The interaction of an atmospheric pressure plasma jet with different dielectric surfaces is investigated using a setup of two ring electrodes around a ceramic capillary. In this study, in addition to electrical measurement methods such as the determination of voltage and current, special emphasis was placed on the power measurements at the electrodes and the effluent. The power dissipation is correlated with Fourier-transform infrared (FTIR) absorption spectroscopy measurements of O3 and NO2 densities. The results show the correlation between the dielectric constant and the dissipated power at the target. The ratio between power dissipation at the grounded ring electrode and the grounded surface shows an increase with increasing dielectric constant of the target. A correlation of the results with bacteria, tissue and water as envisaged dielectric targets shows four times the power dissipation at the treatment spot between bacteria and tissue.