The smallest branch circuit conductors that can be installed between a 3-pole circuit breaker and the motor is ___ AWG.

The smallest branch circuit conductors that can be installed between a 3-pole circuit breaker and a motor should be capable of handling the motor's full-load current, which is determined by the motor's horsepower and the voltage rating. In the context of National Electrical Code (NEC) requirements, for most applications, the minimum conductor size is typically based on the motor's full-load current as outlined in NEC tables, which provide the appropriate ampacity ratings for various sizes of copper and aluminum conductors.

In this case, a 6 AWG conductor is commonly used because it provides a suitable balance between capacity and protection for the circuit. It can handle higher currents typical in motor applications while allowing for necessary adjustments related to factors like ambient temperature and insulation types. This choice ensures safe operation without excessive voltage drop or overheating, which could occur with insufficient conductor sizes.

While a 10 or 12 AWG conductor might seem adequate for lower current loads, they do not provide adequate capacity for the higher current levels expected in motor circuits connected to a 3-pole circuit breaker, which leads to their unsuitability. As such, while all options listed may have their uses, a 6 AWG conductor is the most appropriate selection for this specific motor application