6-B] MEASUREMENT OF POWER. 237 



By referring to Fig. 3, power factor can be found directly 

 from the ratio W 2 -f- W . 



42. When there is an appreciable difference between the 

 phase voltages (which we may term E and E 2 ) across which the 

 potential circuit is connected when W^ and W 2 are read, a more 

 accurate value of power factor will be obtained by correcting 

 W v or W z by direct proportion to obtain values correspond- 

 ing to equal voltages. The ratio W z -=- W^ then becomes 

 EiWz -f- E 2 W^. The power factor thus determined is quite 

 accurate, being independent of the calibration of any instrument 

 and of any slight inequality in the phases. Even for an un- 

 balanced load, it gives accurately the value of cos 6 for /z, where 

 6 is the phase difference between /z and the voltage OZ (Fig. 2) 

 midway in phase between XZ and FZ. The method is more 

 accurate with one than with two wattmeters, 28. 



43. Power Factor by Sine Method. The power factor of a 

 balanced 3-phase circuit can be determined by the sine method 

 ( J 3) with only a single reading of voltmeter, ammeter and 

 wattmeter. The method does not require the neutral to be 

 available, nor does it require any auxiliary resistances or other 

 devices. 



Representing the three line wires as X, Y and Z, the ammeter 

 and the current coil of the wattmeter are connected in one line, 

 as Z. The voltmeter and the potential coil of the wattmeter 

 are connected across the other two lines, X and Y. The watt- 

 meter reading gives the wattless or quadrature volt-amperes, 



sin 0, 

 from which 6 and cos are determined. 



