We study the limitation possibilities of bulk Bi high T _c materials. For this we test these materials with a.c. or d.c. currents above their critical currents. We study particularly the evolution of the voltage with time or with current. The material, the value of the current and the time duration play important parts. For sintered Bi samples the voltage depends only on the current even for values much larger than the critical current. With textured samples the V(I) curves shows an hysteretic behaviour due to a warming up. The textured materials are more interesting than sintered ones in terms of required volume for the current limitation. In both cases the superconductors are in a dissipative state but not in the normal state. This state is nevertheless reached if the dissipated energy inside the sample is sufficient. We have tried to apply a magnetic field on the samples in order to trigger a more effective limitation. The voltage increases but with a limited effect for currents much higher (3–4 times) than the critical zero field current. We think that the dissipative state is due mainly to the grain boundaries which become resistive above the critical current.