The voltage drop of a conducting wire depends on both the electrical resistance of the wire and the amount of current carried. A wire's gauge determines its diameter and cross-sectional area. Wires with larger cross-sections have lower resistance values and therefore smaller voltage drops for the same current flow. The increased resistance arising from increasing a wire's length can be countered by using larger diameters for long wires.
The American wire gauge (AWG) look-up tables give the diameter of a round, solid wire for a given gauge. Increasing AWG values denote decreasing diameters. The cross-sectional area, A, of a round wire with diameter D is A = 3.14 x D-squared/4 = 0.785 x D x D.
The overall resistance R in ohms of an electric cord is given by the formula R = (rho x 2L)/A, where rho (ohm.ft) is the resistivity of the wire, A is its cross-sectional area (square ft.) and L is the length (ft.) of the cord. The formula uses 2L, since the current must travel to the electrical device and back again. The value of rho depends on the conducting material used and the internal temperature of the conductor. For copper, the value of rho in ohm.ft for a given temperature T (degrees C) is rho = 0.000000047622 + 0.000000000374803xT.
Ohm's law, VD = I x R, gives the voltage drop, VD, in volts for a conducting wire, where I is the current (amps) and R is the total resistance (ohms) of the wire. This equation is for direct-current (DC) circuits but also can be used for single-phase, alternating-current (AC) circuits with purely resistive loads (no inductive or capacitive elements).
A 25-ft., 16-gauge (0.004235 ft. diameter) cord with a copper conducting wire, an internal temperature of 70 degrees C (158 degrees F) and carrying a 10-amp current has a total resistance of 0.26 ohms and a voltage drop of 2.6 volts. A 50-ft., 16-gauge cord has a voltage drop of 5.2 volts, while a 50 ft, 14-gauge (0.005340 ft diameter) cord would have a voltage drop of 3.3 volts, assuming the same current and temperature.
For a standard 120-volt household outlet, the recommended voltage drop from the cord should be less than 3 percent (3.6 volts). Minimize the voltage drop by using the shortest possible cord. If a long cord is unavoidable, reduce the voltage loss by using a cord with a larger diameter (lower gauge) wire.
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