Solving the last equation for the unknown quantity, the following equation is obtained for size of wire:
[Illustration: FIGS. 830 and 831.—Symmetrical and unsymmetrical distribution. When a main is supplied by a feeder, the junction of the two, if practicable, is located at the electrical center of the main, as indicated in fig. 830, so that the distribution is symmetrical, that is, the ampere feet each way from the junction are the same. This is nearly always practicable in surface wiring, and when it is practiced it is only necessary to calculate the wire size for one-half of the main, as the other half is identical. In fig. 830 there are four lamps on each side of the junction, J; the center of each group is at a distance, M, so that the lamp feet in each half of the main are 5 × M. The lamp feet of the feeder would be 10 × N, N being the distance from the feeder fuse block to the junction, J. In concealed work, however, it does not always happen that a feeder can be made to join a main at its electrical center; when this is not practicable, each end of the main should be figured separately. In fig. 831, for instance, the main has five lamps on one side and two on the other, and the distances from the junction to the centers of the two groups are at unequal distances S and S'. If the distance S be 14 feet, and the lamps, 16 c. p., the lamp feet in the left hand main equals 5 × 14 = 70, while in the main to the right, taking S' at 10 feet, there are only 2 × 10 = 20 lamp feet. Hence what appears to be one continuous main in this case would have to be treated as two mains, and each part figured separately.]
I × feet × 21.6 amperes × feet × 21.6 circular mils = ———————————————- = ————————————————————— (5) E "drop"
The following practical example is given to illustrate the application of the formula just obtained:
EXAMPLE.—What size wire should be used on a 250 volt circuit to transmit a current of 200 amperes a distance of 350 feet to a center of distribution with a loss of three per cent. under full load?
The volts lost or drop is equal to 250 × .03 = 7.5 volts.
+————————+————————+——————————+—————————————————————————————+———————————————————————-+ | Number |Diameter| Area in | Weight in pounds | Resistance at 68° Fahr.| |of gauge| in | circular |——————————————————————————————————————————————————————| |B. & S. | mils | mils | 1,000 feet| mile |feet per| 1,000 feet | mile | | | | | | | pound | | | +————————+————————+——————————+———————————+—————————————————+———————————————————————-+ | 0000 | 460 | 211,600 | 640.5 |3,381 | 1.561 | .04893 | .2583 | | 000 | 409.6 | 167,800 | 508 |2,682 | 1.969 | .06170 | .3258 | | 00 | 364.8 | 133,100 | 402.8 |2,127 | 2.482 | .07780 | .4108 | | 0 | 324.9 | 105,500 | 319.5 |1,687 | 3.130 | .09811 | .5180 | | | | | | | | | | | 1 | 289.3 | 83,690 | 253.3 |1,337 | 3.947 | .12370 | .6531 | | 2 | 257.6 | 66,370 | 200.9 |1,062 | 4.977 | .1560 | .8237 | | 3 | 229.4 | 52,630 | 159.3 | 841.1 | 6.276 | .1967 | 1.0386 | | 4 | 204.3 | 41,740 | 126.4 | 667.4 | 7.914 | .2480 | 1.3094 | | | | | | | | | | | 5 | 181.9 | 33,100 | 100.2 | 529.0 | 9.980 | .3128 | 1.6516 | | 6 | 162.0 | 26,250 | 79.46 | 419.5 | 12.580 | .3944 | 2.0824 | | 7 | 144.3 | 20,820 | 63.02 | 332.7 | 15.87 | .4973 | 2.6257 | | 8 | 128.5 | 16,510 | 49.98 | 263.9 | 20.01 | .6271 | 3.3111 | | | | | | | | | | | 9 | 114.4 | 13,090 | 39.63 | 209.2 | 25.23 | .7908 | 4.1754 | | 10 | 101.9 | 10,380 | 31.13 | 166.0 | 31.82 | .9972 | 5.2652 | | 11 | 90.74| 8,234 | 24.93 | 131.6 | 40.12 |1.257 | 6.6370 | | 12 | 80.81| 6,530 | 19.77 | 104.4 | 50.59 |1.586 | 8.374 | | | | | | | | | | | 13 | 71.96| 5,178 | 15.68 | 82.79| 63.79 |2.000 | 10.560 | | 14 | 64.08| 4,107 | 12.43 | 65.63| 80.44 |2.521 | 13.311 | | 15 | 57.07| 3,257 | 9.858 | 52.05|101.4 |3.179 | 16.785 | | 16 | 50.82| 2,583 | 7.818 | 41.28|127.9 |4.009 | 21.168 | | | | | | | | | | | 17 | 45.26| 2,048 | 6.200 | 32.74|161.3 |5.055 | 26.690 | | 18 | 40.30| 1,624 | 4.917 | 25.96|203.4 |6.374 | 33.655 | | 19 | 35.89| 1,288 | 3.899 | 20.59|256.5 |8.038 | 42.440 | | 20 | 31.96| 1,022 | 3.092 | 16.33|323.4 |10.14 | 53.540 | +————————+————————+——————————+———————————+—————————————————+———————————————————————-+