Bryan P. Kibble

An initial measurement of Planck's constant using the NPL Mark II watt balance

During 2006 modifications were made to the NPL Mark II moving-coil watt balance which eliminated several significant sources of error. The apparatus was run from October 2006 to March 2007 to check its operation and to produce a preliminary value of Plancks constant h. This paper reports the current state of the work and predicts the uncertainty that is expected to be achievable with the existing apparatus. The preliminary value of h is 6.626 070 95(44) × 10−34 J s, which corresponds to a value of the Avogadro constant of NA = 6.022 139 99(40) × 1023 mol−1.

A Realization of the SI Watt by the NPL Moving-coil Balance

Mechanical and electrical power in SI units have been equated by measurements made on a coil part of which is in a strong magnetic field. The force due to a current I flowing in the coil, is weighed by opposing it with a mass M subject to the earths gravitational acceleration g. This is combined with a separate measurement in which a voltage V is generated in the coil when it is moved vertically with velocity u through the relationship IV = M g u. If the current produces a voltage V across a resistor whose value R is known in SI units, then V = (M g u R)1/2. Hence the voltage V and the current I are known in SI units and can be used to express the value of the NPL working standards in SI units. The working standard of voltage has hitherto been maintained in terms of a Josephson effect apparatus by ascribing the value 483 594 GHz/volt (maintained) to the Josephson constant KJ presumed equal to 2e/h. The measurements reported here suggest a different value of KJ 483 597,903 ± 0,035 ought to be used, based on the premise that the SI value of the quantum Hall resistance is RK = 25 812,8092 ± 0,0014 Ω. If one presumed also that RK = h/e2 exactly, the values of elementary charge e and the Planck constant, h, which may be deduced from these measurements are e = 1,602 176 35 ± 0,000 000 14 × 10-19 C, h = 6,626 068 21 ± 0,000 000 90 × 10-34 J s, which may be compared with the values recommended by the CODATA Task Group on Fundamental Constants which are e = 1,602 177 33 ± 0,000 000 14 × 10-19 C, h = 6,626 075 5 ± 0,000 004 0 × 10-34 J s.

The NPL moving-coil apparatus for measuring Planck's constant and monitoring the kilogram

In a moving-coil balance, a coil threaded by a strong magnetic flux is moved with linear velocity u to induce a voltage V. In a separate measurement a force F caused by a current I (=V/R where R is a resistance) flowing in the coil is then weighed as a mass M times gravitational acceleration g. The relationship M=V/sup 2//Rgu is obtained by eliminating the rate of change of magnetic flux threading the coil. A relative uncertainty of some parts in 10/sup 9/ seems possible, enabling the stability of the kilogram to be monitored in terms of the Josephson effect (/spl sim/h/2c) used to measure V and the quantum Hall effect (/spl sim/h/e/sup 2/) used to measure R. Therefore M=Ah where A is a measured quantity involving only meters and seconds, and either Plancks constant h could be measured in terms of the present kilogram or the kilogram could be redefined in terms of a defined value of h. We report progress with the NPL apparatus toward these ends.

Measurement of the AC quantized Hall resistance

The flatness and frequency dependence of the i=2 and four quantized Hall resistance plateaus have been investigated. It was observed that for frequencies up to 6.4 kHz, a flat region exists at the center of the plateaus where the relative resistance is constant to /spl plusmn/2/spl times/10/sup -8/, and its relative value has a linear frequency dependence of (0.119/spl plusmn/0.001) (/spl mu//spl Omega///spl Omega/)/kHz and (0.107/spl plusmn/0.007) (/spl mu//spl Omega///spl Omega/)/kHz for i=2 and 4, respectively.

Towards accurate measurement of the frequency dependence of capacitance and resistance standards up to 10 MHz

Progress toward an understanding of the frequency dependence of capacitance and resistance standards at frequencies up to 10 MHz is presented. A qualitative comparison is also made for capacitance and dissipation factor measurements between the National Physical Laboratory (NPL) high-frequency four terminal-pair (4TP) bridge and a commercial impedance analyzer for the first time. A set of novel high-frequency calculable coaxial resistance standards, of nominal 100 /spl Omega/ and 1 k/spl Omega/ values, have been developed and their calculated frequency dependence up to 1 MHz is given.

Comparison of capacitance with AC quantized Hall resistance

A quadrature bridge operating at a frequency of 1.233 kHz has been developed to compare 10 nF capacitances to the quantized Hall resistance on the i=2 plateau in order to realize the farad in terms of R/sub K/. Portable precision ceramic capacitance transfer standards of remarkable performance have been developed for this purpose.

A new four terminal-pair bridge for traceable impedance measurements at frequencies up to 1 MHz

A new four terminal-pair bridge has been developed and used for traceable measurement of capacitance and resistance at frequencies up to 1 MHz. The apparent capacitance of a gas-filled 100-pF standard agrees with calculated values to better than 200 /spl mu/F/F at 1 MHz. This is an order of magnitude improvement on existing capabilities at NPL. The frequency dependence of the dissipation factor of capacitance standards is discussed, and the capacitance and dissipation factor of ceramic NPO-dielectric standards has also been measured. The frequency dependence measurements of the calculable coaxial 100-/spl Omega/ and 1-k/spl Omega/ resistance standards are also presented.

The relationship between the SI Ohm, the Ohm at NPL, and the quantized Hall resistance

New measurements relating the quantized Hall resistance R<inf>H</inf>(= h/ie²), International System (SI) Ohm (Ω<inf>SI</inf>), and the National Physical Laboratory maintained ohm (Ω<inf>NPL</inf>) have now been completed at NPL in the U.K. with improvements and simplifications in the cryogenic current comparator measurements and 1000-Ω dc resistance measurements. From the measurements over the past four years the relationship between Ω<inf>NPL</inf> and Ω<inf>SI</inf> can be described by the equation Ω<inf>NPL</inf> − Ω<inf>SI</inf> = −1.049(0.020) − 0.0478(0.0074)[t − 1986.0] μΩ in which t is measured in years. For the previous two years the equivalent relationship between R<inf>H</inf> and Ω<inf>NPL</inf> is R<inf>H</inf> = 25 812.8(1 + 1.452(0.038) × 10 ⁻⁶ + 0.0694(0.0772) · [t − 1986.0] × 10⁻⁶) Ω<inf>NPL</inf> in which the uncertainties (in parentheses) are one-standard-deviation (1σ) random uncertainties of the least squares fit to the data. Combining the most recent measurements of R<inf>H</inf> and Ω<inf>SI</inf>, using a more direct method of measurement R<inf>H</inf> = 25 812.8106(17) Ω<inf>SI</inf> in which the relative combined uncertainty is 0.067 × 10⁻⁶.

Programmable Josephson Arrays for Impedance Measurements

Arbitrary impedance ratios can be determined with high accuracy by means of a programmable Josephson system. For a 1 : 1 resistance ratio at 10-kΩ level, we demonstrate that the novel system allows measurements over a wide frequency range from 25 Hz to 6 kHz. Uncertainties are in the range of a few parts in 108 and thus comparable to those of conventional impedance bridges. Two methods for four-terminal-pair impedance measurements have been investigated, i.e., the potential comparison circuit and the coaxial setup. Both methods are capable of measuring from dc to 6 kHz with uncertainties to a few parts in 108. The potential comparison circuit has an upper bound at 6 kHz due to the use of the sampling method. The four-terminal-pair coaxial setup has the potential to decrease the relative uncertainty down to 10-9 once systematic errors are analyzed and canceled.

The ac quantum Hall resistance as an electrical impedance standard and its role in the SI

Since 1990, the quantum Hall resistance measured with direct current (dc) has been established to represent and maintain the dc resistance unit and thereby has replaced the former derivation from calculated inductance and capacitance standards. Because of this success, it has been suggested to measure this quantum effect with alternating current (ac) and in this way to derive the units of resistance, capacitance and inductance consistently from the same quantum effect. In this paper, we recall the relations between these units, their role in the determination of the von Klitzing constant and the relations between the fundamental constants involved in the conventional and the quantum approach. Then, we review the first ac measurements of the quantum Hall resistance and show how the difficulties uncovered have been solved by relatively simple means. As a result, the measurement of the ac quantum Hall resistance has become as precise and reliable as its dc counterpart and much more accurate than any conventional impedance artefact.