The design circuits of an electromagnetic short-circuit current limiter of inductive type with movable armature and moving core are considered. A comparative analysis of the design features of the electromagnetic current limiter with copper or superconducting winding is carried out. The operation principle of the electromagnetic short-circuit current limiter of inductive type with copper or superconducting winding is considered. The peculiarities of operation modes of the electromagnetic short-circuit current limiter of inductive type with copper or superconducting winding are analyzed. Using results of the mathematical modeling of the magnetic system of the electromagnetic short-circuit current limiter by the Finite Element Method in the FEMM software environment, the character of the distribution of the magnetic flux density in the nominal mode and in the current limiting mode is determined, which allows to determine the parameters of the current limiter and design features. In accordance with the design features of the electromagnetic short-circuit current limiter of inductive type, the sequence of calculation of the basic parameters of the magnetic system, taking into account the voltage drop factor, is given. The basic equations of the electric equilibrium of the voltage drop of the electromagnetic short-circuit current limiter of inductive type for nominal mode and short-circuit conditions are given. The use of the design circuit of the electromagnetic short-circuit current limiter with superconducting winding can provide energy-saving in nominal mode. The use of high-temperature superconducting wire due to increased critical parameters will ensure preservation of the superconducting state of the winding in short-circuit mode.