Apprentice answerWhy is a cold supply tap sweating above the ceiling
2nd YearInsulation, Liner & CondensationCheck first
Cold supply metal exposed to humid plenum air can sweat. Dry it, verify insulation/vapor barrier requirements, and wrap/seal it so humid air cannot reach the cold metal.
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Plain-English answer
Sweating duct is usually a vapor barrier problem. Cold supply air chills the metal skin; humid air touches it; water forms and drips onto ceiling tile, drywall, equipment, or finished space.
The correction is to stop the water damage, dry the surface, and install/repair the specified insulation and vapor barrier. The seams, corners, collars, and tap connections need to be sealed airtight on the vapor barrier side, not just wrapped loosely.