As far as I understand, the electric potential is the amount of energy that a third party agent has to spend to move a positive charge from infinite separation to a point. Thus, the electric potential due to a battery cell depends only on the position of the charge with respect to the cell's terminals. So it seems illogical to me that the potential difference across a resistor should be different from the potential difference across a piece of wire with no resistance. I understand that pushing an electron through a wire and through a resistor requires different amounts of energy but I struggle to understand why it has anything to do with the difference of the electric potential.
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