In this experimental work, the physical and electrical characteristics of a fabricated positive DC corona jet are analysed. The designed plasma jet operates with the direct current (DC) applied voltage and Ar/CO$_2$ mixture at the atmospheric pressure (760 Torr). The emitted spectra are analysed by the optical emission spectroscopy technique. Then, the rotational, vibrational and excitation temperatures, electron density and CO$_2$ dissociation degrees are obtained. Besides, using the actinometry method, the carbon dioxide dissociation process is studied.The CO$_2$ excitation and ionisation from $X^2\Pi_g \rightarrow A^2\Pi_u$ transitions along with the OH emission band from the $A^2\Sigma\rightarrow X^2\Pi$ transitions are detected. It is seen that at all the temperatures, electron number density and CO$_2$ dissociation to CO, O$_2$ and O species are increased at higher input electrical currents.