The design of a battery-powered system ideally requires the simultaneous sizing of all its components. To contribute to this purpose, we propose a physical approach to couple the electrical parameters of a battery equivalent-circuit-model (ECM) to the electrodes dimensions of the battery. Because it only requires non-invasive measurements, it can be easily used by system integrators. To test the proposed approach, we choose three commercial coin cells with different sizes and nominal capacities (25 mA h, 60 mA h and 120 mA h). Only the electrodes length of these cells varies, and this study is therefore focused on creating dependency-models that predict the ECM parameters values with respect to this specific dimension. The proposed ECM brings accurate voltage simulations and the dependency-models predictions are satisfactory for the three cells, with a mean accuracy of 6.3%. Thanks to the proposed approach, the parameters of any cell size and capacity can be predicted in the characterization range (between 25 mA h and 120 mA h here). It is thus a promising tool for developing custom-made cells.