THEORY OF THE INDUCTION MOTOR. 153 



CURRENTS IN THE LINE WIRES. 



1O5. Di-phase Systems. Consider Figs. 55 and 57, 

 and suppose the current strengths in the coils a, a', b, b', to be the 

 same. 



Let the current in a, a be i sin pt, and that in b, b', 



i sm(pt + |)- 



Then in the star-grouping (Fig. 55) the current in the line 

 wire o is evidently the same as that in the coil a. 



In the mesh-grouping (Fig. 57) the current in o is the algebraic 

 sum of the currents in a and b } and is given by 



i' = i sin pt + * sin (pt -f- ^ 

 = \/2i sin pt + (4) 



That is, the currents in the line wires are \/2 times those in the 

 coils, and differ from them in phase by one-eighth of a period. 



106. Tri-phase Systems. In a similar manner the 

 currents in the line wires of a tri-phase system are 



Star-grouping : the same as the currents in the stator coils. 

 Mesh-grouping. The current in line wire, g, is given by 



t' = i sin pt i sin (pt - ) 



(5) 



where i sin pt, and i sin (pt =-J are respectively the currents 

 in coils A and B. 



THEORY OF THE INDUCTION MOTOR. 



107. The following theory of the induction motor is perfectly 

 general, and independent of the number of phases in the stator 

 and rotor. 



Before attacking the problem analytically, it will be well to 

 form a mental picture of what really takes place in an induction 

 motor. 



The currents in the stator windings produce a rotating magnetic 

 field. At the instant of switching on the stator currents the rotor 



