188 GENERAL DIAGRAMS FOR SYNCHRONOUS MOTORS 

 or, substituting for JQ, 



This is the most suitable reactance -value for reducing i to a min- 

 imum. Inasmuch as, on the other hand, the supply-voltage required 

 increases with the reactance X, and inasmuch as this voltage must 

 be kept as low as possible in order to utilize the apparatus to the greatest 

 advantage (i.e., to obviate the necessity of making it too large and, 

 consequently, more expensive), for the effective output, we may con- 

 clude that, in general, the reactance value should be comprised between 

 zero and the value (Xo) corresponding to the minimum zero-load 

 reactive current. 



NOTE i. Formulas 5, 6, 7, 8 can be put into a form which is often 

 more convenient practically, by expressing the values of /o in terms 

 of I w , the values of RI in terms of e, the values of e' in terms of e, 

 and the values of X in terms of R. 

 Let us take 



X i 



' 



=a; 



cos < being the power-factor, and m being the value of tan 

 From these equations, we deduce 



XI m 



Z a\/i+m 2 

 and also the equivalent formulas: 



. (5') 



2 



-- 9 



2 



= ___ __ a 



a(i -tan 2 0) 1 \ 2 (i -tan 2 <f>) i -tan 2 <f> 



t 

 muumumof 



. . (8') 



a 



