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How does potential difference cause an electric current to flow through a metallic conductor?
The potential difference or voltage is just the electrical pressure, which arises due to the difference in potential (i.e higher potential and lower potential).
The higher potential contains more number of charges (electrons), and the lower potential contains lower number of charges (electrons). Thus, charges from higher potential will flow to lower potential till their number becomes equal in both places.
It is similar to how water flows from a higher position to a lower position.
Let's understand it with an activity.
Consider 2 tanks (Voltage Sources) say the tanks 1 and tank 2. Tank-1 (Voltage source 1) has a higher potential (more electrons) and Tank-2 (Voltage source 2) has a lower potential (fewer electrons) so due to the difference in pressure (voltage difference), there will be a flow of water (and in an electric circuit there is a flow of charge, which is known as current) .