Under what conditions must a switch be derated from its nominal rating?

The correct choice highlights the necessity for derating a switch in inductive circuits with high in-rush current. When a switch operates in an inductive circuit, the initial surge of current (in-rush current) can significantly exceed the normal operating current. This phenomenon occurs because inductive loads, such as motors and transformers, create a magnetic field when energized. During this initial start-up phase, the in-rush current can be several times greater than the load's steady-state current.

If the switch is not derated appropriately for this in-rush current, it may experience overheating, which could lead to premature failure or safety hazards. Derating ensures that the switch can handle the expected load without exceeding its thermal limits and electrical characteristics, thus enhancing reliability and safety in the application.

In summary, when using switches in inductive applications with high in-rush currents, proper derating is crucial to maintain function and prevent damage, making this option the correct answer.