Does that matter? In general a switch only needs to be rated for the load, not the circuit rating. E.g. it's fine to use a 15A snap switch on a 20A circuit. The reference in Article 404 was already given.
Cheers, Wayne
Before I answer your question, I should say that 404.14(A) is for snap switches and I don't know if a 60A handle switch is considered a snap switch. I always thought of light switches as snap switches because they snap between poles. Turning off a normal handle switch doesn't snap.
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404.14 Rating and Use of Switches.
Switches shall be listed and used within their ratings. Switches of the types covered in 404.14(A) through (E) shall be limited to the control of loads as specified accordingly. Switches used to control cord-and-plug-connected loads shall be limited as covered in 404.14(F). "
A through D are snap switches. E is for dimmers or occupancy type switches and F is for cord and plug. So arguably only the first sentence of 404.14 would apply to a general use switch, "Switches shall be listed and used within their ratings.". Which is why I quoted 110.3(A)(5), & (7), 110.3(B).
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To your point, when you consider OCPD, wire sizing, disconnect rating, etc. for a transformer you can size things based on the load and not FLA. It raises a good point though. Does a switch need to be protected against overload?
That is why I quoted the sections 110.3 & 110.9. Saying that their ratings should not be exceeded. But a transformer's rating is more vague and so I defaulted to the rating of the OCPD and conductor. No necessarily the load (since there is no load in the OP, just FLA). If you just consider a transformer of 50kVA that only feeds a single light bulb, you could use a 15A switch. But I doubt it would survive the inrush. lol