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In order to investigate how a superconducting fault current limiter (SFCL) can enhance the performance of a power system, an accurate circuit model of the device needs to be introduced in power system simulators. In this paper, we present a finite-element numerical model to calculate the time evolution of the voltage across a magnetic-shield-type SFCL, when it is connected to an external circuit. The calculation of the voltage is carried out by using the energy conservation law, and requires the calculation, at any instant, of the current density distribution inside the superconducting tube and magnetization distribution inside the ferromagnetic core of the device. These distributions are determined by means of two coupled equivalent electric and magnetic circuits, whose topology and components are obtained through the spatial integration of quasi-static form of Maxwell equations. Comparisons between numerical and experimental results are shown.