An improved method for the measurement of the power consumed in low pressure, radio frequency discharges is presented. The method involves the measurement of current and voltage waveforms outside the reactor, and the determination of the discharge impedance and the network of parasitics. The measured waveforms are transformed to the equivalent ones at the powered electrode, by using an electrical circuit model of the stray impedance of the cell, with experimentally determined components. A tunable shunt circuit is used for minimizing displacement currents. The equivalent circuit contains elements which account also for resistive power losses in the cell-shunt circuit. The obtained discharge power is compared with measurements of the total power output of the generator made by a power meter. Results concerning power consumption and impedance in argon and silane discharges are presented as a function of the excitation voltage and the pressure. In both cases there is a discharge impedance drop, for higher voltage or pressure, which leads to higher power consumption in the discharge. The measurements show that only a small, nonconstant part of the power is; consumed in the discharge, whereas, the inclusion of resistive loses leads to more accurate results. The mechanisms of the discharge impedance drop are further discussed in terms of their relation to microscopic plasma phenomena and quantities.