The article presents the justified use of functions containing the exponential component for the approximation of the static current-voltage characteristics of electric arc. The Author proposed a new function approximating the above-named characteristics which were next used in the mathematical Mayr-Pentegov model, expressed in two, i.e. differential and integral, forms. The two forms constituted the basis enabling the development of macromodels using controlled voltage and current sources. The article also presents families of dynamic current-voltage characteristics obtained through the simulation of processes in a circuit containing macromodels of arc powered by the source of current characterised by sinusoidal and trapezoidal waveforms and various frequency. The article demonstrates the usability of the proposed variants of the Mayr-Pentegov model.