The relationship between the current through a resistor and the potential difference (voltage) across it at constant temperature is described by Ohm's Law. According to Ohm's Law, the current flowing through a resistor is directly proportional to the potential difference across the resistor, provided the temperature remains constant. Mathematically, this is expressed as:

V=IRV=IRV=IR

where VVV is the potential difference across the resistor, III is the current through the resistor, and RRR is the resistance, which remains constant if the temperature does not change. This means that if the voltage across the resistor increases, the current increases proportionally, and if the voltage decreases, the current decreases proportionally, assuming resistance is constant. This relationship implies that for a resistor at constant temperature, doubling the voltage will double the current, and halving the voltage will halve the current. The resistance acts as the constant of proportionality between voltage and current.