Well, the point is that in a fixed resistor, the higher the potential difference at is terminals, the higher the current that biases it. Evidently, if we have a variable resistor being fed by a constant voltage, the lower the resistance, the higher the current. Again Ohm's law. Lots of possiblities, but there is no need to loose the focus here when the question was about a fixed resistor and a variable voltage.I am not objecting to that. What I am saying is that a "high voltage" does not necessitate a high current. So, it is (possible) to have a high voltage but still a low current. It all depends upon the resistance.
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by Jake Hertz