Final answer:
For a 3 HP 240 volt single phase motor with an 80% power factor, a #12 copper wire is necessary. This wire size provides a margin for the calculated 11.625 amps full-load current and adheres to safety standards.
Step-by-step explanation:
To determine the appropriate wire size for a 3 HP 240 volt single phase motor with an 80% power factor, we need to first calculate the full-load current the motor will draw. The horsepower to current formula for single-phase motors is I = (746 * HP) / (V * η * PF), where I is the current in amps, HP is the horsepower, 746 is the number of watts in one horsepower, V is the voltage, η is the motor efficiency (which we'll assume to be 100% for this calculation as it's not provided), and PF is the power factor.
Let's calculate the full-load current for a 3 HP motor: I = (746 * 3) / (240 * 1 * 0.8) = 11.625 amps. Now that we have the current, we can refer to the National Electric Code (NEC) tables to find the suitable wire size. Typically, a #14 wire is rated for 15 amps, #12 for 20 amps, #10 for 30 amps, and #8 for 40 amps.
In this case, a #12 copper wire would be more than adequate for the load of 11.625 amps, providing a safe margin under its 20 amp rating. Choosing a wire that is too small could cause excessive heat buildup and potentially result in a fire hazard. It is also good practice to consider voltage drop, especially over long distances, and further derate the wire size if necessary. However, with the information provided, #12 gauge is the correct answer.