Abstract We are measuring current-voltage characteristics of silver-sheathed Bi(2223) tape samples. One of our aims is the reliable determination of our samples' critical currents, in DC and AC conditions (with frequencies between 0 and 1000 Hz). The method generally used to do this consists in choosing a more or less arbitrary voltage or differential resistance (Δu/Δi) threshold. However, this choice influences notably the critical current value announced. The measurement noise increases significantly with the frequency, making it necessary to use a higher threshold and taking all significance out of the comparison of results obtained in different experimental conditions. In this paper, we present a less arbitrary critical current determination method, based on the search for an optimal fit of our current-voltage curves. Above the critical current, these curves are approximated by an exponential law with three parameters, one being the critical current. The other two can also be determined and used to compare the characteristics of different samples, or the performances of a sample at different frequencies. The critical currents thus obtained with our method are generally inferior to those obtained with threshold methods.