Studies on the development of high voltage superconducting apparatuses, such as transmission superconducting fault current limiters (SFCLs) and superconducting cables, have been performed worldwide. In this paper, a study on the electrical insulation characteristics of electro negative gas according to various pressures and utilization factors was conducted as a part of developing a high voltage superconducting coil with a sub-cooled nitrogen cooling system. Some gases such as helium (He), nitrogen ($N_2$), and sulfur hexafluoride ($SF_6$) are considered for pressurizing the sub-cooled nitrogen cooling system of high voltage SFCLs and superconducting cables. $SF_6$ is used to pressurize and enhance the dielectric performance of a superconducting system of a sub-cooled nitrogen cooling system for superconducting cables being developed in the Republic of Korea. In this paper, dielectric experiments on AC voltage, as well as lightning impulse voltage of $SF_6$, are conducted according to various utilization factors by using several kinds of sphere-to-plane electrode systems. As results, it is known that the empirical formulae of $SF_6$, known as an electro negative gas, are derived according to various pressures and utilization factors. Also, the appropriate pressure condition for designing a high voltage superconducting coil is found from the viewpoint of dielectric performance.