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The hybrid superconducting fault current limiter (SFCL) can be constructed to perform either first half cycle limiting operation or first half cycle non-limiting operation through rearrangement of the SFCL's components. Especially, the first half cycle non-limiting operation of the hybrid SFCL is expected to be preferred for the protection coordination with the protective device. However, if the components of the hybrid SFCL with the first half cycle non-limiting operation is designed with improper parameter, the hybrid SFCL can result in the continuous conduction of the fault current into the high-TC superconducting (HTSC) element after the fault occurs, which can sometimes bring about the destruction of the HTSC element comprising the hybrid SFCL. In this paper, among the components to affect the operational characteristics of the hybrid SFCL, the current limiting characteristics of the hybrid SFCL with the first half cycle non-limiting operation due to the resistances of HTSC element and the current limiting resistor (CLR) were investigated. Through the short circuit tests, the stable current limiting operation of the hybrid SFCL with the first half cycle non-limiting operation was confirmed to be performed by designing the resistances of both the HTSC element and the CLR to be larger values.