150 



SYNCHRONOUS MOTORS 



M.M.F., since these are proportional to each other in magnitude and 

 bear to each other a fixed phase relation. 



E.g., in Fig. 72 there are shown vectors which represent three 

 M.M.F.'s, A,.F, and their resultant R, each one of which would, 

 under the above assumption, produce a flux of the same phase and 

 proportional in magnitude. These fluxes &A&F and their resultant 

 <$> are shown in Fig. 73, as well as the corresponding E.M.F.'s EA', 

 Ep', and 2', which would be induced by the cutting of the armature 

 conductors through these fluxes, and which are 90 behind their 

 respective fluxes. There are thus three M.M.F.'s, three fluxes, and 

 three E.M.F.'s, each set being proportional to the other two, and 



FIG. 72. 



the three triangles representing the relations between the elements 

 of the three sets being similar. 



E.M.F. Diagram 



In Fig. 73 Ep, E A , and E\ are the parts of the impressed E.M.F. 

 consumed by the induced E.M.F.'s Ep', E A ', and 2' respectively, 

 just as Ir and Ix are the parts of the induced E.M.F. consumed by 

 resistance and leakage reactance. Moreover, since EA is propor- 

 tional to and in quadrature with A (and therefore /), it is in phase 

 with Ix and may be written, 



EA=!*A, 



where X A (the constant of proportionality) is an equivalent reactance 

 representing the armature M.M.F. The sum x+x A = X is called 



