ELECTRIC CIRCUITS 77 



scale is used and RQ is the resistance at C., the value of a for 

 copper is 0.00428. This value can be considered as constant 

 over the range of temperatures from C. to 100 C. With the 

 Fahrenheit scale of temperature and RQ taken as the resistance 



at 32 F., the value of a is ' 1 f 28 = 0.00249. If the tempera- 



l.o 



ture 1 C. is chosen as standard the formula can be written 



ft = flJl + (*-*i)l, ...... (115) 



where a is not the same as before but is smaller because the in- 

 crease of resistance is expressed as a fraction of the resistance at 

 ti C. which is larger than the resistance at C. When ti degree 

 is taken as the standard room temperature of 25 C. the value of 

 a is 0.00386. 



If the resistance at ti C. is known, but the corresponding 

 value of a is not known, the resistance at temperature t can be 

 found from the formula 



+ 0.00428 n 



/I 

 = Ml 





+ 0.00428 

 This is derived by eliminating R from the two equations, 



R t = R (i+ 0.00428 0, 

 and R tl = R Q (1 + 0.00428 fe). 



Example. If the resistance of a copper conductor at 25 C. 

 is 10 ohms, determine its resistance at 65 C. 

 From formula 115 the resistance is 



#65 = 10 { 1 + 0.00386 (65 - 25) j = 11.55 ohms; 

 or from formula 116 



0.00428 X65 



\ 



J = 1L 



65 



0.00428 X25 



The temperature coefficients for all pure non-magnetic metals 

 are practically the same as for copper and the formulae above may 

 be used. For alloys the temperature coefficient varies from the 

 values given for pure metals to zero. In certain compositions it 

 has a value approximately zero over the range at temperatures 

 met in ordinary practice. Such alloys are very useful in the 

 manufacture of standard resistances, as ammeter shunts, etc., 

 where the resistance must remain constant. 



Iron has a temperature coefficient of resistivity of 0.006 per 

 degree centigrade. 



