We introduce the complete electrode model in the modeling of electrical capacitance tomography (ECT), which extends the model with the commonly used model for electrodes. We show that the solution of the complete electrode model approaches the solution of the corresponding common electrode model as the impedance effect on the electrodes vanishes. We also derive the nonlinear relation between capacitance and permitivity and the sensitivity maps with respect to both the permittivity and the impedance constants, and present a finite difference scheme in polar coordinates for the case of circular ECT sensors that retains the continuity of displacement current with piecewise-constant permitivities.