742 INDUSTRIAL APPLICATIONS. 



If we assume that the duration of the period is very small, 

 we have sensibly 



M 2 

 /=L-- = 0, 



M 2 N 2 



_-R + R'_, 



The efficiency is 



U *A' 2 x 



W R A 2 + (' + *) A' 2 A 2 ' 



This efficiency increases still with w, and its maximum value 



x x 



N 2 

 gives for N = N' 



In the case in which the two wires of the transformer are coiled 

 in the same way, the efficiency is equal to the quotient of the 

 useful resistance by the total resistance, as for permanent currents. 

 The maximum useful work corresponds to the condition x = b' + R, 

 and the efficiency is then o^o. 



It should be observed that the maximum efficiency u m is the 



N' 

 greater the smaller is the ratio . It is then advantageous 



that the secondary wire should have a smaller number of turns 

 than the primary wire. 



On the other hand, the primary circuit comprises two resistances, 

 the one a in the electromotor, and the other b in the transformer ; we 

 may say that the efficiency for the transformer itself is expressed by 



' + *) A' 2 



