An extension of the model for electrode polarization of Cirkel et al. Physica A 235 (1997) 269 is given. The problem is solved using both classical boundary conditions and the new boundary conditions using excess densities presented in a previous paper J. Phys. Chem. B 105 (2001) 11743. In the present paper, the electrodes are supposed to be ideal, meaning that charge transfer or adsorption are not considered. The advantage of the new boundary conditions lies in the possibility to extend to more complicated situations including for instance specific ion adsorption. We prove that the new boundary conditions and classical ones give the same results. A comparison of the model predictions, involving no adjustable parameters, experimental dielectric spectroscopy data is performed and fairly good agreement is found.