256 



ELECTRICAL ENGINEERING 



tion OF is n/ cos 2 6 + n! sin 2 6 = n/ and in the direction OX 

 is nI cos sin 6 n! cos sin 6 = 0. 



Thus the resultant armature m.m.f. is n/ in fixed direction 

 relative to the field m.m.f. and, therefore, revolving synchronously 

 relative to the armature. (Fig. 233.) 



The direction of the resultant armature m.m.f. relative to the 

 field m.m.f. is determined by the angle of phase difference between 

 the current and the e.m.f. generated at no load. 



If the current is in phase with the e.m.f., the armature m.m.f. 

 acts at right angles to the field m.m.f. and is, therefore, cross 

 magnetizing only; if the current lags by angle <, the armature 

 m.m.f. can be separated into two components n/ sin $ which is de- 

 magnetizing and n/o cos $ which is cross magnetizing. (Fig. 231.) 



If the two-phase winding, Fig. 232, is replaced by a three-phase 

 winding, Fig. 234, with the first phase AB in the same position as 



FIG. 234. 



FIG. 235. 



before and the other phases CD and EF displaced 120 degrees and 

 240 degrees from it, the m.m.f .'s of the three phases will be respec- 

 tively n/o cos 6, n/o cos (6 120) and n/ cos (6 240) and will 

 act in the directions represented. As before 6 is measured from 

 the instant of maximum current and the currents in the three 

 phases are assumed to lag behind the e.m.f. 's by angle </>. 

 The sum of the components of m.m.f. in direction OF is 



n/o cos 2 6 + n/o cos 2 (0 - 120) + n/ cos 2 (0 - 240) = | n/ , 

 and the sum of the components in the direction OX is 



n/o cos sin + n/ cos (0 - 120) sin (0 - 120) 



-f nI cos (0 - 240) sin (0 - 240) = 0. 



