Electrical current is the flow of electrons within an electrical circuit. In the conditions you have described, remember electrons have a negative charge, while hydrogen ions have a positive charge. In the first example, the unnoble metal would have electrons to donate to the electrical current, so it would be necessary to have an electrolyte with low hydrogen ions. Otherwise, the electrons would not complete the electrical circuit and chemically bond with the hydrogen ions, producing hydrogen atoms. In the second set of conditions, the overabundance of hydrogen ions in the electrolyte would tend to strip electrons from the outer energy level of the two noble metals, causing an imbalance to occur. Electrical current has a tendency to flow from high potential to low potential, so if a high potential were created on the noble metal that was less electronegative, this imbalance could be created.
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