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The way I thought of it was similar to potential and kinetic energy. When there is no movement/work done, potential energy is at a max and kinetic energy is 0. However, once something happens, potential energy is converted into kinetic energy, therefore being used and not staying at a maximum. Similarly, when there is current flowing, the cell potential in the cathode is decreasing as it flows as a current. Therefore, when there is no current flowing (or as it approaches 0), the potential difference will be at a maximum as it will be stored rather than used
The cell potential is different at each time after you flip the switch because the battery is slowly dying/reaching equilibrium. Because of this, it is not at max potential anymore. Max potential is right before you flip the switch because the battery is building up, and then once you flip the switch it drains.
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