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March Articles:

Adjusting the Values of the Fundamental Constants

Time Measurement at the Millennium

Joseph Loschmidt, Physicist and Chemist
Box 3. Watt-Balance Experiment: The Planck Constant

The Planck constant h can be measured by comparing a watt of mechanical power expressed in terms of the meter, kilogram, and second to a watt of electrical power expressed in terms of the Josephson constant KJ = 2e/h (which relates frequency and voltage through the Josephson effect) and the von Klitzing constant RK = h/e2 (which has units of resistance and originates in the integer quantum Hall effect) in the combination

The apparatus that makes the comparison is called a watt balance.8 The basic principle of the watt balance is illustrated by one of its implementations.9 A horizontal coil of wire is suspended in a radial magnetic field. The current in the coil needed to support the weight of a mass standard is measured in one phase of the experiment. In the second phase, the strength of the field is determined by slowly moving the coil vertically and measuring the induced voltage. The current I and mass m in the first phase and the velocity v and induced voltage U in the second phase are related by

mgv = IU = Af1f2h,

where g is the local acceleration of free fall, which is accurately measured with an absolute gravimeter. Since the voltage U and the voltage and resistance that determine I are calibrated in terms of the Josephson and von Klitzing constants, the constant A is, in principle, exactly known, and f1 and f2 are the accurately known frequencies applied to the Josephson junctions in the two phases of the experiment. This equation gives h in terms of quantities directly measured in the experiment. The 1998 recommended value of the Planck constant, which is determined primarily by the watt-balance experiment, is

h = 6.626 068 76(52) ´ 10-34 J s.

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© 2001 American Institute of Physics

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