GENERAL THEORY OF THE INDUCTION MOTOR. 283 



flux $ emanating from the polar region of the stator, and from this the calculation of 

 the flux density in the gap space under that stator tooth which happens at a given in- 

 stant to be in the center of a polar region, () The calculation of the power component 

 M of the magnetizing current per phase, and (<:} The calculation of the wattless 

 component M w of the magnetizing current per phase. 



In the calculation of the power component of the magnetizing current the resistance 

 loss M^R' in each stator winding will be ignored, since both M and R f are fairly 

 small ; to ignore the resistance loss is to assume that the only power delivered by the 

 magnetizing current is the eddy current and the hysteresis loss in the stator iron.* 



In the calculation of the wattless component of the magnetizing current the reluc- 

 tance of the stator and rotor iron will be neglected on account of relatively large re- 

 luctance of the air gap. 



(a) Calculation of flux $. When the rotor runs at synchronous speed the elec- 

 tromotive force induced in each stator winding by the rotating stator magnetism is 

 sensibly equal to E f , inasmuch as the electromotive force MR' required to force the 



of polar region 

 stator iron 



\ 



Fig. 245. 



magnetizing current through the resistance of each stator winding is small. Now the 

 flux $ which emanates from a polar region of the stator iron is harmonically distrib- 

 uted (see Art. 61) and the electromotive force induced in each stator winding by the 

 rotation of the stator magnetism at speed n is 



from which we have 



kpZn 



(i) 



in which / is the number of polar regions on the stator, Z is the total number of con- 

 ductors in one stator winding (one phase), n is the speed of the stator magnetism in 

 revolutions per second, and k is the "phase constant" of one stator winding; 

 ( = 0.901 for a two-phase stator winding, and = 0.955 f r a three-phase stator 

 winding see Art. 61.) 



*The eddy current and hysteresis loss in the rotor is very small under ordinary 

 operating conditions of an induction motor on account of the low speed of the rotor 

 relative to the stator magnetism. 



