Packed bed dielectric barrier discharges exhibit an improved energy efficiency and selectivity in nonthermal plasma based gas conversion. They enable the direct interaction between plasma and catalyst. In this contribution a compact coaxial DBD reactor enabling the end-on imaging of the discharge with and without packed beds is constructed and studied. The discharge morphology is correlated with electrical measurements such as V-Q plots. The studies are performed for different packed bed materials, binary gas compositions of argon and carbon dioxide, voltage amplitudes, average powers, and pressures. The analysis points outs the role of parasitic capacitances and parasitic discharges as often overlooked aspects. The introduction of the packed bed material into the coaxial barrier discharge arrangement increases the total capacitance, but the barrier of the outer glass tube mostly determines the maximum effective dielectric capacitance. The choice of the packed bed material determines the voltage threshold and the average discharge power. The investigations leads to a revision of the equivalent circuit for packed bed barrier discharge reactors, which also accounts the properties of different filling materials.