The evolution of the thermal and electric states of high-Tc composite superconductors is theoretically investigated as a function of a sweep rate of fully penetrated current. The electric field and temperature induced by current charging were simulated using the temperature dependences of the composite heat capacity and matrix resistivity. It is proved that the stable high-field part of the voltage-current characteristics of high-T c composite superconductors might depend on the sweep rate even at relatively slow sweeps. As a result, the critical currents determined in accordance with the fixed voltage criterion may increase with increasing sweep rate. However, the fully penetrated current stability boundary defining the limiting current that stably flows in a superconductor without irreversible superconducting-to-normal transition, is not affected by the sweep rate. These regularities depend on the corresponding composite temperature rise preceding instability onset. The analysis reveals also the connection between different criteria used to determine the current stability conditions for both low-T c and high-Tc superconducting composites.
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