A low potential difference in a wire does not prevent current flow if resistance is also low, as described by Ohm's Law (I = V/R). When both voltage (V) and resistance (R) are very small but non-zero, the current (I) can still be significant. For example, a potential difference of 0.001 volts across a resistance of 0.0001 ohms results in a current of 10 amps. The ability to control voltage and resistance through battery choice and wire properties ensures that current can flow even with low potential differences. Understanding these parameters clarifies why current can exist in such conditions.