THE TRANSFORMER. 207 



and t 



rT _E^ 



RI"~ E" 

 But 



E 9 N' 



E" = W r 

 and 



// TV 7 ' 



so that 



_ N ' 



Example of the use of the ideas of equivalent primary resistance 

 and reactance. A 10:1 step-down transformer has a resistance 

 of 150 ohms and a reactance of 100 ohms connected in series 

 with its primary coil which takes current from 2,000 volt supply 

 mains, and the secondary coil of the transformer delivers current 

 to a receiving circuit of which the resistance is 2.5 ohms and the 

 reactance is 2.0 ohms. Required the values of /', I", E', E" , 

 and all the phase angles. Multiplying 2.5 ohms (= R) and 

 2.0 ohms (= X) by (--f-) 2 we have the primary equivalent 

 values, namely, 250 ohms (= r) and 200 ohms (= x), so that 

 the primary current flows, as it were, through a circuit of which 

 the resistance is 150 ohms + 250 ohms and of which the react- 

 ance is 100 ohms + 200 ohms. That is, the impedance of this 

 equivalent simple circuit is i/(4OO) 2 -f (soo) 2 = 500 ohms, so 

 that the current is 2,000 volts -7- 500 ohms or 4 amperes. Tak- 

 ing this current as the reference axis, the components of the 

 supply voltage are 4 amperes x 400 ohms = 1 ,600 volts parallel 

 to the current and 4 amperes x 300 ohms = 1,200 volts perpen- 

 dicular to the current ; the components of E 1 are 4 amperes 

 X 250 ohms = 1,000 volts parallel to the current and 4 

 amperes x 200 ohms = 800 volts perpendicular to the current ; 



