  In this work, the classical and the quantum capacitances are calculated for a
Fabry-P\'{e}rot interferometer operating in the integer quantized Hall regime.
We first consider a rotationally symmetric electrostatic confinement potential
and obtain the widths and the spatial distribution of the insulating
(incompressible) circular strips using a charge density profile stemming from
self-consistent calculations. Modelling the electrical circuit of capacitors
composed of metallic gates and incompressible/compressible strips, we
investigate the conditions to observe Aharonov-Bohm (quantum mechanical phase
dependent) and Coulomb Blockade (capacitive coupling dependent) effects
reflected in conductance oscillations. In a last step, we solve the
Schr\"odinger and the Poisson equations self-consistently in a numerical manner
taking into account realistic experimental geometries. We find that, describing
the conductance oscillations either by Aharanov-Bohm or Coulomb Blockade
strongly depends on sample properties also other than size, therefore,
determining the origin of these oscillations requires further experimental and
theoretical investigation.
