90 ALTERNATING CURRENTS 



Substituting 



As the line voltages in a Y-system are the differences of the 

 proper coil voltages (Page 80, Par. 45) 



Wi reads (e\ 62)1*1 

 and W% reads (e 3 62)1*3 



The same proof may be used for a delta-load, except that 

 ei -h e 2 + e 3 = 



It is shown in Pars. 45 and 46, that a phase difference of 30 

 exists between the line voltage and line current at unity power- 



O) 



Eao 



I ao 



FIG. 89. Vector diagram illustrating 2-wattmeter method for measuring 

 3-phase power, balanced load. 



factor. For power-factors other than unity, this phase difference 

 becomes (30 0), where 6 is the power-factor angle of the coil. 

 Figure 89 (a) shows two wattmeters, W\ and T7 2 , measuring 

 the power taken by a balanced three-phase, Y-connected load. 

 The wattmeter W\ is so connected that the current /& flows in 

 its current-coil and the voltage Eb a is across its potential-circuit. 

 Therefore, the reading of W\ is equal to the product of /&<,, 

 Eba and the cosine of the angle between this current and this 

 voltage. Figure 89 (6) gives the vector diagram of the load. 

 The three coil voltages E ao , E bo , and E co are all equal and 120 

 apart. The coil currents /, /&,, and I co are equal and lag their 

 respective coil voltages by the angle 6. The voltage Eb a is found 

 by reversing E ao , giving E oa , and then adding Ebo and E oa 



