Wire Loss Calculator

Electricity is useless without a way to move it around, so in order to accomplish that task people invented the wire. A wire is nothing more than a conductor wrapped up in a jacket of insulation, originally cloth but now made of plastic. This insulation prevents conductors from making unwanted contact and causing short circuits, and it also prevents you from making unwanted contact with a conductor and shocking yourself. In general there are two types of wires:

The first type of wire is called solid wire, and this consists of a solid piece of copper or aluminum wrapped up in some insulation. Solid wire is cheap to make and sell, and that’s why they it’s used for wiring houses. It has a downfall however, and that downfall is that it is stiff and fragile. It is stiff because it’s a large strand of metal, and it is fragile due to metal fatigue. Simply put, if you bend it enough it’ll break.

The second type of wire is called stranded wire, and this type is used when a the conductor needs to be flexible. Inside stranded wire are small strands of metal. These strands are easier to flex and can withstand more bending than a solid wire, so this type of wire is used in cables and computers. The more strands a wire contains, the bendy-er it is. The flexibility of stranded wire can vary from pretty stiff to wet noodle, depending on the the wire’s insulation and the number of strands. Although rather uncommon, silicone insulation is the most flexible.

Since we live in a world of standards the thickness of a wire is called it’s gauge, more specifically the American Wire Gauge (AWG). The smaller a wire’s AWG, the larger the wire’s diameter. Typical wires are 12, 14, 16, 18, and 20AWG, but this goes all the way down to the 4/0 (- 4AWG) wire used in power plants and up to the 40AWG wire used inside earbuds. A chart exists to the right that relates wire diameter to AWG, and tools also exist for measuring AWG directly. But why is AWG important? Why give a damn?

A damn should given because wire is not perfect; it has some resistance. Resistance is the opposition to current flow in a conductor, and when there is resistance there is also heat. This is because some voltage is lost in a conductor with resistance, and when voltage is lost power is lost. That power can’t just disappear, so it turns into heat.

The thinner a wire is the more resistive it is due to the smaller cross sectional area of the wire. With a smaller CSA there are less atoms available for electrons to jump around on, and that makes the wire more resistive. The current-carrying limit of a wire is called it’s ampacity, and there is even a chart for that. Problem is, aside from house electricians few use that chart as it’s very conservatively rated. Real engineers calculate acceptable ampacity themselves using a resistivity table.

Using ohm’s law one can figure out the power dissipated in the wire by using the calcrula above. Power is P = I²R so if we had to push 15 amps through 25 feet of 14ga extension cord, we’d dissipate 0.06313ohms * 15amps² = 14.2watts one way through the cord, and another 14.2W on the return path. A total of 28.4 watts would be lost as heat through the cord. It’ll get a bit warm, but it won’t melt.

There’s another issue with wire resistance we have to be concerned about and that is voltage loss through the wire. As you now know, pushing more current through a wire will dissipate more power, and when you dissipate power you are also dissipating voltage. In order to calculate how much voltage is lost in a length of wire you find the wire’s resistance, then multiply that by current (E = I * R). Using our 25 foot extension cord, we’d find that pushing 15A through that would cause 0.94V to be dropped one way. This leads to a total voltage loss of 1.88V since the electricity has to return through the other wire in the cord as well.

Now what happens when you lose too much power in a wire? Well not only will the load fail to work due to reduced voltage, but the wire will heat up, sometimes to the point where the insulation melts. This creates the potential for shorts and shocks and fires, so in aid of preventing that manufacturers usually print wires with a working temperature range, often -30°C to 170°C. It is ideal to keep a wire as cool as possible because resistance increases as the wire heats, and as resistance increases voltage loss does the same.

In order to prevent wiring from being overloaded, fuses are used. A fuse is nothing more than a thin piece of wire that burns out before the rest of the wiring does. Fuses have a current rating, and too many amps start to flow the element inside the fuse will burn out. It’s important to never use a bigger fuse than directed in a fusebox, for if you do and there is a short the fuse might not burn out fast enough and your wiring will be damaged.

Now there is one last type of wiring that you may see, and that is the busbar. A busbar is nothing more than a copper or aluminum strip, and it is used to carry very high currents, typically 200 amps or more. They are used where wires would either be too large or too costly to be practical. Busbars are neat because they have what I call “selective insulation.” By this I mean, bus bar will electrocute uninformed people, yet leave most others alone. Note that, such insulation also does not work where there is no light. See the associated image if you don’t understand what I mean. ∎