COMPENSATED INDUCTION MOTOR 



261 



from the mains, and short-circuited through negligible resistances 

 HI, Rj, Itg, which, however, contain alternating e.m.f.'s. The supply 

 mains are, in fact, bridged by the low-resistance generator coils at 

 the station, and by numerous lamps, motors, etc., throughout the 

 entire area of supply, so that the resistance across any two mains is 

 extremely low. If, then, the combined resistance of the entire net- 

 work were the only point to be considered, the rotor might just us 

 well be simply short-circuited by connecting together its three sets 

 of brushes, and it would then be equivalent to an ordinary short- 

 circuited rotor.* The mains, however, in addition to offering paths 

 of negligible resistance, also contain e.m.f.'s 

 furnished by the generators at the sta- 

 tion. Hence, in order to render the 

 arrangement of Fig. 160 equivalent to that 

 of Fig. 159, we must suppose that into 

 the short-circuiting resistances of the rotor 

 there are injected e.m.f.'s, equal in magni- 

 tude and phase to the p.d.'s across the 

 mains. 



It is the injection of these e.m.f.'s 

 due to the connection of the brushes across 

 the mains instead of across simple short- 

 circuiting resistances that so profoundly 

 modifies the behaviour of the motor. 



For the sake of simplicity, we shall 

 neglect magnetic leakage, and shall, further, 

 assume that the stator and rotor windings 

 are of the same type, so that the e.m.f. 

 induced in each winding by the rotating 

 field is simply proportional to the product 

 of the number of conductors into the rela- FIG. 160. Equivalent of C'om- 

 tive velocity of the conductors and the ponsated Induction Motor, 

 rotating field. Let C 8 = number of stator 



conductors, and C r = number of rotor conductors. We shall con- 

 sider the effect on the behaviour of the motor due to a variation in 

 the number of rotor conductors. 



* The only difference being that in an ordinary rotor tlio points of short-circuit 

 are three fixed points in the winding, whereas in a commutator rotor whose brushes are 

 short-circuited the position of the points varies during the rotation. This, however, 

 does not introduce any material difference : in the first case, the frequency of the 

 currents in the short-circuiting connections is the same as- that of the rotor currents : 

 in the second, it is equal to the frequency of the stntor currents. 



