The flux-lock type superconducting fault current limiter(SFCL) can apply the magnetic field into the high-$T_C$ superconducting(HTSC) element by adopting the magnetic field coil in its third winding. To apply the magnetic field into the HTSC element effectively, the capacitor for LC resonance is connected in series with the magnetic field coil. However, the current waveform of third winding for the application of the magnetic field is affected by the LC resonance condition for the frequency of the source voltage and can affect the waveform of the limited fault current. In this paper, the current waveform of the third winding in the flux-lock type SFCL according to LC resonance condition during a fault period was analyzed. From the differential equation for its electrical circuit, the current equation of the third winding was derived and described with the natural frequency and the damping ratio as design parameters. Through the analysis according to the design parameters of the third winding, the waveform of the limited fault current was confirmed to be influenced by the current waveform of the third winding and the design condition for the stable fault current limiting operation of this SFCL was obtained.