The usefulness of different voltage-current characteristics is defined for describing different properties (static, dynamic, energy, frequency etc.) of an arc in the electrical circuits of electrotechnological devices. The influence of different physical factors on the shape of characteristics has been analysed. The study presents the analytical forms of functions developed for approximating the static and commutative characteristics of an arc in AC plasma torches with a pre-set parameter in the form of a gas mass stream and/or a plasma column length.