POLYPHASE POWER 399 



Then we may put 



P 

 so that 



The loss of power, single-phase Iine = 

 The loss of power, three-phase line = 



These two losses must be equal if the efficiency of the 

 two systems is to be the same, hence 



Putting for Is its equivalent, /i/A/3, we have 



or 



If the cross-section of the wire for the single-phase line 

 is A i and for the three-phase line AS, we may put 



At 

 A a =-, 



There are two wires for the single-phase line and three 

 wires for the three-phase, so that the total cross-section 

 of copper for the single-phase line is 2Ai and for the three- 

 phase line 3 As- 



Hence, the total cross-section of the line for 



Single-phase 



= 2Ai, 

 and for three-phase 



