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A two-dimensional Particle-in-Cell based Monte Carlo Collision model is used to study the dynamics of a spark-type electric discharge pulse within narrow dielectric cavities of submillimeter dimensions. The gas within the cavity is taken to be air at atmospheric pressure. The development of an avalanche through primary and secondary ionization processes, is followed till extinction. Secondary processes including photo-emission and ion-emission from the cathode are considered. The model is seen to successfully simulate the evolution of the discharge and yield useful information about the build-up of space charge within the gaseous channel, consequent modification of the electric field, ionic and electronic currents, and charge accumulation on the electrodes at end of discharge pulse. A significant contribution of this work is that the simulated discharge within the cavity is coupled through the electrodes, with an external circuit comprising of a voltage source. The effect of different electrode configurations viz. metallic-metallic, dielectric-metallic and dielectric-dielectric, as might occur at pd initiation sites, is studied. This is seen to significantly affect many of the parameters studied, especially the charge deposition at discharge extinction. The magnitude of the discharge pulse and its rise-time are also seen to be affected. The phase-space scatter plots for electrons, positive and negative ions are obtained, which help to understand the manner in which the discharge progresses over time.