In this paper, we show how plasma discharge capillaries can be numerically modeled as resistors within an RLC-series discharge circuit, allowing for a simple description of these systems, while taking into account heat and radiation losses. An analytic radial model is also provided and compared to the numerical model for plasma discharge capillaries at thermal equilibrium, with corrections due to radiation losses. Finally, diagnostic techniques based on visible spectroscopy of plasma emission lines are discussed both for atomic and molecular gases, comparing experimental results with numerical simulations and theoretical calculations.