Electrical resistance standards and the quantum Hall effect

This review of electrical resistance standards begins with a description of classical standard resistors and their limitations. Methods of comparing resistance are described; these include bridges based on cryogenic current comparators capable of achieving statistical uncertainties approaching one part in 1010 in the measurement of resistance ratios. Such reproducibility is nearly two orders of magnitude smaller than the overall uncertainty of the most accurate determinations of the ohm from its SI definition via the calculable capacitor. The quantum Hall effect can provide an invariable reference standard of resistance linked to the fundamental physical constants. Many factors, however, limit the accuracy of practical realizations of quantized Hall resistance standards. Ultimately, the accuracy of a specific realization must be confirmed by comparison with similar standards; methods for doing this and the resulting agreement are presented. The ac techniques used in the determinations of the SI ohm by means of the calculable capacitor are now being applied to accurately link the quantized Hall resistance to the impedance of standard capacitors and thereby to provide a new reference standard of capacitance.