The absolute measurement of electrical resistance by a new rotating-coil method

A rotating coil of mean radius α lies symmetrically between two fixed twin coils of radius a. If the ratio α/a lies between 0.58 and 0.53 it is easy to arrange, by merely adjusting the distance between the twin coils, that the mutual inductance M between the rotating coil and the two fixed coils shall be very accurately proportional to the angle θ of displacement from the conjugate positions over a range of some 10° of arc on either side of the zeros. The constant K of the relation M = Kθ can then be accurately measured by a method here described in which θ is deduced from a mutual-inductance ratio. At the same time errors in the calibration of the inductometer used are eliminated. If such a coil spins with an angular velocity ω, while a current C traverses the fixed twin coils, a uniform e.m.f. ωCK can be drawn off a commutator on the rotating shaft and made to balance an e.m.f. CR drawn off an adjustable resistance R carrying the same current. Thus R = ωK. If now the twin coils are brought rather closer together, the law of variation of M with theta takes the form M/θ = K + Aθ2 - Bθ4 over a displacement of 35° of arc from the zeros, where A and B are very small positive constants and M/θ attains a maximum value K', where θ2 = A/2B and scarcely changes over a range of 3° in this neighbourhood. This allows larger sectors to be used on the commutator and the constant K' of the relationship R = K'ω can be accurately determined for a suitable commutator in situ. The experimental work is mainly devoted to a study of the laws of inductance on which the method depends and to the determination of the constants K and K', but preliminary spin experiments are very hopeful and resistances of between 0.32 Ω. and 0.64 Ω. have been measured absolutely by means of commutators with sector contacts of 23° and 47° of arc. Owing to the relatively large e.m.f.'s involved, the method is very sensitive and a fluxmeter can be used as the balance-detector for hand-controlled stroboscopic spins. In other experiments a synchronized television motor was used.