The effect of the dye-impregnation time on the electrical impedance of a dye-sensitized solar cell is theoretically investigated. The proposed model is based on the assumption that during the impregnation processes the covering of the titania electrodes, initially incomplete, arrives to saturation and the adsorption coverage can be described by a diffusive process, depending on the square root of the impregnation time. An equivalent circuit, formed by an electrical impedance related to the bulk contribution due to the electrolyte, and by a contribution due to the presence of the porous electrode partially covered by the dye is derived. The equivalent circuit is able to justify the experimental data recently reported on the influence of the dye-impregnation time on the electrical response of a solar cell. We show that a more complete analysis of the response of the solar cell to an external excitation, performed using the equations of continuity of the ions present in the electrolyte, and the equation of Poisson for the actual electric potential across the cell, allows to justify the proposed equivalent electric circuit.