210 THE MAGNETIC CIRCUIT [ART. 64 



The leakage fluxes induce e.m.fs. in the windings in lagging 

 quadrature with the respective currents, and thus affect the 

 voltage regulation of the transformer. That part of the applied 

 voltage which balances these e.m.fs. is known as the reactance 

 drop in the transformer. It is customary to speak about the 

 primary reactance and the secondary reactance, also about the 

 primary and the secondary leakage fluxes, as if they had a 

 separate and independent existence. However, it must be under- 

 stood that each leakage flux is produced by the combined action 

 of both windings, as is explained above. Moreover, where the 

 leakage fluxes enter the iron they combine with the main flux 

 in the proper direction, so that they form there only a com- 

 ponent of the resultant flux. 



In reality, the primary ampere-turns are not exactly equal 

 and opposite to the secondary ampere-turns, so that, in addition 

 to the leakage fluxes shown in Fig. 50, there is a leakage flux 

 due to the magnetizing ampere-turns. However, this correction 

 is negligible, when the load is considerable, and the calculation 

 of the leakage flux is greatly simplified by assuming the primary 

 ampere-turns to be exactly equal and opposite to the secondary 

 ampere-turns. 



The effect of the leakage reactance upon the performance 

 of a transformer is treated in The Electric Circuit; there the 

 value of the reactance is supposed to be given. Here the problem 

 is to show how to calculate the leakage inductance from the given 

 dimensions of a transformer. The two types of winding to be 

 considered are the one with cylindrical coils (Fig. 50) and the 

 one with flat coils (Fig.51). Both types of winding can be used 

 with any of the three kinds of magnetic circuit which are used 

 with transformers (Figs. 12, 13, and 14). 



The problem of calculating the leakage inductance, according 

 to the fundamental formula (106), is reduced to that of finding 

 the permeances of the individual paths of the leakage flux. It 

 would l)e out of the question here to determine the actual paths 

 and to express their permeances mathematically. Therefore, in 

 accordance with Dr. Kapp's proposal, 1 simplified paths are 

 assumed, shown in Fig. 50 to the right. The inductance so 

 calculated is corrected by an empirical factor, obtained from 

 experiments on transformers of similar type and proportions. 

 1 G. Kapp, Transformers (1908), p. 177. 



