The electrical current profile in a liquid sample containing ionic impurities, submitted to a time-dependent external voltage, is determined in the framework of the Poisson-Nernst-Planck (PNP) diffusional model. The boundary conditions at the limiting electrodes include the situations of blocking electrodes, generalized Chang-Jaffe (specific adsorption), and the adsorption-desorption of positive and negative ions at the interface, governed by a kinetic equation in the Langmuir's approximation. The current-voltage characteristics of the confined system are obtained in the presence of an arbitrary time-dependent applied potential of small amplitude (linear approximation). The calculations are potentially useful for modeling and interpreting experimental situations found in biological cells and liquid crystals samples. (C) 2013 Elsevier B. V. All rights reserved.