! 



of the Synchronous Motor. 



61 



■ also the equation to an ellipse. These ellipses are represented 

 in fig. 2. 



Fig- 2. 



Minimum Current at Given Power. 



6. We have 



p 4- c 2 R = Ec cos tJt. 



dc 

 The current is a minimum when -=-7- =0. Now, differentiating 



ay* 7 



with respect to yjr, 



do 

 (2cB-E cos yfr) J^ + E c sin i/r = ; 



therefore, when -7-7- =0, we have 

 dy 



or 



sin^=0, 



that is, the current is a minimum when in phase with the 

 impressed E.M.F., as is otherwise obvious. Putting, there- 

 fore, ^=0, we have 



p + c 2 R=Ec (7) 



This curve is of the second degree in c and p, and is 

 satisfied by the following system of points : — 





w 



w 





E 

 R 



» = 



:' 



