EN
The two extended formulae in the power form of the Kim critical state model were used to fit the critical currents versus the dc applied magnetic field. Two samples of thallium based superconductors: the (Tl_{0.6}Pb_{0.24}Bi_{0.16})(Sr_{0.9}Ba_{0.1})_2Ca_2Cu_3O_y film on single-crystalline lanthanum aluminate and the bulk (Tl_{0.5}Pb_{0.5})Sr_2(Ca_{1.8}Gd_{0.2})Cu_2O_y were chosen to test the models. The formulae were compared to the percolation model described by the exponential expression. The first model fits the experimental data better for the thallium based film whereas the second approach is better for the thallium based bulk sample.