what happens to a DC motor if connected across to an AC supply?
It depends on the type of DC motor. Most will vibrate at the frequency of the AC supply. There is a type of motor, in which both the armature and field windings make for one that will run on either AC or DC voltage. But a DC motor that uses magnets, will just vibrate instead of spin.
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Nothing good. DC- direct current and AC-alternating current wouldn't be able to work together or with parts built for the other.