The smallest branch conductor size that can be used for a motor with the given specifications is ___ AWG.

To determine the smallest branch conductor size for a motor, it’s essential to consider the motor's specifications such as the full-load current, the type of motor, and applicable electrical codes, especially the National Electrical Code (NEC) guidelines.

In this context, the smallest size of 8 AWG wire is appropriate because 8 AWG wire can safely carry the current associated with smaller to medium-sized motors, while also taking into account the allowable voltage drop and temperature ratings. The NEC provides specific tables that dictate the minimum conductor sizes based on the motor's full-load current. For many typical applications, an 8 AWG conductor is commonly suitable for branch circuits feeding motors, particularly for those with lower horsepower ratings.

Larger conductor sizes, such as 6 AWG or 4 AWG, are generally reserved for higher-powered motors or special conditions requiring more current-carrying capacity. The selection criteria must consider safety, efficiency, and compliance with electrical standards, which is why 8 AWG is a feasible and compliant choice for this scenario.