Cable Length vs. Power Drop

Cable Length vs. Power Drop
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The power drop, or power lost in a cable, depends on the cable length, cable size and the current through the cable. Larger cables have less resistance and can therefore transmit more power without large losses. Losses in smaller cables remain low if the amount of power transmitted is small, or if the cable is not very long. Engineers have to design the power system so that the power loss in the cables is acceptable for the length of cable required to supply the load.

Basics

Electric cables have a resistance per foot, and the longer the cable, the larger the resistance. When current flows through the cable, the current flowing through the resistance results in a voltage drop according to Ohm's law, voltage = current x resistance. Power in watts is voltage x current. A given current and cable resistance defines the applicable voltage drop. If it is 10 volts for a current of 10 amps, the power lost in the cable is 100 watts.

Cable Size

Larger cables have less resistance per foot than smaller cables. Typical household wiring is AWG 12 or 14 gauge with resistances of 1.6 and 2.5 ohms per 1000 feet. For a typical residence, a run of cable might be up to 50 feet. The corresponding resistances for these common cable sizes are 0.08 and 0.13 ohms. The larger cable has a resistance 36 percent less than the smaller cable and will lose 36 percent less power. For longer cable runs, such as outdoor connections, AWG 10 gauge cable with a resistance of 1 ohm per 1000 feet will have a power drop 60 percent less than the 14 gauge cable.

Voltage

While the resistance of the cables shows which cable will lose the least power, the power lost in watts is determined by the voltage drop. For 100-foot runs, the resistances of AWG 10, 12 and 14 gauge cables are 0.1, 0.16 and 0.25 ohms. A household circuit is rated 15 amps. A 15-amp current through 100 feet of these cables would result in voltage drops of 1.5, 2.4 and 3.75 volts respectively.

Power

The voltage drop multiplied by the current gives the power in watts. The three cable runs of 100 feet, carrying 15 amps, will have power drops of 22.5, 36 and 56.25 watts for the 10, 12 and 14 gauge cables respectively. This power heats up the cable, and the voltage drop reduces the voltage available for the load. A voltage drop of 3.6 to 6 volts gives an acceptable power drop for a 120-volt circuit. The AWG 14 gauge cable is borderline, as is evident from the power loss that is more than that of a 40-watt light bulb.

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