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The resistive superconducting fault current limiters are very attractive devices for electric power circuits. We have investigated the operating properties of a parallelized superconducting fault current limiter made from YBCO thin film and gold film on sapphire substrate by numerical simulation. In order to improve the operating properties and the stability, the YBCO films need to be parallelized. However, it is necessary to investigate whether a few sheets of YBCO film with different critical current density will deteriorate the device's operating properties and stability. That is, when the fault current occurs in power circuit, all YBCO films with different critical current density have not simultaneously quenched. It causes the deterioration of the operating properties. Therefore, it is necessary to investigate the influence of the unbalanced critical current density on the quench characteristics of the parallelized superconducting fault current limiter by numerical simulation. The simulation is performed by a newly developed code coupling the thermal diffusion and the current circuit. It takes into account the E-J power low depending temperature, obtained by experiments. The current limiting properties and the recovery properties are evaluated from quench behavior when the YBCO films have some inhomogeneities. Moreover, the influence of the thickness of gold film on the current limiting properties is also investigated. To grasp such properties is required when the resistive fault current limiter using YBCO thin film is designed.