Both the critical current intensity at zero applied magnetic fieldIc(T), from nitrogen temperature up to the critical temperature, and the normal‐state resistivity &rgr;n(T) have been measured in granular Bi1.5Pb0.5Sr2Ca2Cu3Oy(BiPbSCCO) superconductors, with different granular characteristics. It is found that the combination [Ic(T)/P][&rgr;n(0)/&rgr;’n], where &rgr;(0) is the residual normal‐state resistivity, &rgr;’nis the temperature derivative andPis the sample’s perimeter, is essentially constant from sample to sample at any temperature. It thus constitutes a universal temperature‐dependent critical current for the polycrystalline BiPbSCCO family. ©1995 American Institute of Physics.