Breakdown characteristics of insulator-liquid nitrogen ($LN_2$) composite insulation for resistor type High $T_c$/ superconducting fault current limiter (HTSFCL) under ac and impulse voltage in $LN_2$ has been studied using model electrode systems. Electrodes for model electrode systems were made of SUS 304 contacted fiberglass reinforced plastic (FRP) and Au coated sapphire. The breakdown characteristics of model electrode systems were investigated experimentally for FRP thickness ranging from 1 mm to 5 mm. surface distance ranging from 2.5 mm to 7 mm and electrode gap ranging from 1 to 5 mm. The experimental data suggested that the breakdown voltage of model electrode systems in $LN_2$ is highly dependent on the surface distance, electrode gap as well as on the FRP thickness. Also, we had observed discharge traces and puncture due to high-voltage 60-Hz AC stress.