# Kibble balance

(Redirected from Watt balance)
The NIST-4 Kibble balance, which began full operation in early 2015, measured Planck's constant to within 13 parts per billion in 2017, which was accurate enough to assist with the redefinition of the kilogram planned for 2019.

A Kibble balance (or watt balance) is an electromechanical weight measuring instrument that measures the weight of a test object very precisely by the strength of an electric current and a voltage. It is a metrological instrument that can be used with a definition of the kilogram unit of mass based on fundamental constants,[1][2] a so-called "electronic" or "electrical" kilogram. The name watt balance came from the fact that the weight of the test mass is proportional to the product of the current and the voltage, which is measured in units of watts. In June 2016, two months after the death of the inventor of the balance, Bryan Kibble, metrologists of the Consultative Committee for Units of the International Committee for Weights and Measures agreed to rename the device in his honor.[3][4]

Accuracy criteria were agreed upon in 2013 by the General Conference on Weights and Measures (CGPM) for replacing the current definition of the kilogram (which has, since 1889, been based on a physical object known as the international prototype kilogram) with one based on the use of a Kibble balance. These criteria have since been met, and it is expected that the definition of the kilogram and several other units will change on May 20, 2019, following a final vote by the CGPM in November 2018.[3][5][6][7]

## Design

Precision Ampere balance at the US National Bureau of Standards (now NIST) in 1927. The current coils are visible under the balance, attached to the right balance arm. The Kibble balance is a development of the Ampere balance.

The Kibble balance is a more accurate version of the Ampere balance, an early current measuring instrument in which the force between two current-carrying coils of wire is measured and then used to calculate the magnitude of the current. In this new application, the balance will be used in the opposite sense; the current in the coils necessary to support the weight of a standard kilogram mass will be measured, "weighing" the kilogram. The weight of the kilogram is then used to compute the mass of the kilogram by accurately determining the local gravitational acceleration. This will define the mass of a kilogram in terms of a current and a voltage, as described below. Since current and voltage units are defined in terms of fundamental physical constants such as the speed of light and Planck's constant, this will provide an alternative definition of the kilogram in terms of these absolute constants. This may be a better definition than the current one, which defines the kilogram as the mass of a physical artifact, the international prototype kilogram, which is vulnerable to deterioration or damage.

## Origin

The principle that is used in the Kibble balance was proposed by Bryan Kibble of the UK National Physical Laboratory (NPL) in 1975 for measurement of the gyromagnetic ratio.[8] The main weakness of the ampere balance method is that the result depends on the accuracy with which the dimensions of the coils are measured. The Kibble balance method has an extra calibration step in which the effect of the geometry of the coils is eliminated, removing the main source of uncertainty. This extra step involves moving the force coil through a known magnetic flux at a known speed. This step was done in 1990.[9]

The Kibble balance originating from the National Physical Laboratory was transferred to the National Research Council of Canada (NRC) in 2009, where scientists from the two labs continued to refine the instrument.[10] In 2014, NRC researchers published the most accurate measurement of the Planck constant at that time, with a relative uncertainty of 1.8×108.[11] . A final paper by NRC researchers was published in May of 2017, presenting a measurement of Planck's constant with an uncertainty of only 9.1 parts per billion, the measurement with the least uncertainty to date. Other Kibble balance experiments are being undertaken[when?] in the US National Institute of Standards and Technology (NIST), the Swiss Federal Office of Metrology (METAS) in Berne, the International Bureau of Weights and Measures (BIPM) near Paris and Laboratoire national de métrologie et d’essais (LNE) in Trappes, France.[12]

## Principle

A conducting wire of length L that carries an electric current I perpendicular to a magnetic field of strength B will experience a Lorentz force equal to BLI. In the Kibble balance, the current is varied so that this force exactly counteracts the weight w of a standard mass m. This is also the principle behind the ampere balance. w is given by the mass m multiplied by the local gravitational acceleration g. Thus

${\displaystyle w=mg=BLI.}$

The Kibble balance avoids the problems of measuring B and L with a second calibration step. The same wire (in practice, a coil of wire) is moved through the same magnetic field at a known speed v. By Faraday's law of induction, a potential difference U is generated across the ends of the wire, which equals BLv. Thus

${\displaystyle U=BLv.}$

The unknown product BL can be eliminated from the equations to give

${\displaystyle UI=mgv.}$

With U, I, g, and v accurately measured, this gives an accurate value for m. Both sides of the equation have the dimensions of power, measured in watts in the International System of Units; hence the original name "watt balance".

## Measurements

Accurate measurements of electric current and potential difference are made in conventional electrical units (rather than SI units), which are based on fixed "conventional values" of the Josephson constant and the von Klitzing constant, ${\displaystyle K_{\text{J-90}}=2e/h}$ and ${\displaystyle R_{\text{K-90}}=h/e^{2}}$ respectively. The current Kibble balance experiments are equivalent to measuring the value of the conventional watt in SI units. From the definition of the conventional watt, this is equivalent to measuring the value of the product KJ2RK in SI units instead of its fixed value in conventional electrical units:

${\displaystyle K_{\text{J}}^{2}R_{\text{K}}=K_{\text{J-90}}^{2}R_{\text{K-90}}{\frac {mgv}{U_{90}I_{90}}}.}$

The importance of such measurements is that they are also a direct measurement of the Planck constant h:

${\displaystyle h={\frac {4}{K_{\text{J}}^{2}R_{\text{K}}}}.}$

The principle of the "electronic kilogram" would be to define the value of the Planck constant in the same way that the meter is defined by the speed of light. In this case, the electric current and the potential difference would be measured in SI units, and the Kibble balance would become an instrument to measure mass:

${\displaystyle m={\frac {UI}{gv}}.}$

Any laboratory that had invested the (very considerable) time and money in a working Kibble balance would be able to measure masses to the same accuracy as they currently measure the Planck constant.

In addition to measuring UI, the laboratory must also measure v and g using experimental methods that do not depend on the definition of mass. The overall precision of m depends on the precisions of the measurements of U, I, v and g. Since there are already methods of measuring v and g to very high precision, the uncertainty of the mass measurement is dominated by the measurement of UI, which is the value measured by the Kibble balance.

## In popular culture

One has even been built from Lego.[13]

## References

1. ^ Robinson, Ian A.; Schlamminger, Stephan (11 July 2017). "The watt or Kibble balance: a technique for implementing the new SI definition of the unit of mass". Metrologia. 53 (5): A46. Bibcode:2016Metro..53A..46R. doi:10.1088/0026-1394/53/5/A46.
2. ^ Palmer, Jason (2011-01-26). "Curbing the kilogram's weight-loss programme". BBC News. Retrieved 2011-02-16.
3. ^ a b "The Kibble Balance". Education. UK National Physical Laboratory website. 2016. Retrieved 15 May 2017.
4. ^ Consultative Committee for Units (CCU), Report of the 22nd meeting (15-16 June 2016), pp. 32-32, 35
5. ^ Cho, Adrian (May 19, 2017). "Plot to redefine the kilogram nears climax". Science. 356 (6339): 670–671. Bibcode:2017Sci...356..670C.
6. ^ Milton, Martin (14 November 2016). "Highlights in the work of the BIPM in 2016" (PDF). p. 10.
7. ^ Decision CIPM/105-13 (October 2016)
8. ^ Kibble, Bryan Peter (1975), Sanders, J. H.; Wapstra, A. H., eds., "A Measurement of the Gyromagnetic Ratio of the Proton by the Strong Field Method", Atomic Masses and Fundamental Constants 5, New York: Plenum, pp. 545–51
9. ^ Kibble, B. P.; Robinson, I. A.; Belliss, J. H. (11 July 1990). "A Realization of the SI Watt by the NPL Moving-coil Balance". Metrologia. 27 (4): 173. Bibcode:1990Metro..27..173K. doi:10.1088/0026-1394/27/4/002.
10. ^
11. ^ Sanchez, C. A.; Wood, B. M.; Green, R. G.; Liard, J. O.; Inglis, D. (31 March 2014). "A determination of Planck's constant using the NRC watt balance" (PDF). Metrologia. 51 (2): S5. Bibcode:2014Metro..51S...5S. doi:10.1088/0026-1394/51/2/S5.
12. ^ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006". Reviews of Modern Physics. 80 (2): 633–730. arXiv:. Bibcode:2008RvMP...80..633M. doi:10.1103/RevModPhys.80.633.
13. ^ Chao, L. S.; Schlamminger, S.; Newell, D. B.; Pratt, J. R.; Sineriz, G.; Seifert, F.; Cao, A.; Haddad, D.; Zhang, X. (2014-12-04). "A LEGO Watt Balance: An apparatus to demonstrate the definition of mass based on the new SI". American Journal of Physics. 83 (11): 913. arXiv:. Bibcode:2015AmJPh..83..913C. doi:10.1119/1.4929898.