Quote:
I guess I've never understood how it is that sometimes current is a variable determined by the voltage and resistance and how sometimes it's a constant, as you're saying here.


Well, in this case it really is a variable, but the important bit is that the voltage will also vary. As soon as a load is connected, allowing current to flow, the voltage drops to zero (or darned close..). When you plug that back into ohms law, you get zero (or close enough to it) current flow.

Things interact, there's no static fixed value here, other than the resistance.

Cheers