Atmospheric pressure plasma jets driven by ac and pulsed-dc voltage were characterized, operating in helium with different admixture fractions up to 2% pure air, N2, and O2. The absolute production efficiency of nitrogen dioxide, nitric oxide, ozone, hydroxyl, and atomic oxygen was measured when plasma was processing real biological tissue. The power consumption of each power source, the effect of frequency, and gas composition were investigated. It has been found that the power consumption of 10-kHz ac-driven plasma jets increases with gas mixture increasing from 0% to 0.5% and then decreases slightly with gas mixture increasing from 0.5% to 2.0%, while 1-kHz ac-driven plasma jets are almost constant. Moreover, the average dissipated power of 10-kHz ac-driven plasma jets was about ten times more than that of the 1-kHz case, while the power consumption of P-dc-driven plasma jets was not drastically affected by gas admixture. Furthermore, O2 and air were important impurities contributing to the O, O3, and NO2 production efficiency, while N2 admixture would enable the diminution of O and O3 production efficiency. Especially, an admixture of O2, N2, and air to the main helium flow led to a reduction of OH and NO production efficiency for both ac and pulsed-dc power supply. This research may prove to be valuable both for an attainable range of RONS production efficiency and plasma medical research as a tool for assigning specific RONS or RONS mixtures.