Having calculated the circular mils of weight of a transmission line by the foregoing formulæ, it appears that the only material increase of this weight required by the use of alternating current is that due to inductance. This increase cannot be calculated exactly beforehand because of the uncertain elements in future loads, but experience shows that it is seldom more than ten per cent of the calculated size or weight of conductors.
Maximum power, voltage, loss, and weight of conductors having been fixed for a transmission line, the number of circuits that shall make up the line, and the relations of these circuits to each other, remain to be determined.
In practice wide differences exist as to the number and relations of circuits on a single transmission line between two points. Cases illustrating this fact are the 147-mile transmission from Electra power-house to San Francisco and the 65-mile transmission between Cañon Ferry, on the Missouri River and Butte, Mont. At the Electra plant the generator capacity is 10,000 kilowatts, and the transmission to San Francisco is carried out over a single pole line that carries one circuit composed of three aluminum conductors, each with an area in cross section of 471,000 circular mils. From the generators at Cañon Ferry, which have an aggregate capacity of 7,500 kilowatts, a part of the energy goes to Helena over a separate line, and the transmission to Butte goes over two pole lines that are 40 feet apart. Each of these two pole lines carries a single circuit composed of three copper conductors, and each conductor has a cross section of 105,600 circular mils. The difference in practice illustrated by these two plants is further brought out by the fact that their voltages are not far apart, as the Cañon Ferry and Butte line operates at 50,000, and the Electra and San Francisco line at 60,000 volts.
Economy in the construction of a transmission line points strongly to the use of a single circuit, because this means only one line of poles, usually but one cross-arm for the power wires per pole, the least possible number of pins and insulators, and the smallest amount of labor for the erection of the conductors. In favor of a single circuit there is also the argument of greatest mechanical strength in each conductor, since the single circuit is to have the same weight as that of all the circuits that may be adopted in its place. Where each conductor of the single circuit would have a cross section of less than 83,690 circular mils, if of copper, corresponding to a No. 1 B. & S. gauge wire, the argument as to mechanical strength is of especial force, since two equal circuits instead of one, in the case where one circuit of No. 1 wires would have the required weight, reduce the size of each conductor to No. 4 wire, of 41,740 circular mils cross section, and this is the smallest wire that it is practicable to use on long lines for mechanical reasons. Opposed to these arguments for a single circuit are those based on the supposed greater reliability of two or more circuits, their greater ease of repair, their more effective means of regulation, and the influence on inductance of a reduction in the size of conductors.