Say you have a 9 volt battery, and you connect the two ends of the battery with a wire to form a circuit with no resistor. If you measure the potential difference between the two ends of the battery, the difference will obviously be 9 volts. This suggests that as you move along the wire, the potential slowly decreases incrementally. Now say you have the same battery and circuit, but you add a resistor. I've been told that the voltage drop across this resistor will be 9 volts. But this implies that now, as you move along the wire, there is no incremental change in voltage; voltage is constant until you get to the resistor, and then it drops 9 volts, and then it remains constant until you get to the other end of the circuit. This seems wrong to me, because if there is no voltage change in the wire, there must be no electric field, so what moves the electrons along? On the other hand, the drop in voltage across the resistor along with the resistance should determine the current in the circuit, so if the voltage drop across the resistor is not directly linked to the voltage drop in the battery, there would be no way to find the current, which also seems wrong. Unless, of course, we just approximate that most of the voltage drop occurs across the resistor. But in that case, are there any cases where that approximation does not work/ why is most of the voltage drop across the resistor?
In summary, I think that conceptually, I'm being tripped up as to why the simple act of adding a resistor to a circuit would supposedly cause the voltage change to occur at an isolated location (the resistor) and not over the whole wire. I'm just starting to learn about circuits so any insight would be helpful, and apologies if this is a trivial matter.