TRANSFORMERS 



295 



on account of the lag of flux due to hysteresis. This is shown in 

 Fig. 270. Curve (1) abed is a hysteresis loop for the transformer 

 iron, plotted with values of flux as ordinates on a base of exciting 

 current. Curve (2) is the sine wave of flux in the core and curve 

 (3) is the wave of exciting current. The method of obtaining 

 curve (3) can be seen from the figure. The maximum values of 

 flux and current must occur together; when the flux is zero the 

 current has a value oa and when the current is zero the flux has a 

 negative value og. 



(2) Flux to Core 



iting Current 

 Equivalent to (3 > 



FIG. 270. Exciting current. 



For purposes of analysis the current wave (3) is replaced by the 

 equivalent sine wave (4). The current wave (4) leads the flux 

 wave (2) by an angle a, which is called the angle of hysteretic 

 advance. If the eddy current loss is small enough to be neglected, 

 a = 90 , where cos is the no-load power factor. 



180. Leakage Reactances. Figs. 271 and 272 show the leak- 

 age paths around the windings of a "shell" type and "core" type 

 transformer. Since the low-voltage windings are placed next to 

 the iron, the leakage path surrounding the low-voltage winding is 

 of slightly lower reluctance than that surrounding the high-voltage 

 winding and the reactance is correspondingly larger. 



In the shell-type transformer the two windings are divided into 

 a number of sections and high-voltage and low-voltage coils placed 

 alternately to reduce the reactances. 



The reactance voltage of a transformer with full-load current is 

 about 10 per cent of the total voltage. If, therefore, full voltage 

 were impressed on a transformer primary with the secondary 

 short circuited about ten "-imes full-load current would flow. 

 When, however, full volta^ A impressed on the primary with the 



