6-B] 



MEASUREMENT OF POWER. 



231 



power factor (0 = o), the three line currents are shown by the 

 heavy arrows /x, /Y, /z. The dotted arrows show these currents 

 for lower power factors, = 30, = 6o and = 90. 



0=60 



FIG. 2. Currents and voltages in a balanced 3-phase system. 



If two wattmeters are connected as in Fig. I, wattmeter (i) 

 has a current /x in its current coil and a voltage Exz across its 

 potential coil, the phase difference between this current and 

 voltage being 6 30. The component of /x in phase with Exz 

 is, accordingly, /x cos (0 30) ; hence writing E for Exz and 

 / for /x wattmeter (i) reads 



WI = E! cos (0 30) =EI (cos 30 cos + sin 30 sin 0). 



In a like manner, wattmeter (2) has a voltage EYZ and a cur- 

 rent /Y, having a component 7y cos (6 -f- 30) in phase with EYZ. 

 Hence writing E for yz and / for 7y wattmeter (2) reads 



W 2 = EIcos (0 + 3o)=E7 (cos 30 cos (9 sin 30 sin 6). 

 Adding W z to W it we have 



W i +W 2 = 2EI cos 30 cos e = V^EI cos 0, 



