PHASE METERS 539 



At unity power factor the current in the fixed coil is in time 

 phase with the voltage Vao or the current I ao , so taking Vao 

 as the datum for phase displacement, 



c 

 FIG. 322. Connections for Punga power-factor meter. 



Field due to fixed coil = KI sin (co* 6) 

 Current in coil ao = I' sin co* 



Current in coil bo = I' sin (cot 120) 



Current in coil co = /'sin (co* 240). 



For equilibrium the net turning moment due to the three coils 

 must be zero, and 



T 



sin D JT, I sin (co* 6) sin utdt 

 1 Jo 



+ sin (D - 120) * ("sin (co* - 0) sin (co* - 120) dt 

 1 Jo 



+ sin (D - 240) -* \ sin (co* - 61) sin (co* - 240) dt = 0. 

 1 Jo 



Integrating and substituting the values of the functions of 

 120 and 240, 



% cos 6 sin D - % cos D sin = 



.'. D= 0, 

 the same result as was obtained with the two crossed coils. 



Power -factor Charts. In tests of industrial plants, it is fre- 

 quently important to gain an idea of the power factor under 

 ordinary operating conditions. In three-phase work the two 

 wattmeter method of measuring power will usually be employed. 

 For a balanced load the power indicated by the two wattmeters is 



P! = El cos (0 + 30) 

 P 2 = El cos (0 - 30). 



