A new diagnostic tool to study dielectric barrier discharges (DBDs) at atmospheric pressure by local electrical measurements is introduced. The square ground electrode is divided into 64 square segments (3.44 mm side length) so as to measure the discharge currents and gas voltages with spatial resolutions, which allows a 2D mapping. The electrical measurement results are validated by a comparison with short exposure time photographs taken from the top view of the discharge cell. For this purpose, we changed the local discharge behavior by varying locally the gas gap and the barrier capacitance and also by using a gas flow. Then, in both situations, the breakdown voltage depends on the position, and the discharge current and gas voltage are different as well. The measurements performed for a planar DBD in nitrogen with admixed nitrous oxide gas show that even if the discharge operates in a diffuse regime, the discharge does not behave exactly homogeneously on the whole surface area. The resulting electrical parameters allow us to refine the understanding of planar DBDs. The discharge activity changes the gas composition and thus, the level of preionization in the direction of the gas flow. This influences the local breakdown voltage and thus, the discharge morphology and local power density on the surface. The use of this new electrical diagnostic tool will allow us to refine the analysis of the spatial development of the discharge. This work gives some clues to improve the spatial resolution of this tool in the future.