An Absolute Determination of Resistance Based on a Calculable Standard of Capacitance

Abstract

A determination of the NSL unit of resistance based on standards of length and frequency has been made. A cylindrical cross-capacitor, for which the change in capacitance for a measured change in length may be calculated very precisely, is used to calibrate a number of small fixed capacitors (1/6 or 1/4 pF). AC bridge techniques are used to build up to 10 nF and also to measure the resistance of a 10 kΩ resistor in terms of this capacitance and a measured frequency (ω = 10 4 ). DC measurements are used to relate the 10 kΩ resistor to the Laboratory's 1 Ω standard resistors. The estimated uncertainty in the measurements is 2 in 10 7 but the accuracy of the determination is limited to ± 7 in 10 7 because of the uncertainty in the speed of light. Mean values, derived from a number of determinations, and corresponding to the times of the BIPM international comparisons, are Jan. 1964 Ω NSL = 1 Ω - 3.58 μΩ Feb. 1967 Ω NSL = 1 Ω - 3.80 μΩ. The standard deviation of a series of determinations was 0.06 μΩ.