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In this paper, a dielectric-barrier discharge (DBD) of Ar:N2 mixtures at atmospheric pressure is studied in relation to plasma jet production. The discharge takes place in a capillary dielectric tube, and it is sustained by positive high-voltage pulses. It is herein claimed that, apart from the traditional DBD (which is developed perpendicularly to the gas flow and can produce afterglows), plasma jet propagates simultaneously parallel to the gas flow due to ionization waves guided by the dielectric tube. A quite simple electrical model is applied to simulate the proposed DBD and plasma jet coexistence. The concept of capacitive behavior of both barrier discharge and jet is taken into account. This model in combination with UV-visible optical emission spectroscopy and conventional photography supports the aforementioned statements. The dependence of the jet domination against the afterglow on the gas mixture is demonstrated, and the N2 additive at 2.5 %-3% in Ar is found to be the most efficient for jet production. The model runs with the measured interelectrode voltage as input and yields the circuit total current as output. Matching between the measured current and the model output is attempted by adjusting two free parameters. This tuning of the free parameters provides reliable values for the electrical components of the model. Thus, a simple mean for realistic representation of both DBD and jet is achieved. This tool could be applied to the design of plasma jet reactors.