The limitation depends on your working electrode, electrolyte, range of potential molecule study among other variables.
Usually you specify the program to perform this measurement in CV.
The equation that governs the speed is E = E_i - vt or E =E_i -vt
In any case you are able to determine the stability range of the species within your solution, for example in acqueous solutions, you are able to measure the oxygen and hydrogen evolution, as well as the adsorption of molecular species on your electrode. If you measure the electrode capacity in parallel, you are also able to detect the charging of your electrode, and the onset of electrochemical reactions such as oxidation or reduction of surface species, or the layer formation (i.e. oxidation of the electrode itself, or the electrodeposition or dissolution). Electrocatalytical reaction are another important issue. There are so many things that may be derived from CVs ... You may fill books with that!
Look in the book of Bard.
You see that cyclic voltammetry is used at stagnant conditions so it can only be used for anodic reaction. Some researcher used it for cathodic reaction but you need rotations ( rotating disk electrode) to eliminate the effect of diffusion limitations.
Even at high concentrations CV cannot be used for cathodic reaction.
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