When this equation describes a capacitor, the constant Y0 = C (the capacitance) and the exponent n = 1. For a constant phase element, the exponent n is less than one.
The "double layer capacitor" on real cells often behaves like a CPE instead of like a capacitor. Several theories have been proposed to account for the non-ideal behavior of the double layer but none has been universally accepted. In most cases, you can safely treat a as an empirical constant and not worry about its physical basis.
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