304 



ELECTRICAL ENGINEERING 



L 



183. Measurement of the Impedance of a Transformer. The 



equivalent primary resistance and react- 

 ance of a transformer can most easily 

 be obtained from a short-circuit test. 



If ESC is the impressed e.m.f. re- 

 quired to produce full-load current in 

 the short-circuited secondary, Fig. 278, 

 then ESC is the impedance drop in the 

 transformer at full load and 



Esc = hz = 7iVr 2 + x 2 , 



FIG. 278. Short-circuited 

 transformer. 



and the equivalent primary impedance is 



z = Vr*+~x 2 = ' 

 h 



The power factor may be obtained by connecting a wattmeter in 

 the circuit; it is 



Cos6sc = Wsc 



where Wsc is the power consumed in the transformer and includes 

 the primary and secondary full-load copper losses and a very small 

 iron loss which may be neglected. 

 The equivalent primary resistance is 

 r = z cos dsc, 

 or it may be obtained as 



_ Wsc _ I*TI + IZ^TZ _ 

 /i 2 = /i 2 



The equivalent primary reactance is 

 x = z sin dsc = Xi- 



Since the current densities in the two windings are approximately 

 the same, the copper losses are about equal, or 



/iVi = 7 2 V 2 



and, therefore, 



/~ \ 2 



r z (approximately). 



Similarly, since the leakage paths about the two windings are 

 similar and the m.m.fs. of the two windings are the same, the 

 leakage fluxes are approximately equal. But the inductance or 



