ALTERNATE CURRENT GENERATOR. 



91 



It is interesting to note that the armature and alternating field 

 currents which flow when an e.m.f. = E sin {oit + li) is acting in the 

 armature circuit, the angular velocity of the armature is oj, and the 

 exciting current C would be unchanged if the e.m.f. E sin {ott -\- li) be 

 removed, the speed maintained, and the exciting field-current changed 

 from C to — 



V 



C^+ -^CE cos h+ ^ 

 oj/n w' mr 



W 



This follows immediately from the vector equations in section 24 

 connecting a,, a,, o,, &c., with a^-\- k when k^, k^, &c., are zero. 



26. The case of the synchronous motor with sinusoidal applied 

 e.m.f., discussed in the last paragraph, can easily be represented 

 geometrically. 



Fig. IV. 



In Eig. IV. let Oa„ taken in the axis of Tbe equal, as in section 13, 

 to twice the steady exciting current of the machine. Draw the vector 

 OE' to represent Iq amplitude and phase 2/w/?i times the applied e.m.f.; 

 that i^ if the latter = e' sin (o)^ -|" h) OE' ^ ^e'^/wm, and the angle 

 from OX to OE' measured positively is = h. 



