386 ELECTRICAL ENGINEERING 



These ampere turns are distributed over -th of the circumfer- 



n 



ence of the armature and their resultant is, Fig. 368, 



zr chord zr 



m = 



2 n arc 2 n 2irr 



n 



, 2rsin- 



ZI n 



/ , . TT 2irr 

 v 2 n 2 sm - 



n 

 ZI 



(366) 



The maximum value of the m.m.f. per phase is 



71 



mo = \/2 m = ampere turns. . . (367) 

 irn 



To find the resultant m.m.f. of the alternating current in the 

 armature it is necessary to combine n m.m.fs. of maximum 

 ZI 2?r 



value mo = -- displaced in direction by angle and displaced 



in phase by -th of a period or by angle 



In Fig. 369 phase 1 is shown in the position of maximum 

 m.m.f. if the power factor is unity. The direction of the m.m.f. 

 is OB and it is in quadrature ahead of the field m.m.f. If time 

 and angular displacement are measured from OB, then at time t 

 and angle 6 the m.m.f. of phase 1 is m cos 6 in direction OBi, 

 and its component in direction OB is mo cos 2 0. 



At time t the m.m.f. of phase 2 is mo cos f + - - ) making an 

 angle ( 6 -\ ) with OB and its component in direction OB is 



mo cos 2 f B + -- j 



The resultant m.m.f. of the n phases in the direction OB at 

 any time t is 



, 2 (n - 1) 



77 



= mo X n X average (cos) 2 = m ~ 



a 



since the average cos 2 is = f . 



