The capacitance of a grain immersed in a steady state plasma containing a size distribution of dust particles is calculated. Assuming the equilibrium potential has been obtained by a simple balance of electron and ion collection currents, the grain charge is also obtained. It is shown that the validity of the analytical treatment given here for the linearized Poisson's equation is confined to a certain region of &lgr;D-R (Debye length; interparticle spacing radius) space. Outside this region, a numerical solution of the full nonlinear Poisson's equation will be needed. Within the valid linear region and starting at very small &lgr;D (or R), the capacitance at first exhibits a monotonic increase with increasing &lgr;D (or R). Eventually, the capacitance reaches a maximum, and this is followed by a monotonic decrease. The charge density of the dust in the plasma, however, is found to be only a function of the Debye length; there is no significant dependence on the interparticle spacing. Finally, the results of similar calculations by Goertz and Ip (1984) and Whipple et al. (1985) for a dusty plasma with a single grain size are shown to be qualitatively different from the results given here. The reason for this is the limited &lgr;D-R space investigated by these authors and the inconsistent use of a linearized calculation to interpret dust behavior in a nonlinear regime. ¿ American Geophysical Union 1987