GENERAL THEORY OF THE INDUCTION MOTOR. 295 



rotor speed is below synchronism (n' less than n) then B r is 

 less than B p the net electromotive force (B p r ) produces a 

 load current I" in the rotor rods in the regions B and B 1 ', 

 the magnetizing action of this load current is balanced by a cor- 

 responding load current /' in the stator winding, and the load 

 currents in the rotor rods in the regions B and B f are pushed 

 sidewise by the cross-flux <3> c thus developing mechanical power. 



It is evident that the flux <I> is independent of the rotor 

 speed, inasmuch as it must by its pulsations induce sufficient 

 electromotive force in the stator winding to balance the supply 

 voltage E r t and it is 90 behind E f in phase. This flux is 

 called the " transformer flux " for brevity. 



The cross -flux O c on the other hand is proportional to the 

 rotor speed n f , and it is equal numerically to <E> when n' 



electromotive 



forces due to 



pulsation 



electromotive 



forces due to 



rotation 



B' 



Fig. 255- Fig. 256. 



equals n. This is evident when we consider that the electromo- 

 tive force A r due to cutting of the transformer flux <I? at speed 

 n 1 must be balanced by the electromotive force A p due to the 

 pulsations of the cross-flux <E> c . 



It is interesting to note that at synchronous speed (n' = n) 

 the magnetism of the single-phase induction motor is exactly 

 like the magnetism of the polyphase induction motor, that is to 

 say, the stator magnetism is constant in value and rotates at 

 speed n. This is evident when we consider that the two fluxes 

 <l> and < c are equal in value when n 1 = n y and that they are 

 in time quadrature with each other. 



In order to proceed further in the analysis of the action of the 

 single-phase induction motor, it is necessary to consider the exact 



