﻿Electrical Resistance of Alloys. C05 



The theory is as follows : — When electricity flows from 

 one metal to another there is an absorption or development 

 of heat at the junction — the Peltier effect. The temperature 

 disturbance thus created increases until the conduction of 

 heat through the metals balances the Peltier effect at the 

 junctions, and it sets up a back electromotive force. The 

 difference of temperature at the alternate junctions is pro- 

 portional to the current, so is also the back E.M.F. called 

 into play. But a reverse E.M.F, proportional to current is 

 indistinguishable experimentally from a resistance, so that 

 an alloy should on these grounds possess a spurious resistance, 

 differing in nature from that of a pure metal. Payleigh's 

 calculation shows that the false resistance, R, per unit length 

 is given by 



R=273«7(*/p+*'/p')j 



where £= thermo-electric force of a couple for 1° difference 

 of temperature between the junctions : k and k! are the heat 

 conductivities of the metals in ergs ; p andy/ are the pro- 

 portions by volume in which the two metals are taken. The 

 temperature is supposed to be near 0° C. 



It will be noticed that », the number of couples per unit 

 length, does not enter into the above expression. The 

 number co-operating is indeed increased by finer subdivision, 

 but the efficiency of each is decreased owing to the readier 

 conduction of heat between the junctions. An alloy of equal 

 volumes of copper and iron should have a false resistance 

 amounting to 1*5 per cent, of that of copper, as is readily 

 shown by substitution of the appropriate numbers in the 

 above formula. 



It may be noted in passing that this expression shows that 

 it is possible always to choose the proportions of the metals 

 present so that the resulting alloy shall have a maximum 

 resistance. For p +p f = 1, 



K= — , 



K K 



P W' 

 and for a maximum or minimum dR/dp = ; 

 whence K / f - K ' j { l- p y =0 . 



or 



P = 



The positive sign is to be taken with the square root, since 



