Self-consistent fluid and particle-in-cell Monte Carlo (PIC-MC) models in conjunction with experimental measurements have been used to study the electrical characteristics of rf discharges in pure argon and in argon contaminated with dust particles (at 0.11 torr argon, 13.56 MHz). In the experiments, the dust particles were first created in a silane-argon rf discharge and subsequently trapped in an argon discharge in order to stop the growth process. The concentration and radius of the dust particles were measured experimentally and found equal to ${10}^{8}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ and 0.05 \ensuremath{\mu}m, respectively. The PIC-MC discharge model has been used to check the validity of the fluid model in pure argon. The discharge in dusty argon has been described with a fluid model modified to account for the presence of dust particles. This model uses as input data the number of negative charges carried by the dust particles and the frequency of electron loss to the particles deduced from a two-dimensional particle-in-cell Monte Carlo simulation of a dusty dc plasma. The results show good agreement between experiments and models within the whole range of rf voltages considered and for the pure and dusty argon plasmas. The presence of dust particles in the plasma modifies considerably the discharge impedance, which becomes much more resistive. The electron number density in the plasma is much smaller than the positive ion density and than the number density of negative charges carried by the dust particles. It appears that the phase shift between current and voltage is very sensitive to the presence of powders. This property could be useful for the detection of powder formation in a processing plasma.