I 



GENERAL DIAGRAMS FOR SYNCHRONOUS MOTORS 187 



The minimum value of i could be obtained by making the derivative 

 of Eq. (5) equal to zero and solving; but it is simpler to equate to 

 zero the expression under the radical sign in Eq. (6), because the 

 minimum value of 7 is evidently that below which the value of X 

 would become imaginary. Hence, the positive and negative quantities 

 under the radical sign must offset each other, when there is a minimum. 



Equating the quantity under the radical sign in (6) to zero, and 

 simplifying with respect to (/J 2 o 2 ), instead of i Q 2 , we have 



(7) 



Since the ohmic drop of voltage should be only a small fraction of E, 

 the last term, 7? 2 (7 W) 2 i ) may be neglected, and we thus obtain the 

 approximate value 



I W E\ 2 



t 

 and the minimum value of i n 2 is 



mnmum = 



Since the quantity under the radical sign in (6) practically vanishes 

 for this minimum value of io 2 , the expression for X which corresponds 

 to the minimum reactive current IQ is, simply, by approximation, 



