What minimum size copper wire is needed for a 120-volt single-phase branch circuit supplying a 30-ampere load at a distance of 205 feet to limit the voltage drop within the recommended Code limit?

To determine the minimum size of copper wire needed for a 120-volt single-phase branch circuit supplying a 30-ampere load, while considering the distance of 205 feet and the voltage drop limits prescribed by the National Electrical Code (NEC), it's essential to calculate the voltage drop for each wire gauge and find the one that keeps the voltage drop within acceptable limits.

The voltage drop can be calculated using the formula:

[

\text{Voltage Drop (V)} = \frac{2 \times \text{Length (ft)} \times \text{Current (A)} \times R}{1000}

]

Where ( R ) is the resistance per 1000 feet of the wire, which varies by gauge. For copper wire, the resistance values are approximately:

• 10 AWG: 1.24 ohms

• 8 AWG: 0.778 ohms

• 6 AWG: 0.391 ohms

• 4 AWG: 0.246 ohms

• 3 AWG: 0.197 ohms

• 2 AWG: 0.156 ohms

Using this formula, we calculate the voltage drop for each gauge using