In this study, an atmospheric pressure cold plasma jet has been generated based on dielectric barrier discharge plasma. The double ring electrode configuration is used and analysis has been performed subjected to wide range of supply frequencies up to 25 kHz and supply voltage up to 6 kV. The electrical characterization of the plasma jet has been carried out using a high voltage probe. The V-I characteristics of the developed cold plasma jet have been studied and the consumption of the power has been analyzed at various input combinations of supply frequency and applied voltage. Consequently, the supply voltage and supply frequency are optimized with respect to the discharge current and jet length for optimum power consumption. The peak power consumed for glow discharge operation has been found to be 1.27 W in the optimized configuration.