A previous paper reported some features of atmospheric Tungsten inert gas arc plasmas obtained with Langmuir probes operating in floating conditions and results on averaged quantities were given. This paper develops the method for probes in biased conditions. Because in the available literature sources, the construction of characteristic curves (V-I) in arcs is not discussed, a description of directly observed quantities is presented and some constructive methods are shown for a range of arc currents (50 to 200 A) and probe positions with considerable detail. The main result of this work is that these curves are incomplete in the column of atmospheric pressure arcs so that the traditional methods to extract plasma parameters are of little use. In contrast to previous works dealing with the anode region of the arc, it is found that the only useful portion of the V-I curve is the ion saturation part for all the arc currents investigated. Also, it is not possible to identify the plasma potential from the V-I curve. Ion saturation occurs for all probe locations at the lowest arc currents, whereas saturation is uncertain for probes closer to the cathode at higher arc currents. When saturation does occur, it is characterized by the flatness of the curve with respect to the potential: no power law dependencies on the voltage are found. Also, for the higher arc currents, an inner arc region can be identified where ion saturation is uncertain or does not occur. An accompanying paper exploits the ion saturation part of the characteristics to estimate the arc plasma temperature.