12.2. Conductor sizeIt should be commonsense knowledge that liquids flow through largediameter pipes easier than they do through smalldiameter pipes (if you would like a practical illustration, try drinking a liquid through straws of different diameters). The same general principle holds for the flow of electrons through conductors: the broader the crosssectional area (thickness) of the conductor, the more room for electrons to flow, and consequently, the easier it is for flow to occur (less resistance). Electrical wire is usually round in crosssection (although there are some unique exceptions to this rule), and comes in two basic varieties: solid and stranded. Solid copper wire is just as it sounds: a single, solid strand of copper the whole length of the wire. Stranded wire is composed of smaller strands of solid copper wire twisted together to form a single, larger conductor. The greatest benefit of stranded wire is its mechanical flexibility, being able to withstand repeated bending and twisting much better than solid copper (which tends to fatigue and break after time). Wire size can be measured in several ways. We could speak of a wire's diameter, but since its really the crosssectional area that matters most regarding the flow of electrons, we are better off designating wire size in terms of area.
The wire crosssection picture shown above is, of course, not drawn to scale. The diameter is shown as being 0.1019 inches. Calculating the area of the crosssection with the formula Area = πr^{2}, we get an area of 0.008155 square inches:
These are fairly small numbers to work with, so wire sizes are often expressed in measures of thousandthsofaninch, or mils. For the illustrated example, we would say that the diameter of the wire was 101.9 mils (0.1019 inch times 1000). We could also, if we wanted, express the area of the wire in the unit of square mils, calculating that value with the same circlearea formula, Area = πr^{2}:
However, electricians and others frequently concerned with wire size use another unit of area measurement tailored specifically for wire's circular crosssection. This special unit is called the circular mil (sometimes abbreviated cmil). The sole purpose for having this special unit of measurement is to eliminate the need to invoke the factor π (3.1415927 . . .) in the formula for calculating area, plus the need to figure wire radius when you've been given diameter. The formula for calculating the circularmil area of a circular wire is very simple:
Because this is a unit of area measurement, the mathematical power of 2 is still in effect (doubling the width of a circle will always quadruple its area, no matter what units are used, or if the width of that circle is expressed in terms of radius or diameter). To illustrate the difference between measurements in square mils and measurements in circular mils, I will compare a circle with a square, showing the area of each shape in both unit measures:
And for another size of wire:
Obviously, the circle of a given diameter has less crosssectional area than a square of width and height equal to the circle's diameter: both units of area measurement reflect that. However, it should be clear that the unit of "square mil" is really tailored for the convenient determination of a square's area, while "circular mil" is tailored for the convenient determination of a circle's area: the respective formula for each is simpler to work with. It must be understood that both units are valid for measuring the area of a shape, no matter what shape that may be. The conversion between circular mils and square mils is a simple ratio: there are π (3.1415927 . . .) square mils to every 4 circular mils. Another measure of crosssectional wire area is the gauge. The gauge scale is based on whole numbers rather than fractional or decimal inches. The larger the gauge number, the skinnier the wire; the smaller the gauge number, the fatter the wire. For those acquainted with shotguns, this inverselyproportional measurement scale should sound familiar. The table at the end of this section equates gauge with inch diameter, circular mils, and square inches for solid wire. The larger sizes of wire reach an end of the common gauge scale (which naturally tops out at a value of 1), and are represented by a series of zeros. "3/0" is another way to represent "000," and is pronounced "tripleought." Again, those acquainted with shotguns should recognize the terminology, strange as it may sound. To make matters even more confusing, there is more than one gauge "standard" in use around the world. For electrical conductor sizing, the American Wire Gauge (AWG), also known as the Brown and Sharpe (B&S) gauge, is the measurement system of choice. In Canada and Great Britain, the British Standard Wire Gauge (SWG) is the legal measurement system for electrical conductors. Other wire gauge systems exist in the world for classifying wire diameter, such as the Stubs steel wire gauge and the Steel Music Wire Gauge (MWG), but these measurement systems apply to nonelectrical wire use. The American Wire Gauge (AWG) measurement system, despite its oddities, was designed with a purpose: for every three steps in the gauge scale, wire area (and weight per unit length) approximately doubles. This is a handy rule to remember when making rough wire size estimations! For very large wire sizes (fatter than 4/0), the wire gauge system is typically abandoned for crosssectional area measurement in thousands of circular mils (MCM), borrowing the old Roman numeral "M" to denote a multiple of "thousand" in front of "CM" for "circular mils." The following table of wire sizes does not show any sizes bigger than 4/0 gauge, because solid copper wire becomes impractical to handle at those sizes. Stranded wire construction is favored, instead.
WIRE TABLE FOR SOLID, ROUND COPPER CONDUCTORS
Size Diameter Crosssectional area Weight AWG inches cir. mils sq. inches lb/1000 ft =============================================================== 4/0  0.4600  211,600  0.1662  640.5 3/0  0.4096  167,800  0.1318  507.9 2/0  0.3648  133,100  0.1045  402.8 1/0  0.3249  105,500  0.08289  319.5 1  0.2893  83,690  0.06573  253.5 2  0.2576  66,370  0.05213  200.9 3  0.2294  52,630  0.04134  159.3 4  0.2043  41,740  0.03278  126.4 5  0.1819  33,100  0.02600  100.2 6  0.1620  26,250  0.02062  79.46 7  0.1443  20,820  0.01635  63.02 8  0.1285  16,510  0.01297  49.97 9  0.1144  13,090  0.01028  39.63 10  0.1019  10,380  0.008155  31.43 11  0.09074  8,234  0.006467  24.92 12  0.08081  6,530  0.005129  19.77 13  0.07196  5,178  0.004067  15.68 14  0.06408  4,107  0.003225  12.43 15  0.05707  3,257  0.002558  9.858 16  0.05082  2,583  0.002028  7.818 17  0.04526  2,048  0.001609  6.200 18  0.04030  1,624  0.001276  4.917 19  0.03589  1,288  0.001012  3.899 20  0.03196  1,022  0.0008023  3.092 21  0.02846  810.1  0.0006363  2.452 22  0.02535  642.5  0.0005046  1.945 23  0.02257  509.5  0.0004001  1.542 24  0.02010  404.0  0.0003173  1.233 25  0.01790  320.4  0.0002517  0.9699 26  0.01594  254.1  0.0001996  0.7692 27  0.01420  201.5  0.0001583  0.6100 28  0.01264  159.8  0.0001255  0.4837 29  0.01126  126.7  0.00009954  0.3836 30  0.01003  100.5  0.00007894  0.3042 31  0.008928  79.70  0.00006260  0.2413 32  0.007950  63.21  0.00004964  0.1913 33  0.007080  50.13  0.00003937  0.1517 34  0.006305  39.75  0.00003122  0.1203 35  0.005615  31.52  0.00002476 — 0.09542 36  0.005000  25.00  0.00001963 — 0.07567 37  0.004453  19.83  0.00001557 — 0.06001 38  0.003965  15.72  0.00001235 — 0.04759 39  0.003531  12.47  0.000009793 — 0.03774 40  0.003145  9.888  0.000007766 — 0.02993 41  0.002800  7.842  0.000006159 — 0.02374 42  0.002494  6.219  0.000004884 — 0.01882 43  0.002221  4.932  0.000003873 — 0.01493 44  0.001978  3.911  0.000003072 — 0.01184
For some highcurrent applications, conductor sizes beyond the practical size limit of round wire are required. In these instances, thick bars of solid metal called busbars are used as conductors. Busbars are usually made of copper or aluminum, and are most often uninsulated. They are physically supported away from whatever framework or structure is holding them by insulator standoff mounts. Although a square or rectangular crosssection is very common for busbar shape, other shapes are used as well. Crosssectional area for busbars is typically rated in terms of circular mils (even for square and rectangular bars!), most likely for the convenience of being able to directly equate busbar size with round wire.
