On The Inductance Of The Calculable AC/DC Resistance Standard Of Toriod Type

The quantum Hall resistance is valuable in practical applications for its superiority over object standard in accuracy and stability, thus CIPM has given an international recommended value of the quantum Hall resistance for the values of resistance unity. The natural standard of DC quantum Hall resistance been completed in China. However, the AC resistance standard has not been set up yet. In order to keep consistency with international units after joining the WTO, it is urgent to accomplish the transform of AC/DC quantum Hall resistance standard. Therefore, a new kind of calculable resistor with toroid shape is proposed by Prof. Zhang Zhonghua NIM. With this design it is possible to get better result than the traditional calculable resistors.This paper describes the inductance of calculable resistor of toroid design which influences the transform of AC/DC quantum Hall resistances standard. Theoretical models were built based on the complex logarithm transform function. Using this model, the vectormagnetic potential A of long straight current-carrying wires with discrete distribution iscalculated and the value of A at any point is gained by numerical calculations. Thus, the distribution of magnetic field can be obtained, demonstrating the relation of the field and the wires. It also displays the distribution of main magnetic flux and the leakage flux. Furthermore, the equations of boundary magnetic field line and the position of the boundary on the axis can be calculated theoretically on the model. Because the high precision is required in this work, it remains to be discussed the magnetic field of the double layer lines which carryreverse current. Two conclusions are drawn. The first one is that the lines of A in the double lines inner magnetic are ellipses. The other is the ratio of long axis and short one is related with R and d. These results are the same as the single turns'. Discussing the external magnetic field of wires, boundary magnetic field lines are also given. By analyzing the model and its figure, their characteristics are given. Another method is utilized to validate the result of the equations of magnetic-curve boundary and the same results are present. According to the results, the leakage inductance of the current with discrete distribution is computed and then the distinction between the practical inductance and the perfect one is presented.The analysis of the leakage inductance, which influences the transform of AC/DCquantum Hall resistance standard, is indispensable in building the AC quantum Hall resistance standard which based on the AC calculable resistor standard. Therefore, the method of calculation and the conclusion in this paper can give a reference for valuing leakage flux and inductance in engineering electromagnetic...