PRINCIPLES OF ALTERNATING CURRENT 217 



The inductance reaction = 2x/L7 = 188 X 0.517 = 97.2 volts. 



The resistance reaction = 7^ = 100X0.517 = 51. 7 volts. 



The resultant of these two reactions is equal to 

 A/97. 2 2 +51.7 2 = 110 volts and this serves to check the 

 accuracy of our calculation as we know that the sum of the 

 reactions must be equal to the impressed force. 



The pov/er factor of this circuit is equal to 



resistance reaction 51.7 

 cos$= =-7^7, = 0.47. 



total reaction 110 



The amount of actual power used in the circuit is equal 

 to / 2 # = 0.517 2 X 100 = 26.7 watts. The apparent power 

 (volts X amperes) used in the circuit is equal to 110X0.517 

 = 56.9 volt-amperes. As we know, 



watts 

 Power factor = 



volt-amperes 



~56.9~ 



which is the same as that obtained above and so checks 

 our calculations. 



Current Depends upon Frequency. If the frequency 

 impressed on the circuit were only 25 cycles, the reactance 

 would be only 2xX 25X0.5 = 78. 5 ohms, and the resistance 

 would be the same as it was before. The impedance would 

 be 127 ohms and the current would be 110/127 = 0.867 

 amperes. The power used would be PR = 75 watts and the 

 volt-amperes 110 X 0.867 = 95.4. The power factor would be 



= 0.787, which is greater than it was before. If the 

 95.4 



frequency were increased to 133 cycles the reactance would 

 be 418 ohms, the impedance 430 ohms, and the current 



=0.256 ampere. The power used in the circuit would 

 4oU 



be 6,56 watts and the power factor would be 0.233. 



