214 



THE MAGNETIC CIRCUIT 



[ART. 64 



secondary windings on the core alternately. At a given voltage, 

 and with a given type of construction, the spacing a between 

 the coils may be considered as constant and independent of the 

 number of sections. In transformers for extra-high voltages a 

 is large as compared to ^(bi-}-b 2 ), so that the leakage reactance 

 is almost inversely proportional to the number of sections q. 

 In low-voltage transformers a is small as compared to 61 and 

 6 2 ; hence, L^ is almost inversely proportional to q 2 , because 

 &! and 6 2 are themselves inversely proportional to q. Thus, 



FIG. 51. The leakage field in a transformer with flat coils. 



in general, the inductance of a transformer is inversely pro- 

 portional to q n ) where n has a value between 1 and 2. 1 



Dr. W. Rogowski has given an exact mathematical solution 

 for the flux distribution in the case of flat transformer coils, 

 assuming the coils and the core to be indefinitely long in the 

 direction perpendicular to the cross-section shown in Fig. 5 1. 2 



1 For experimental data in regard to the effect of the subdivision and 

 arrangement of transformer windings upon the leakage reactance see Dr. W. 

 Rogowski, Mitteilungen Ueber Forschungsarbeiten, Heft 71 (Springer, 1909), 

 p. 18, also his article Ueber die Streuung des Transformators, Elektrotechnische 

 Zeitschrift, Vol. 31 (1910), pp. 1035 and 1069; also Faccioli, Reactance of 

 Shell-type Transformers, Electrical World, Vol. 55 (1910), p. 941. 



2 Dr. W. Rogowski, loc. cit. 



