Il6 ELEMENTS OF ELECTRICAL ENGINEERING. 



Furthermore, 4/? 2 / 2 2 is the power lost in the two-phase line, and 

 is the power lost in the three-phase line, so that 



Therefore, using equation (a), we have 



That is, the wires have the same resistance and therefore the same 

 weight, and, since four wires are used in the two-phase line and 

 only three wires in the three-phase line, it follows that the total 

 weight of copper in the two-phase line is times as great as in 

 the three-phase line. The same result is reached on the basis of 

 equal percentage drops of electromotive forces in the two sys- 

 tems. The result is independent of the power factor of the re- 

 ceiving circuits provided the power factor is the same for both 

 systems. 



The three-wire two-phase transmission line requires less copper 

 than the three- wire three-phase line in the ratio 2.914 to 3, but 

 the three-wire two-phase arrangement is not desirable for reasons 

 explained in Art. 49, and, furthermore, a three-wire two-phase 

 line with "-volts between the middle wire and each outside wire 

 has 1/2 E- volts between the outside wires, whereas, in a three- 

 wire three-phase line with ^-volts between any two wires, there 

 is no higher voltage than E anywhere in the system. Therefore, 

 it is unfair to compare the three-phase system with the three-wire 

 two-phase system on the basis of equal voltages E. 



On account of the greater copper economy and on account of 

 the use of three wires instead of four, the three-phase system is 

 nearly always used for long distance transmission. 



