92 



ALTERNATING CURRENTS 



Another convenient method for determining the power-factor 

 from the wattmeter readings is to divide the smaller wattmeter 

 reading by the larger, 



W, _ cos (30 + 0) 



W[ " cos (30 - B) 



and then to use the curve shown in Fig. 90. 



This curve is plotted with the ratio ^ against power-factor. 



When W 2 /Wi = 1.0, the power-factor is 1.0; when Wt/Wi = 

 0, the power-factor is 0.5; when W 2 /Wi is negative, that is, it 

 becomes necessary to reverse Wz, the power-factor is less than 

 0.5. By means of a curve like that of Fig. 90, the power- 

 factor maybe read directly from the ratio of the two wattmeter 

 readings. 



1.0 



THREE-PHASE POWER-FACTOR 



BALANCED SYSTEM 

 TWO-WATTMETER METHOD 



1.0 





1.0 -.9 -.8 -.7 -.6 -.5 -.4 -.3 -.2 -.1 +.1 +.2 +.3 +.4 +.5 +.6 +.7 +.8 + .9+1.0 



Smaller Reading Co3(0 + 30) 

 m Larger Reading Cos (0-30) 



FIG. 90. Power-factor diagram, 2- wattmeter method. 



Example. In a test of a three-phase induction motor, two wattmeters 

 are used to measure the input. Their readings are 1,900 and 800 watts 

 respectively. Both instruments are known to be reading positive. What is 

 the power-factor of the motor at this load ? 

 Using equation (34) 



1,900 - 800 AJ 1,100 n - n , 

 tan e = ^900 + 800 = ^2/700 = a706 



e = 35.3 



cos 6 = cos 35.3 = 0.815. Ans. 

 This result may be checked by Fig. 90. 



If a polyphase wattmeter is used (page 60, Fig. 57), the adding 

 or subtracting is done automatically, as both elements of the 

 instrument act on the same spindle. Therefore, the polyphase 



