220 POLYPHASE CURRENTS. [Exr. 



ing end or a 4th wire return used, the potential of the line as a whole 

 will be raised by this electromotive force of triple frequency. 



APPENDIX III. 

 COPPER ECONOMY OF VARIOUS SYSTEMS. 



50. In figuring copper economy, it is to be assumed that all sys- 

 tems compared are to have the same line loss and per cent, resistance 

 drop. 



As a general principle, in any given system, the amount of copper 

 necessary varies inversely as the square of the voltage; thus, if the 

 voltage is doubled, the current will be halved and the copper reduced 

 to one fourth, increasing R four-fold. This gives the same RI 2 loss 

 in the line and the same per cent. RI drop. 



Any comparison of systems should, therefore, be made on the basis 

 of equal voltage; this may mean either the greatest voltage between 

 any two line wires or the voltage between any wire and the neutral. 

 This latter becomes more significant when the neutral is grounded. 



51. On the Basis of the Same Voltage E$ from the Line Wire to 

 Neutral. On this basis all symmetrical alternating systems give the 

 same copper economy, as will be seen from the following. Let us 

 consider all wires to be of a given size and to carry a given current /, 

 thus giving the same drop and loss per wire. We then have 



Single-phase, 2 wires: amount of copper 2; power = 2 Esl. 



Three-phase, 3 wires : amount of copper 3 ; power = 3 



Quarter-phase, 4 wires: amount of copper 4; power = 4 



n-phase, n wires : amount of copper n ; power = n 



The amount of power is seen to be proportional to the amount of 

 copper, giving therefore equal copper economy for all systems on the 

 basis of equal voltage between the line and the neutral or ground. 



52. On the Basis of the Same Voltage Between Line Wires. 

 Between line wires the voltage is 2Es for the single-phase (or 

 quarter-phase) system and V3^s for the 3-phase system. To make 

 the voltage between line wires equal in these systems, the voltage in 

 the 3-phase system can be increased in the ratio \/3 : 2. The amount 

 of copper can accordingly be reduced (see 50) inversely as the 

 square of this ratio, namely, 4 : 3. Hence, for the same line voltage, 

 a 3-phase system requires 75 per cent, as much copper as a single- 

 phase or quarter-phase system. 



