We fabricated resistive superconducting fault current limiters (SFCL) based on YBCO thin films grown on 2-inch diameter $Al_2O_3$ substrates. Two SFCLs with nearly identical properties were connected in series to investigate simultaneous quench. There was a slight difference in the rate of voltage increase between two SFCL units when they were operated independently. This difference resulted in significantly imbalanced power dissipation between the units. This imbalance was removed by connecting a shunt resister to an SFCL in parallel. The appropriate values of shunt resistance were 80 ${Omega}$ at 75 $V_rms$ and 110 ${Omega}$ at 120 $V_rms$, respectively. Increased power input at high voltages also reduced the initial imbalance in power dissipation, but with increase in film temperature to higher than 200 K.