PF.SIGX CHMR.ICTERISTICS OF EI.F.CTROMAGNETS 219 



such as a liiir in series with llie relay is e(|iial to tlie resistance of the 

 rela>- and wliere the resistance external to the relay ^vin(lin^; does not 

 chani^e appreciably with temperature variations. 



The temperature formulae for the constant wattage condition are 

 developed as folU>ws: 



Let Q he the ciuantity of heat in calories supplied to the winding 

 per seconti, and Q dt be the amount supplied in a small increment of 

 time. Let S lie the product of the specific heat and weight of the 

 total wire on the spool expressed in calories. Let T he the tempera- 

 ture (litTerence between the winding and the surrounding air. S d T 

 is then the amount of heat used in raising the temperature of the 

 wire by the amount d T. Let p be the average dissipating constant 

 throughout the temperature range. It depends upon the radiating 

 surfacx; of the winding, metal conducting parts of the structure and 

 external convection of heat by the air. Given the constant p, p T dt 

 represents the calories dissipated during the interval dt. 



The total heat supplied during the time dt is partially used in 

 raising the temperature of the wire, ami partially dissipated, con- 

 sequently 



Qdt^SdT+pTdt. (6) 



If heat is continuously supplied the winding in the form of electrical 

 energy, the rate of dissipation ultimately equals the rate of supply. 

 This is true for temperatures that do not fuse the wire or permanently 

 alter its resistance characteristic. LMtimatelv 



SdT^O 



and 



Qdt = pT„dt. 



If the final temperature reached is designated as Tm then 



Q = pT,„ (7) 



and from equations 6 and 7 



pT„dl^SdT+pTdl, 



-Ut= ''' 



r„-T 



and integrating gives 



|/=iog(r„-r)-t-c. 



