Charging an electrochemical capacitor

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nubie43
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I have a very basic question confusing me about charging electrochemical capacitors -

When you charge a symmetrical electrochemical capacitor to 1V, because one electrode becomes positively charged and the other negatively charged, the electrode potential across one will be +0.5V, and the electrode potential across the other will be -0.5V?

So if you were to measure the CV across each electrode they would both start at 0V, and travel in opposite directions to + and - 0.5V?
 
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You mention a 0v point. Do you have an explanation at which point in the capacitor exactly where this is?
 
Im not really sure about that either. When testing a cell for example by constant current charge discharge, you apply the current, and the voltage will increases to your set limit from 0V then, goes back on discharge.

I suppose 0V would be when the system is at equilibrium, where no current flows after you discharge the device?