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Difference between 2-electrode and 3-electrode cell

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Hi! I'm currently starting to work with supercapacitors performing cyclic voltammetry of carbon electrodes in 2 and 3 electrodes cell.
Since the electrolyte is H2SO4 1M, the scan range is 0.0V to 0.8V. When using the 3-electrodes cell (RE: Ag/AgCl, CE: Pt) I can clearly observe a broad redox signal around 0.4V but when using the 2-electrodes cell (2 carbon electrodes) the redox signal is almost not visible but there seems to be something around 0.0V.
I believe that in the 2 electrodes cell, the potential is divided between the two electrodes so individual electrode potentials will range from -0.4V to 0.4V. Is my reasoning correct?
Will the electrolyte locally decompose when the electrode reaches -0.4V? Thanks!

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