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Many explanations of current flow in electrolytic cells will state that electrons flow from the external power source into the cell (via the cathode). But surely this current flow would stop if there were no reduction at the cathode (which removes electrons).

Doesn't this therefore mean that current is explained by a simultaneous combination of 'push' forces and 'pull' forces? You can't have current being generated in an electrolytic cell without a reaction occurring, right?

On a related note, it's also often said that the rate of electrolysis depends on current. But, based on my understanding, current is simply a measure of the rate of electrolysis: you can't have current without first having a redox reaction occurring in the electrolytic cell. Am I right in thinking this?

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