Inductor-Disconnected-Discharged (IDD) arc resistance model established is foundation of the evaluation of the non-explosive intrinsically safe performance for inductive circuit.The IDD characteristics were studied through test

based on the IEC safety spark test apparatus.The change laws of the discharge resistance with duration were deeply analyzed.By using non-linear regression method

the function relationship was obtained between the IDD time

inductance and initial current.Considering the tungsten and cadmium electrode structures of the IEC spark-test apparatus

a physical model of the inter-electrode arc discharge was established

and the boundary conditions of two-dimension Poisson's equation were inferred.Based on this

the algorithm of variable separation was applied to solve the Poisson's equation.Then

the mathematical expression of arc resistance was deduced.The relational expression between the arc discharge voltage and current of the IDD discharge were obtained for the low voltage circuits.The simulation and experiment results show that the theoretical analysis and proposed model are valid and feasible.