184 TREATISE ON ALTERNATING CURRENTS. 



currents required 0*729 of the copper necessary in mono-phase 

 current transmission. 



126. In the case of a tri-phase installation, mesh-wound, the 



current in each limb of the mesh is 7= the current, /, in the line 

 (see 104). The power absorbed in one limb is, therefore, ~~7IE 



where E is the voltage between the lines. The total power 

 transmitted is, therefore, \/3IJE. Hence, if the same power is 

 transmitted, as by a mono-phase system, the tri-phase current per 



line-wire is ^ where / is the mono-phase current. Now let R 



be the resistance of each of the mono-phase wires, and E\ that of 

 each of the tri-phase wires ; then for the same loss 



= ZR~ = RP 



o 



that is 



or each of the wires on the tri-phase system has one-half the cross- 

 section of each wire on the mono-phase system. That is, the volume 

 of copper required in the tri-phase system, mesh-wound, is 075 that 

 required on the mono-phase system for the same voltage between 

 the lines, the same power transmitted, and the same loss in the lines. 



Consider now a tri-phase system star- wound. 



In this case the voltage between any two line- wires is \/3 times 

 the voltage in one limb of the star while the current in any line- 

 wire is the same as that in the corresponding limb. 



If, therefore, E is the voltage between any two line- wires, the 

 whole power transmitted is \/3EI. Hence, as in the case of a 

 mesh- wound system, the amount of copper required is 0'75 times 

 that required in a mono-phase system with the same voltage, 

 distance, efficiency, and power transmitted. 



127. "We can tabulate these results as follows : 



COMPARISON OF AMOUNTS OF COPPER REQUIRED FOR LINE-WIRES FOR TRANSMIS- 

 SION OF SAME AMOUNT OF POWER, AT THE SAME LINE VOLTAGE OVER EQUAL 

 DISTANCES, AT THE SAME EFFICIENCY. 



Continuous currents ............. 1 



Mono-phase currents ............. 1 



Di-phase currents with four wires ........ 1 



Di-phase currents with three wires ........ 0*729 



Tri-phase currents with mesh-grouping ...... 0*75 



Tri-phase currents with star-grouping ...... 0*75 



