An elongated composite material (60) for current limiting applications is disclosed comprising one more high-temperature superconductor filaments (52) and a second electrically conductive matrix (54) member, which may include a sheath of high bulk resistivity surrounding the filament. The sheat (54) is preferably made of Ag doped with resistivity enhacing metals like Ga, In, Sn, Zn, Cd, Sb. To improve the thermal response a thermal stabilizing element (58), preferably stainless steel or Cu alloy, is bonded to the matrix. The current limiter exhibits dissipation in the range of 0.05-0.5 V/cm at currents of 3-10 times the operating current, thereby minimizing fault currents and improving recovery capability.