This study investigates how quartz and alumina affect atmospheric pressure plasma jet (APPJ) stability using numerical simulations and experiments. Unlike previous research, it uses simulations and equivalent circuits to explore discharge characteristics. Experimental results show a temperature increase in quartz APPJ, leading to decreased gas voltage and enhanced plasma intensity, validated by equivalent circuit analysis. Alumina APPJ maintains more stable plasma intensity. Simulation reveals that higher dielectric coefficients enhance capacitance, leading to higher plasma parameters such as electron density, ion density, and electron temperature. This research clarifies quartz's voltage increase over time, which is crucial for biomedical plasma applications, aiding in selection of stable dielectric materials.