Let me remind you that from mechanics, speed is the first time derivative of a path. those. what distance was covered in a unit of time (100 meters were covered in 2 minutes).
Potential, by definition, is a quantitative characteristic of the work of transferring a charge from a certain point to infinity. In this case, voltage is the DIFFERENCE of potentials between something.
Although you are partly right - voltage is what causes the current to arise.
But what does it mean "by the example of batteries", because these concepts are the same everywhere. The potential does not end if you are aware that the voltage on a charged battery may be slightly more than on a discharged one - this is only without load, under load this difference will be significant more. But this does not mean that the potentials have decreased, it means that the internal resistance of the power source has increased and part of the voltage drops across it, and the EMF remains practically unchanged.
Regarding the resistance, you rightly said, just not the speed, but what prevents this number of charges from passing through. It’s as if you would let a crowd of people pass in a wide empty corridor, and in one filled with various boxes, in the second case, people would not walk along the entire width of the corridor, but would crowd near the aisles, thereby less number of of people
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