POLYPHASE CURRENTS. [Exp. 



were connected with its potential coil on the star voltage, the watt- 

 meter would read one third the total power; with its potential 

 increased 50 per cent. see Fig. 2, it will read one half the total 

 power.) 



38. The power factor is W -f- oz/z. The power factor 

 can be found from the tangent formula, by taking one reading, 

 Wi, of the wattmeter with the connections as described and a 

 second reading, W 29 with the potential circuit of the wattmeter 

 transferred to XY. 



W 2 EXY/Z sin W 2 



jjy- = = r ; hence tan = 0.866 ~- 

 W oz/zcos 9 W v . 



39. Two-reading Method. This is one of the simplest and 

 most satisfactory methods for measuring power and power fac- 

 tor with one wattmeter in a balanced 3-phase circuit. The 



current coil is connected in one line, as 

 Z, Fig. 7, one end of the potential circuit 

 being connected to the same line. The 

 other end of the potential coil is con- 

 nected, successively, to X and Y, and a 

 reading taken in each position. The 

 FIG. 7. Measuring power algebraic sum of the two readings gives 

 by two readings of one the total power. (The smaller readings, 

 wattmeter in a balanced w is considered negative whenever it 



3-phase circuit. 



is necessary to reverse the potential or 

 current coil of the wattmeter to obtain a proper deflection.) 



40. The proof of the method will be seen by referring to 

 Fig. 2, which assumes that voltages and currents follow a sine 

 law. The two readings of the wattmeter are 



W^ = EI cos (0 3 o); W* = EI cos (0 + 3 o). 



Hence, the sum of the two readings gives the total power, 27. 



41. The power factor (cos0) is determined from the tangent 

 formula, 28, 



