True. Ideally you want the winding resistance to be zero so there is no IR power loss in the windings.Real transformers are made with enough primary turns, so that the inductance is the main thing that sets the magnetizing current. The resistance of the primary has little to do with limiting the current in good practical transformers
The laminated iron core makes every winding "worth" quite a bit more inductance, though. I forgot the permeability offhand, but I'll look for it, or at least a range. At 120V, I don't think inductance will fully cancel out resistance, otherwise, idle transformers shouldn't get warm, as the inductance is a reactive load.At the low frequency (50-60 Hz) and low inductance of the OP's 100-turn coil, DC resistance is the primary contributor to the coil's impedance. Do the math. I stand by my statement that such a coil is essentially a short to the power supply. It's better than one loop but it's still too short.
Inductance of a coil increases roughly with the square of the number of turns. At ~500 turns or more, at this frequency, the impedance due to coil inductance will begin to exceed the contribution of DC resistance. Together, the DC resistance and the inductance will keep the current low enough.
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by Luke James