Randles equivalent circuit
The Randles circuit is the standard lumped-element model of an electrode-electrolyte interface: a double-layer capacitance in parallel with a Faradaic branch (a charge-transfer resistance, sometimes in series with a Warburg element representing diffusion), all in series with the solution (spreading) resistance of the electrolyte. It captures the first-order behavior seen in impedance spectroscopy: at high frequency the capacitor shorts and the impedance approaches the solution resistance; at low frequency the capacitive / charge-transfer branch dominates and the magnitude rises steeply.
The Randles model is a useful abstraction rather than a literal physical picture, and real microelectrodes deviate from it: the double-layer capacitance is better represented by a constant phase element, and porous or coated electrodes need distributed (transmission-line) elements. Nonetheless it provides the vocabulary — solution resistance, double-layer capacitance, charge-transfer resistance, Warburg diffusion — used to interpret electrode impedance and to design recording front-ends whose input impedance must exceed the electrode impedance to avoid signal attenuation.
For a typical microelectrode, an equivalent circuit of a few hundred kiloohm solution resistance, a double-layer CPE, and a large charge-transfer resistance reproduces a measured impedance on the order of 100 kilohm to 1 megohm at 1 kHz.
The Randles circuit is a vocabulary, not a literal interface; real microelectrodes need a CPE and often distributed elements.