

MOTORS OPERATING SYNCHRONOUSLY WITHOUT D. C. 143 



and supposing the current passing through it from the inside to the 

 outside to be sinusoidal, and to be out of phase by the angle ^ with 

 respect to the position of coincidence between the poles, we will have 



' 

 7=/o sin (cut f}. 



1e will therefore have, for the voltage at the terminals, 

 u rlo sin (iot </>) 

 a>\ (/' )/o cos dt cos a>t+ (/' + )/o sin <b sin cut \. 

 L\ 2 7 \ 2 7 J 



tne harmonics of the order 30^ introduced by the pulsation of / being 

 ;lected. 

 This equation is represented by the diagram in Fig. 71. It is seen 



FIG. 71. 



that the voltage U at the terminals is the geometrical resultant of the 

 vectors 



- ) / (perpendicular) . 



In this diagram the lag <f> of the current is denned as the interval 

 between the zero-value of the current and the position of coincidence 

 of the poles. 



It is seen that the E.M.F. of self-inductance S makes an obtuse 



angle with the current / so long as ^ is comprised between o and - 

 (the two vectors being in opposition when ^=o), and that it is in quadra- 

 ture when (!f=. 

 r 2 



