In recent years, magnetic fluid and arc plasma simulation models based on local thermodynamic equilibrium have provided an important aid to the analysis of the arc characteristics of switching apparatus. However, existing studies have shown that when the current is small, the arcing process deviates from local thermodynamic equilibrium, but the specific critical value of the current is not clear. In this paper, from the perspective of arc spectral analysis, an arc experimental platform is built with spectral measurement function. Through this platform, the atomic spectral line data of the carbon electrode during arc gap at different currents are measured, and the electron density data are obtained by the Boltzmann plot method and the Stark broadening method. The measured results show that when the current is greater than 40A, the electron density of the arcing process reaches above 10²²/cm³, which is consistent with the recognized data (>10²²) under the local thermal equilibrium. Under the same condition, when the current is less than 40A, the maximum value of the arc electron density order of magnitude is lower than 10²¹/cm³. The change of the arc electron density indicates that the arc motion does not follow the assumption of local thermodynamic equilibrium when the arc current is less than 40A. From this we can get the inference that whether the arcing process follows the local thermodynamic equilibrium depends on the size of the current, and the critical value is 40 A. When the current is greater than this value, the arcing process follows the local thermodynamic equilibrium, and conversely, it is not the case.