Watt balance

# Watt balance

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Encyclopedia
The watt balance is an experimental electromechanical weight measuring instrument
Measuring instrument
In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of real-world objects and events. Established standard objects and events are used as units, and the process of measurement gives a number relating the item...

that measures the weight of a test object very precisely by the strength of an electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

and a voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

. It is being developed as a metrological instrument that may one day provide a definition of the kilogram
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

unit of mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

based on electronic
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

units, a so-called "electronic kilogram". The name watt balance comes 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.

## Design

The watt balance is a more accurate version of the ampere balance
Ampere balance
The ampere balance is an electromechanical apparatus used for the precise measurement of the SI unit of electric current, the ampere. It was invented by William Thomson, 1st Baron Kelvin....

, an early current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

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. This will define the weight of a kilogram in terms of a current and a voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

, as described below. Since current and voltage units are already defined in terms of fundamental physical constant
Physical constant
A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.There are many physical constants in...

s such as the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

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. The weight of the kilogram is then used to compute the mass of the kilogram by accurately determining the local gravitational acceleration using a technique that does not depend on a defined mass.

## Origin

The principle of the watt balance was proposed by B. P. Kibble of the UK National Physical Laboratory
National Physical Laboratory, UK
The National Physical Laboratory is the national measurement standards laboratory for the United Kingdom, based at Bushy Park in Teddington, London, England. It is the largest applied physics organisation in the UK.-Description:...

(NPL) in 1975. 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 watt 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.

The Watt balance originating from the British National Physical Laboratory has been transferred to the National Research Council of Canada
National Research Council of Canada
The National Research Council is an agency of the Government of Canada which conducts scientific research and development.- History :...

and is currently being recommissioned. Other Watt balance experiments are being undertaken in the US National Institute of Standards and Technology
National Institute of Standards and Technology
The National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...

(NIST), the Swiss Federal Office of Metrology (METAS) in Berne, the International Bureau of Weights and Measures
International Bureau of Weights and Measures
The International Bureau of Weights and Measures , is an international standards organisation, one of three such organisations established to maintain the International System of Units under the terms of the Metre Convention...

(BIPM) near Paris and Laboratoire national de métrologie et d’essais (LNE) in Trappes
Trappes
Trappes is a commune in the Yvelines department in the Île-de-France in north-central France. It is located in the western suburbs of Paris from the center in the new town of Saint-Quentin-en-Yvelines.-Transport:...

, France. The present accuracy record is held by the U.S. NIST, with a relative uncertainty
Measurement uncertainty
In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity. The uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity. All measurements are subject to uncertainty and a measured...

of 3.6, and experiments are continuing towards a goal of 1.

## Principle

A conducting wire of length L which carries an electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

I perpendicular to a magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

of strength B will experience a force equal to BLI. In the watt balance, the current is varied so that this force exactly counteracts the weight
Weight
In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:...

of a standard mass m, which is given by the mass multiplied by the local gravitational acceleration
Gravitational acceleration
In physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....

g. This is also the principle behind the ampere balance.

Kibble's watt 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
Faraday's law of induction
Faraday's law of induction dates from the 1830s, and is a basic law of electromagnetism relating to the operating principles of transformers, inductors, and many types of electrical motors and generators...

, a potential difference U is generated across the ends of the wire, which is equal to BLv. Hence the unknown quantities B and L can be eliminated from the equations to give
Both sides of the equation have the dimensions of power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...

, measured in watt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...

s in the International System of Units, hence the name "watt balance".

## Measurements

Accurate measurements of electric current and potential difference are made in conventional electrical unit
Conventional electrical unit
A conventional electrical unit is a unit of measurement in the field of electricity which is based on the conventional values of the Josephson constant and the von Klitzing constant agreed by the International Committee for Weights and Measures in 1988...

s (rather than SI units), which are based on fixed conventional values of the Josephson constant and the von Klitzing constant, KJ–90 and RK–90 respectively. The current watt 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.
The importance of such measurements is that they are also a direct measurement of the Planck constant
Planck constant
The Planck constant , also called Planck's constant, is a physical constant reflecting the sizes of energy quanta in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory, who discovered it in 1899...

h:

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
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

. In this case, the electric current and the potential difference would be measured in SI units, and the watt balance would become an instrument to measure mass.
Any laboratory which had invested the (very considerable) time and money in a working watt balance would be able to measure masses to the same accuracy as they currently measure the Planck constant.

In addition to measuring U times I, the laboratory must also measure v and g (the velocity and the local gravitational acceleration,) 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 measurements for U times I, which is the value measured by the watt balance.