296 ELEMENTS OF ELECTRICAL ENGINEERING. 



fore, almost wholly in the annual charge, including interest on 

 the cost of the wire, depreciation of the wire, and taxes thereon. 

 The advantage * of using large wires, on the other hand, lies in 

 the decreased loss of power in the wires. Therefore, the most 

 economical size of wire is that for which the additional annual 

 charge on a larger wire would exceed the annual value of the 

 power saved by the use of the larger wire, or, in other words, the 

 most economical size of wire is that for which the sum of the 

 annual charge on the total copper plus the annual value of the 

 power lost in the wires is a minimum. The annual charge may 

 be estimated at : interest 5 per cent., depreciation 3 per cent, 

 and taxes 1.5 per cent. 



The economic balance between loss of power and cost of cop- 

 per always leads to a definite number of circular mils of sectional 

 area of wire per ampere of current, without regard to the voltage 

 or to the distance of transmission. 



Electric power is to be supplied for h hours each year to a 

 customer. The cost of power at the switchboard is / dollars per 

 kilowatt-hour, the cost of copper is c dollars per pound, and the 

 interest charge on invested capital (including a small percentage 

 to cover the depreciation of copper wires and taxes) is / per cent, 

 per annum. It is required to find the sectional area of the cop- 

 per wire in circular mils per ampere of current on the condition 

 that any increase in the amount of copper would effect a saving 

 of power of which the annual value would be less than the inter- 

 est on the cost of the additional copper. Let 2/ be the length of 

 the wire in feet (equal to twice the length of the line), s its sectional 

 area in circular mils, R its resistance in ohms, W its weight in 

 pounds, and / the current in amperes. Then R 10.8 x 2ljs so 



that the lost power in kilowatts is - - - I 2 - and the annual loss 



1,000 s 



of energy is - F 2 h kilowatt-hours, of which the value at / 



1 ,000 s 



* It is to be kept in mind that we are not here considering the fact that in the con- 

 stant-voltage system the wires must be large enough to limit the voltage-drop. 



