On a method of comparing mutual inductance and resistance by the help of two-phase alternating currents

Abstract

A standard mutual inductance, after the design recently described by the writer, has now been constructed at the National Physical Laboratory. As the details of its construction will be published later, it is sufficient here to mention that its value calculated from the dimensions is 10.0178 millihenries. It forms an extremely accurate standard, against which both mutual and self inductances can be readily tested. In addition to this, it affords a means of obtaining values of resistance coils in absolute measure, and thus evaluating the ohm. This can be done in an indirect way by finding the capacity of a condenser in terms of resistance and time by Maxwell’s Commutator Method, and in terms of resistance and mutual inductance by Heydweiller’s modification of Carey Foster’s method. The comparison of resistance with mutual inductance can, however, be made far more simply and directly by the use of two-phase alternating currents in the method which I proceed to describe. I shall first take the ideal simple case, and afterwards notice some of the difficulties that may arise in practice. (2) Theory of the Medhod. In fig. 1 let M be the mutual inductance (a small fraction of it being adjustable) and R the resistance; and let A cos pt and B sin pt be currents in quadrature, e. g ., from a two-phase alternator or a phasesplitting device. Let G be a vibration galvanometer tuned to frequency n where p = 2 πn .