The relationship between Potential Difference and flow of electricity is given by Ohm's Law, which states that: The potential difference (voltage) across an ideal conductor is proportional to the rate of flow of electricity through it. The constant of proportionality is called the "resistance", R.
The rate of flow of electricity is known as current
The potential difference is proportional to the rate of flow of electricity.
Thus, If potential difference increases, The rate of flow of electricity also increases to attain equilibrium faster