300 



ELECTRICAL ENGINEERING 



an equivalent primary resistance and x = x\ + ( - J x z is the react- 

 ance of the transformer expressed as an equivalent^ primary 

 reactance. 



*i 



FIG. 276. Simplified circuit diagram of a transformer. 



Referring to Fig. 277, which is the vector diagram of the circuit 

 in Fig. 276, 



#1 = &E cos + 7iA + j (- E sin 6 + !&} 

 and in absolute values 



E! = y/^ E cos 6 + ArY + ^ ^ sin + /i*Y. (290) 

 By substituting for 7i the value 7 2 , equation 290 becomes 



(291) 



which shows the relation between the secondary terminal voltage 



and secondary current for a given 

 primary impressed e.m.f. and 

 a given secondary load power 

 factor. 



182. Examples. 7. A step- 

 down transformer with a ratio 

 i, of turns of 10 : 1 delivers 100 

 kilowatts at 2000 volts to a re- 

 ceiver of power factor 80 per 

 cent lagging. Determine the primary impressed voltage, the cur- 

 rent and the power factor. 

 The primary impedance is 



zi = n +jxi = 50 + 80 j ohms. 



FIG. 277. 



