A study of electrical properties, methodology, and precision of power measurement was made on two types of Ar plasma jets, a single-strip-electrode plasma jet and a single-rod-electrode plasma jet. The dynamics of current peaks, methods for determining discharge power, and power measurement precision (especially important for applications in plasma medicine) are discussed for each type of plasma jet. Lower error in power calculation was obtained when the plasma jet did not touch the substrate, as well as more repetitive dynamics of the current peaks. Averaging high number of periods (over 500) when calculating the power by the Lissajous figure technique led to decrease of the experimental error.