Kibble Balance

A Kibble balance or watt balance is an electromechanical measuring instrument that measures the weight of a test object very precisely by the electric current and voltage needed to produce a compensating force. It is a metrological instrument that can realize the new definition of the kilogram unit of mass based on fundamental constants, termed an electronic or electrical kilogram.


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Kibble balance from NIST is a used to determine the value of the planck constant which defines the mass of the kilogram. image: wikipedia

The name watt balance comes from the fact that the weight of the test mass is proportional to the product of current and 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.

Veritasium video nicely explains the Kibble Balance. 


Since 1889, the definition of the kilogram was based on a physical object known as the International Prototype of the Kilogram (IPK). In 2013, accuracy criteria were agreed upon by the General Conference on Weights and Measures (CGPM) for replacing this definition with one based on the use of a Kibble balance. After these criteria had been achieved, the CGPM voted unanimously on November 16, 2018 to change the definition of the kilogram and several other units, effective May 20, 2019, to coincide with World Metrology Day.

Source adapted from: Wikipedia contributors. (2019, March 4). Kibble balance. In Wikipedia, The Free Encyclopedia. Retrieved 10:36, May 23, 2019, from https://en.wikipedia.org/w/index.php?title=Kibble_balance&oldid=886192779


Commentary

Further specific details from an email from NIST


Unfortunately, a lot of details are left out, when the Kibble balance is explained in popular articles. The measurement takes place in two modes. In the velocity mode, the coil is moved through the magnetic field while simultaneously measuring the induced voltage U and the coil’s velocity v. This allows us to infer the geometric factor of the magnet system, i.e., BL=U/v. In the second mode, the unknown mass of order one kilogram is placed on the balance. A computer controls the current I in the coil so that the balance stays in the equilibrium position. This current is measured, and the weight of the mass can be inferred via mg=BL I, where BL comes from the measurement before. So, two electrical quantities are measured, U and I. To determine the mass, we also need to know the coil’s velocity v and the local acceleration g. Solving the equations for mass, we have m=UI/(vg)

Now your question is how do these quantities relate to Planck’s constant. The answer is as follows. The voltage U is measured by comparing it with a Josephson voltage system. You can think of it as a fancy battery, that makes a known voltage proportional to h/(2e) f, where f is a known microwave frequency (for us 18 GHz).  Note that h/(2e) is 1/Kj. The voltage produced by one Josephson junction is tiny, about 37 microvolts. So, we need many more Josephson junctions. In total, we have n1 Josephson junctions. For the NIST Kibble balance the induced voltage is about 0.69 V; hence n1 is approximately 18,500.  Hence U = n1 h/(2e)f

 

The current is routed through a resistor, and the voltage drop across the resistance is measured I=U2/R. The resistor itself is calibrated against a quantum Hall resistor using a resistance bridge. Such a device can give us ratios of resistances. Hence, we have R= r h/e^2, where r is the ratio determined by the resistance bridge. The Voltage U2 is measured the same way as U is measured above, leading to U2=n2 h(/2e)f. Combining the voltage and the resistance measurement yields I = n2 h/(2e)f /( r h/e^2 )= n2 e f/ (2r). As you can see, the current is independent of h and is just given by the elementary charge multiplied with a frequency and known numbers.

Combining U and I yields, U  I = n1 n2/(4r) h f^2. Here, the elementary charges cancel out, and the Planck constant, the two frequencies, and known numbers remain. Finally combining this with the equation for the mass yields,

m = n1 n2/(4r) h f^2/(vg).

In the NIST-4 Kibble balance, the current is about 7 mA. This current produces a force that corresponds to 500g.

The typeset in the email is a bit cumbersome to read, but the thoughts above are summarized in a free ebook that you can download at http://iopscience.iop.org/book/978-0-7503-1539-5