LEAKAGE COEFFICIENTS 181 



to its own wave of magnetic flux, the actually existing wave 

 being obtained by the superposition of the two hypothetical waves 

 corresponding to the stator and rotor currents. In considering the 

 theory of induction motors, we may either deal with the hypothetical 

 waves which the currents in each winding would produce if those in 

 the other winding were non-existent, or we may take as the basis of 

 our investigation the actually existing flux due to the superposition 

 of the hypothetical fluxes. Both modes of investigation have been 

 employed, and according to the method adopted different writers on 

 the subject have defined and used various so-called " leakage factors " 

 or " leakage coefficients," whose meaning and mutual relationship we 

 now proceed to explain. 



104. Leakage Coefficients 



Let the secondary winding be open, and let polyphase currents 

 be supplied to the primary, the maximum value of the current 

 in each phase being Ii. Let FI stand for the maximum value of the 

 total flux linked with the windings of each phase. Then, according 

 to our assumption, FI is proportional to Ii, so that we may write 



and in addition the instantaneous values of these two quantities are 

 in phase with each other. We may term LI the virtual self-inductance 

 of each phase of the winding, since it represents the maximum value 

 of the total flux linked with one phase of the winding when all the 

 phases are traversed by currents of unit amplitude.* 



Similarly, if we suppose the primary open-circuited, and poly- 

 phase currents supplied to the secondary, we may write 



where F 2 is the maximum value of the flux linked with one phase of 

 the secondary when all its phases are supplied with (polyphase) 

 currents of amplitude I 2 . The constant 1^ we may term the virtual 

 self-inductance of one phase of the secondary. 



In dealing, in 20, with the stationary or alternating flux waves 

 produced around the rotor periphery by the alternating currents in 



* In the case of a two-phase winding, L, is identical with the true self-inductance 

 of either phase, i.e. with the flux which becomes linked with that phase when supplied 

 with unit current; for, as has been shown in 20, the amplitude of the resultant 

 rotating wave is the same as that of the oscillating wave due to one phase only; but in 

 a three-phase motor L, is greater than the true self-inductance, and includes, in 

 addition to the true self-inductance, the effect of the mutual inductance of the 

 neighbouring phnwH ( 20). 



