## Watt balances

### What does the watt balance do?

The watt balance technique provides a route to the redefinition of the kilogram in terms of a fundamental constant by comparing measurements of electrical and mechanical power to establish a link between the SI electrical and mechanical units.

The electrical quantities are measured using macroscopic quantum effects - the Josephson effect for voltage and the quantum Hall effect for resistance. These two effects link the electrical quantities to time and two fundamental constants: the elementary charge *e* and the Planck constant *h*. The watt balance can measure the SI unit of electrical power and, by using the Josephson and quantum Hall effects, determine the Planck constant, in terms of the SI base units of mass, length and time.

### How does it fit into the redefinition of SI units?

Within the existing SI, mass is defined in terms of the International Prototype Kilogram (a platinum-iridium cylinder cast in 1879) held at BIPM in Paris; under these circumstances the watt balance measures the Planck constant in SI units. But, if the SI were to be redefined, fixing the value of the Planck constant, the watt balance would provide a mechanism whereby any suitably equipped laboratory could determine the unit of mass or the SI value of any mass within its operating range; placing mass on the same footing within the SI as length and time. The redefinition process cannot be rushed as this change must be made in a manner that does not affect worldwide measurements of mass, and so agreement must be reached between the independent contributing measurements. The value to be used in the definition will be chosen as a weighted mean of such measurements and, as in previous redefinitions within the SI, there will be no change in the mass unit at the time of redefinition.

The Planck constant, the fundamental constant of quantum physics, is not the only constant that could have been chosen for this purpose but, coupled with a change of the definition of the ampere to fix the value of the elementary charge, this choice presents particular advantages, both to Physics in general, and to electrical metrology in particular, by eliminating the quoted uncertainty of a number of important combinations of physical constants.

### How does it work?

The watt balance makes an indirect comparison of electrical and mechanical power using a coil of wire suspended from one arm of a balance. The coil is suspended in a magnetic flux density *B* and an adjustable current *i* is passed through it. This produces a force *Bli* (where *l* is the length of the wire in the coil) and the current is adjusted to balance the weight *mg* of a mass *m*, (where *g* is the local acceleration due to gravity). The current *i* is measured, and so the weight of the mass is known in terms of that and the product *Bl*. In practice, the flux density *B* of the magnet and the length of wire in the coil *l* are extremely difficult to measure to the required accuracy. To overcome this, the coil is moved through the field at a constant velocity *u*, which is measured with an interferometer. This motion produces a voltage *V* that is equal to *Blu*, the product of the flux density, the coil length and the velocity. By combining the results of the two measurements the product *Bl* can be eliminated to equate virtual mechanical power *mgu* and virtual electrical power *Vi*:

*mgu = Vi*, or *m = Vi/gu*

By measuring the local acceleration due to gravity *g*, the velocity of the coil *u*, the voltage *V* and the current, we can measure mass. The measurements of *g* and *u* depend only upon the metre and the second. The voltage measurement is made using the Josephson effect (*V = hf/2e) *where *e* is the elementary charge. The current measurement is made by measuring the voltage drop *V' = hf'/2e*, caused by the current flowing in a resistor known in terms of the quantum Hall effect *R = h/ne ^{2}*, where

*n*is a small integer, giving

*i = nef'/2*. The product

*iV = hff'/4*depends only upon the Planck constant

*h*and the second via the frequencies

*f*and

*f'*. This gives

*mgu = hff'/4*, or

*m = hff'/4gu*.

### Who designed it?

The principle of the watt balance was originated at NPL by Dr Bryan Kibble in 1975 and underpins the operation of the many such balances in use, or under construction, around the world.

Two watt balances have been operated by NPL both of which were built by NPL scientists Bryan Kibble and Ian Robinson.

The original (Mark I) balance operated in air and, in conjunction with SI measurements of the ohm, was used to determine the ampere in terms of the SI base units: the kilogram, the metre, and the second. These measurements played a leading part in fixing the conventional values for the Josephson constant 2*e*/*h* and the von Klitzing constant *h*/*e*^{2} which are used as the basis for electrical measurements around the world.

The second (Mark II) balance was designed to measure the Planck constant and pave the way for the redefinition of the kilogram. It operates in vacuum to eliminate the effects of the atmosphere on mass and velocity measurements.

In 2009, the NPL Mark II watt balance transferred to the National Research Council, Institute for National Measurement Standards (NRC-INMS) in Ottawa, Canada. This move represented a unique opportunity to transfer a major metrological experiment to a new location and for an independent scientific team to take responsibility for future development of the experiment. This provides a robust test of the results previously obtained at NPL, with an ongoing collaboration between scientists from the two institutes as the apparatus was rebuilt and put into service.

### Who has watt balances?

At the time of writing (2015) there are a number of watt balances in operation or approaching operation worldwide at: America's National Institute for Standards and Technology (NIST), Switzerland's Federal Office of Metrology (METAS), NRC-INMS where the NPL Mark II balance is now operational, the Bureau International des Poids et Mesures (BIPM), at France's Laboratoire National de Métrologie et d'Essais (LNE) and at China's National Institute of Metrology (NIM).

Watt balances are being assembled and tested at New Zealand's Measurement Standards Laboratory (MSL) and at the Korea Research Institute of Standards and Science (KRISS). Many of these laboratories expect to have published measurements of the Planck constant by 1 July 2017, which is the deadline for measurements to contribute to the consensus value of the Planck constant used for the proposed redefinition of the kilogram in 2018.

### Why doesn't NPL have a watt balance?

After originating the idea in the 1970s and pioneering its use, we transferred the latest NPL watt balance, the NPL Mark II, to Canada's National Research Council, Institute for National Measurement Standards in 2009. We continue to collaborate with its new operators in Canada to further knowledge of mass measurement - a key area of measurement science.

Prior to its departure, the Mark II watt balance was producing a consistent value and, due to a number of improvements, its underlying uncertainty was decreasing and had almost halved from 6.6 x 10^{-8} in 2007 to 3.6 x 10^{-8} in 2009, so the transfer to Canada was a great opportunity to see if the value remained consistent once it was in a different location and operated by different people.

In June 2009, just prior to its transfer to Canada, NPL scientists identified a problem in the Mark II watt balance. Because of shipping restrictions the transport of the watt balance had to go ahead regardless of this discovery and there was just sufficient time to identify the cause and scale of the problem, but insufficient time to eliminate the problem and make further measurements. This led to the addition of an extra component to the uncertainty budget for the measurements which increased the uncertainty from

3.6 x 10^{-8} to 20 x 10^{-8}. A full description of the apparatus, the results, a description of the problem and the steps needed to eliminate it were published in Metrologia in February 2012. NPL's experts collaborated closely with their Canadian counterparts to make further investigations and implement the modifications which eliminated the cause of this uncertainty in the apparatus, allowing the apparatus to reach world-class uncertainties below 2 parts in 10^{8}.

The transfer of NPL's watt balance also saved our Canadian counterparts an enormous amount of time and money, as they didn't have to build one of their own from scratch (which takes around 10 years).

### Are the measurements of the Planck constant consistent?

At the time of writing (July 2015), there are two published results for the Planck constant with uncertainties less than 2 x 10^{-8}. One is from the NPL Mark II balance operating at NRC in Canada with an uncertainty of 1.8 x 10^{-8} and the other is from measurements of the Avogadro constant by the International Avogadro Coordination (IAC) with an uncertainty of 1.8 x 10^{-8}. The two results are consistent within their uncertainties. Many other laboratories around the world are working hard to make further measurements to contribute to the forthcoming redefinition of the kilogram.

### What's next for the Watt balance?

Once agreement has been reached on the consensus value of the Planck constant and the redefinition has taken place, a worldwide ensemble of watt balances will provide a stable and robust mass scale which will be disseminated to science and industry via conventional mass standards.

In 2014, Bryan Kibble and Ian Robinson published newly discovered principles of watt balance design, leading to a new generation of watt balances which can be far simpler to build and operate than their predecessors. This should allow more laboratories to build watt balances and contribute to further improvements in the world's measurements of mass.

Contact Ian Robinson for more information.

**Last Updated: 20 Jul 2015**

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