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The Cole single-dispersion impedance model is based upon a constant phase element (CPE), a conductance parameter as a dependent parameter and a characteristic time constant as an independent parameter. Usually however, the time constant of tissue or cell suspensions is conductance dependent, and so the Cole model is incompatible with general relaxation theory and not a model of first choice. An alternative model with conductance as a free parameter influencing the characteristic time constant of the biomaterial has been analyzed. With this free-conductance model it is possible to separately follow CPE and conductive processes, and the nominal time constant no longer corresponds to the apex of the circular arc in the complex plane.