If the potential difference across a resistor decreases to zero, what happens to the current?

When the potential difference across a resistor decreases to zero, Ohm's Law, which states that the current (I) flowing through a resistor is directly proportional to the voltage (V) across it and inversely proportional to the resistance (R), comes into play. According to Ohm's Law, the formula is given as I = V / R.

If the voltage (V) becomes zero while the resistance (R) remains constant, the equation simplifies to I = 0 / R, which clearly shows that the current (I) will also become zero. This implies that no current can flow through the resistor if there is no voltage to push it through, as current requires a potential difference to exist.

In practical terms, if you were to think of it in a circuit, without voltage acting upon the resistor, there are no driving forces for electrical charge to move across it, thus resulting in zero current.