Investigation into nonuniformity of potential distribution in electrodes and its influence on inner resistance by application of mathematical methods

Discussed are one-dimensional and two-dimensional cases of potential distribution in electrode. It is demonstrated that if the rate of current formation in each point of electrode was (according to Faraday's law-) proportional to transferred electrical charge as well as to deviation of potential from equilibrium potential, then the problem of potential determination brings to equation solution in the form: Δφ = k²φ , where Δ – Laplace operator; φ – potential deviation from equilibrium; k – a constant dependent on electrode parameters.
The analysis of solutions obtained demonstrates that the design features of current leads produce unconformity of current and potential distribution in electrodes. As a result, the current-formatting processes over the electrode area occur with different rate The rate of charge/discharge processes in sections adjacent to current leads is higher than in remote sections and periphery of electrode. Calculation indicates that the increase of potential nonconformity in electrodes results in increase of inner resistive component.