What is the smallest size equipment grounding conductor permitted to install between the ground bar in the pull box and Load #2 when using three 12 AWG conductors?

The smallest size equipment grounding conductor required in this situation can be determined based on the National Electrical Code (NEC) guidelines. For branch circuits, the size of the equipment grounding conductor is typically based on the size of the conductors supplying the load.

In this case, with three 12 AWG conductors, the NEC stipulates that the grounding conductor must be sized according to the current-carrying conductors. The minimum size equipment grounding conductor for a circuit using conductors larger than 10 AWG would be based on Table 250.122 of the NEC. For 12 AWG conductors, the code specifies that the grounding conductor should be a minimum of 10 AWG when there are three conductors involved.

This requirement ensures adequate grounding for safety and to facilitate fault clearing in the event of a fault. The choice of 10 AWG as the minimum size for the grounding conductor ensures improved reliability and performance in fault conditions, which is critical for safety in electrical installations. While smaller conductors could technically be used in other situations, specific application requirements or conditions outlined in the NEC ultimately establish 10 AWG as the minimum in this scenario.