## Watt balances

### What does the watt balance do?

A watt balance compares 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; 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*. The current *i* is measured, and so the weight of the mass is known in terms of the product *Bli*. In practice the flux density of the magnet and the length of wire in the coil 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 *i* 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 Planck's 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 and von Klitzing constants 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 (2011) there are three watt balances in operation worldwide at: America's National Institute for Standards and Technology (NIST), Switzerland's Federal Office of Metrology (METAS), and NRC-INMS where the NPL Mark II balance is now operational. All these balances have produced precise measurements of the Planck constant.

Watt balances are being assembled and tested at the Bureau International des Poids et Mesures (BIPM) and at France's Laboratoire National de Métrologie et d'Essais (LNE). China's National Institute of Metrology (NIM) and New Zealand's Measurement Standards Laboratory (MSL) are pursuing research in this area. NIST and METAS are starting the design of their next generation watt balances, which will be operational by around 2020.

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

After originating the idea in the 1970s and pioneering its use, we transferred it to Canada's National Research Council, Institute for National Measurement Standards in 2009. We collaborate closely with its new operators in Canada to further the knowledge of this key area of measurement science.

Prior to its departure our 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. 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).

### Do all the watt balances agree on the value of the Planck constant?

At the time of writing (2011), there are significant discrepancies between the lowest uncertainty values of Planck's constant produced by watt balances (NIST with an uncertainty of 3.6 x 10^{-8}) and measurements of the Planck constant made using a different technique via measurements of the Avogadro constant by the International Avogadro Coordination (IAC with an uncertainty of 3.0 x 10^{-8}). Scientists are working hard to make further measurements to help resolve the discrepancy and are aiming to reduce the individual uncertainties of their measurements to 2 x 10^{-8} or better.

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 scale of the problem. 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 are collaborating closely with their Canadian counterparts to make further investigations and to implement the modifications which will eliminate the cause of this uncertainty in the apparatus.

### 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.

Contact Ian Robinson for more information.

**Last Updated: 2 May 2013**

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