ALTERNATING-CURRENT TRANSFORMER. 



through Xi and X t , F, and the leakage-fluxes fa and ^, respectively.* 

 We have then, 



(i) Xi = t lPl 



(2) X, = <f t P, 



Treating X t and Xi not as scalar quantities but as vectors, we may 

 write, 



(3) X l X* = F . R. 



133. The phase of the leakage-fields fa and fa is the same as that of 

 the magnetomotive forces which produce them, hence they are in 

 phase with the currents. 



134. Let Ei, Fig. 40, represent the voltage at the terminals of a non- 

 inductive resistance in the secondary of the transformer, then the cur- 

 rent will be in phase with E 3 . The magnetic field which is required to 

 produce by its variation, is Ft, in quadrature with E* The lines 

 of induction in phase with the secondary current, whose e. m. f. is in 

 quadrature with the current, are represented by 0. We shall first 

 treat the case in which these lines are all within the transformers, 

 and next we shall deal with the case of an external inductance or ca- 

 pacity. 



135. The flux F, as mentioned above, links together the primary and 

 secondary coils. The vector-sum of 0, and F is equal to F. 



136. If we neglect for the moment the lag of phase between the 

 magnetomotive force and the flux, then the magnetomotive force of 

 the magnetizing current is in phase with the flux F. It may be rep- 

 resented by the vector X. 



137. X must be the vector-difference between A'i and X*. 



138. Xi, X 2 , and X have real existence. 



139. The leakage-flux fa of the primary is in phase with the pri- 

 mary magnetomotive force X t , and may be represented in the diagram 

 by fa. The vector-sum of fa and F is equal to the total primary 

 flux F t . 



The notation of fluxes in this chanter is different from that of the preceding 

 chapters, the main flux being called /' instead of <t>. I hope that this reference 

 will prevent readers from making a mistake. 



75 



