Electrode polarization (EP) happening due to accumulation of ions at the electrode/electrolyte interface is an inevitable phenomenon while measuring impedance spectrum in high conductivity buffers and at low RF spectrum. Well-characterized time scales elucidating the EP effect are important for the rational design of microfluidic devices and impedance sensors. In this Article, interfacial impedance at the electrode/electrolyte interface is investigated considering channel height and Debye length effects on characteristic time scale in a binary electrolyte solution using parallel plate electrode configuration. Experimental results reveal self-similarity of normalized electrical impedance as a function of the normalized frequency. The experimental results also match with numerical solutions obtained by finite element simulation of unsteady fully coupled Poisson-Nernst-Planck (PNP) equations. Furthermore, fractal shaped gold nanostructured electrodes are examined, and it has been proven that electric double layer (EDL) formed on porous electrode surfaces acts as a thick EDL and modifications to the characteristic time scale is necessary for porous electrodes. Finally, a constant phase element (CPE) model is proposed to account for the self-similar impedance spectrum, which can be used for different channel heights and solution conductivities.