CHAP. XII] INDUCTANCE OF WINDINGS 221 



Substituting the value of (P^ from eq. (149) into eq. (148) 

 we obtain 



L PP =C PP 2 ( (p A+ (p a^a+^;U10" 8 henrys. . (150) 



In the following three articles formula (150) is applied to 

 the calculation of the leakage reactance of 



(a) Induction machines; 



(6) Synchronous machines; 



(c) Coils undergoing commutation in a direct-current machine. 



In each case somewhat different values of the unit permeances 

 <P' are ijsed, because of the diversity of the magnetic paths. 



66. The Leakage Reactance in Induction Machines. It is 

 explained in Art. 35 and shown in Fig. 23 that the actual flux 

 in a loaded induction machine is the resultant of three fluxes, 

 of which the useful flux is linked with both the primary and 

 the secondary windings. The component fluxes 0j and 2 , 

 linked with the primary and secondary windings respectively, 

 are called the leakage fluxes. They induce in the windings e.m.fs. 

 in quadrature with the corresponding currents, and these e.m.fs. 

 have to be balanced by a part of the terminal voltage. Con- 

 sequently, that part of the applied voltage which is balanced by 

 the useful flux is reduced; in other words, the useful flux and 

 the useful torque are reduced with a given current input. As 

 a matter of fact, the maximum torque and the overload capacity 

 of an induction machine are essentially determined by its leakage 

 fluxes, or what amounts to the same thing, its leakage inductances. 



Knowing the primary and secondary leakage reactances, the 

 actual induction machine is replaced by an equivalent electric 

 circuit (or a circle diagram is drawn for it), after which its 

 performance can be predicted at any desired load. Tin* problem 

 in re is to determine the values of these leakage reactances and 

 inductances, from the given dimensions of a machine. The 

 rest of the problem is treated in the Electric Circuit. 



The leakages fluxes, which are indicated schematically in 

 Fig. 23, are shown more in detail in Fig. 54. The primary 

 conductors in one of the phases and under one pole arc marked 

 with dots, and the adjacent secondary conductors are mai 

 with crosses, to indicate the currents which are flowing in them. 



Assuming the rotor to be provided with a squirrel-cage 



