Dissipation in a weak-link-limited superconductor as a problem of percolation theory

Broadening of the resistive transition of sintered ${\mathrm{GdBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ superconductor has been studied varying the measuring current over the range of five orders of magnitude. The observed well-defined branching points in the resistive transition coincide with the quasi-Ohmic saturation of V-I curves and scale with the average grain size. The results suggest the validity of a simple percolation model for dissipation in systems whose global superconductivity is realized by Josephson coupling of the superconducting grains. A common origin of structured resistive transition, observed in many superconducting systems, has been also discussed.