240 



ELEMENTS OF ELECTRICAL ENGINEERING. 



O 



Let A, Fig. 205, be the primary coil, B the secondary coil, 

 and C the iron core of a transformer. As the (harmonic) alter- 

 nating currents in coils A and B pulsate in value, harmonically 

 varying fluxes are produced through the core and around each 

 coil. Let the line OC in the clock diagram, Fig. 206, represent 



the harmonically varying flux 

 through the core, let Op rep- 

 resent the harmonically vary- 

 ing flux which encircles coil 

 A, and let Os represent the 

 harmonically varying flux 

 which encircles coil B. The 

 fluxes Op and Os are pro- 

 portional to and in phase with 

 /' and I" respectively. But 

 I" is proportional to and op- 

 posite in phase to /', so that pOs, Fig. 206, is a straight line 

 and its length ps is proportional to /' and of course in phase 

 with /'. 



The total harmonically varying flux through coil A is the 

 vector sum of Op and OC which is Oa, and the total har- 

 monically varying flux through coil B is the vector sum of Os 

 and OC which is equal to Ob, but Oa is equal to the vector sum 

 of Ob and ba, and ba is parallel and equal to sp. Therefore 

 the flux Oa which passes through the primary coil can be con- 

 sidered to be made up of two parts, one of which Ob passes 

 through both coils, and the other of which ba passes through 

 the primary coil only and is proportional to and in phase with /'.* 



* The student will find that many writers on alternating current theory represent 

 the effects of magnetic leakage of transformers and induction motors as equivalent to 

 a certain reactance in the primary circuit together with a certain reactance in the 

 secondary circuit ; but when the effects of magnetizing current are ignored (and all 

 writers do ignore them because to take these effects into account in the discussion of 

 magnetic leakage leads to great complications which do not seem to be justified by the 

 requirements of practice) it is only possible to separate the effects of magnetic leakage 

 into two such reactances arbitrarily arid without any basis in fact. 



