On the Measurement of the Resistivity in an Exploding Wire Experiment

Explosion of a metallic wire due to a large electrical current can be used for studying metallic states difficult to reach with other methods. Due to experimental constraints, direct measurement of the voltage drop across the wire is impractical, although many characteristics of the metal state in the wire can be derived from these waveforms. Usually, the transformation of the electrical signals is made with the assumption of a lumped model for all the elements of the circuit, including the wire. We discuss the validity of a lumped model, and we show that due to the variation in time of the current density distribution on the wire, this model will not provide accurate values for the wire resistivity. Wire resistivity inaccuracies are specially clear in gas and plasma states, due to the diffusion and movement of the current that produce a large variation of the magnetic flux inside the wire. In order to obtain more precise results in the resistivity of the wire metal, regardless of its state, a better approach is the use of Faraday's law of induction on a path along the border of the wire. Our experiments of exploding wires in atmospheric air present the advantage of the clear electrical boundary between the expanding wire and the surrounding air, where no current circulates. As the state of the wire boundary layer changes from solid to plasma, it is possible to estimate the resistivity of the metal in those states in a more precise way.