18 



SYNCHRONOUS MOTORS 



that it increases with the phase-difference of e 2 with respect to e\. In 

 consequence of the lag, ?-, of the current, measured with respect to this 



resultant E.M.F. (when f is near - in value j, it will be seen that the 



current is approximately in phase with this mean value; it would be 

 completely so if there were no resistance-losses. 



Fio. ii. 



The power-outputs of the two machines will be obtained by multi- 

 plying the instantaneous current i by the E.M.F. 's. e\ and e^. For 

 example, in the case where Ei=E2, we have 



4 



i = 



. e I 0\ 



sin cos (a)t r) sin I cat + 

 2 V 2) 



= sin - sin 



- + sm 



,<?Y1 



t-r-\ . 



2 /J 



Likewise, on multiplying by e 2 , we will have 



f . / 0\ I Q\~\ 



sin sin [r +sm I 2ojt Y . 

 UP L V / V 2/J 



These equations show that the power is not constant, in either case, 

 but pulsating, i.e., it presents variations of frequency = 27", as repre- 

 sented in Fig. 1 1 . 



