Under what condition is the uninsulated conductor in nonmetallic-sheathed cable not permitted to be used as a current-carrying conductor?

The uninsulated conductor in nonmetallic-sheathed cable is not permitted to be used as a current-carrying conductor specifically when it is used in service-entrance cable. This stems from safety concerns and code compliance. In service entrance applications, all conductors are typically expected to be insulated to prevent any potential electrical hazards, including shock or short circuits. The uninsulated conductors could cause arcing or create unintended paths for electrical flow, leading to dangerous conditions.

It's important to understand the inherent risks associated with uninsulated wires in certain applications, especially in areas where safety is paramount, like service entrances that connect utilities to a building. This regulation is intended to enhance the protection of both the wiring and the occupants of the building.

In contrast, other scenarios mentioned in the question, such as the conductor being insulated, not grounded, or being used as a neutral, do not inherently present the same level of risk when it comes to current-carrying capacity in the appropriate contexts outlined by electrical codes. For example, an insulated conductor can safely carry current without posing the same hazards as an uninsulated one.