182 TREATISE ON ALTERNATING CURRENTS. 



where / is the current in amperes, given by 



EI= W 



in the case of continuous currents, or mono-phase currents with 

 power-factor unity. 



Let R be the total resistance of the line ; then for two line- 

 wires only 



where A is the cross-section of the line conductor, and p the 

 specific resistance. 



Also, the volume V of the conductor, which we will take to be 

 proportional to the cost, is given by 



therefore 



- 



We therefore have 



1 - E = El 



W_ 

 V ' E 



that is 



This shows that the volume of copper in the line-wires for con- 

 tinuous currents, or mono-phase currents with power-factor unity 

 for a given power to be transmitted over a given distance at a 

 given efficiency, is inversely proportional to the square of the 

 voltage of transmission. Thus the volume of copper required for 

 continuous currents and for mono-phase currents is the same. 



125. In the case of di-phase currents with four wires, it is 

 obvious that the current in each wire is one-half that of the 

 current in a mono-phase system with the same voltage for the 

 same power transmitted, so that the total volume of copper is 

 the same. 



When, however, di-phase currents with a common return are 



