C., to any other temperature t C. 



ohms 



100,03 



,100.02 



\ 



30 40 50 

 degrees centigrade 



Fig. 15. 



160 



70 



80 



is approximately proportional to /, and in every case the increase 

 of resistance is exactly proportional * to the resistance of the wire 

 at the standard temperature. Therefore the increase of resist- 

 ance from o c C. to t C. may be expressed as fiR t, where 

 RQ is the resistance of the wire at o C. and /3 is a factor 

 which is approximately constant for a given metal. The resistance 

 of the wire at t C. is equal to R + f3R t, so that, writing 

 R t for the resistance of the wire at t C, we have 



R t = R (i+8t) (5) 



* This is analogous to the fact that the increase of length of a metal bar due to a 

 given rise of temperature is exactly proportional to the initial length of the bar. Con- 

 sider for example, a bar 10 feet long at o C. When the temperature is increased, 

 each foot of the bar increases its length by a certain fractional part of a foot, and the 

 entire bar increases its length by the same fractional part of its total initial length. 



r-KOPEKTY OF KUCTRlCAl LABORATORY, 





i 



