A complete potential profile of an electrical double layer is calculated from a distribution function of charged particles based upon a model where the effect of a charged electrode and the finite size of ion are explicitly included. Electrons which are distributed on the electrode surface are assumed not to penetrate the electrode/electrolyte boundary. Formation of the constant density regions and their effects on potential and the electrical double layer capacitances are studied in great detail. The distribution of surface electrons as well as the constant density regions are found to be essential in characterizing the electrical double layer. The introduction of the ion size into the prior electrical double layer model of an ideally polarizable electrode/point charged electrolyte system, shows a great improvement in its characteristics mostly at negative potential region.