We examine oscillations as a function of Fermi energy in the capacitance of a mesoscopic cavity connected via a single quantum channel to a metallic contact and capacitively coupled to a back gate. The oscillations depend on the distribution of single levels in the cavity, the interaction strength and the transmission probability through the quantum channel. We use a Hartree-Fock approach to exclude self-interaction. The sample specific capacitance oscillations are in marked contrast to the charge relaxation resistance, which together with the capacitance defines the RC-time, and which for spin polarized electrons is quantized at half a resistance quantum. Both the capacitance oscillations and the quantized charge relaxation resistance are seen in a strikingly clear manner in a recent experiment.