Mechanical and electrical power in SI units have been equated by measurements made on a coil part of which is in a strong magnetic field. The force due to a current I flowing in the coil, is weighed by opposing it with a mass M subject to the earth's gravitational acceleration g. This is combined with a separate measurement in which a voltage V is generated in the coil when it is moved vertically with velocity U through the relationshipIf the current produces a voltage V across a resistor whose value R is known in SI units [I], then
During 2006 modifications were made to the NPL Mark II moving-coil watt balance which eliminated several significant sources of error. The apparatus was run from October 2006 to March 2007 to check its operation and to produce a preliminary value of Planck's constant h. This paper reports the current state of the work and predicts the uncertainty that is expected to be achievable with the existing apparatus. The preliminary value of h is 6.626 070 95(44) × 10 −34 J s, which corresponds to a value of the Avogadro constant of N A = 6.022 139 99(40) × 10 23 mol −1 .
When measured with ac at kilohertz frequencies the quantized Hall resistance (QHR) of a quantum Hall effect (QHE) device is usually found to be current- and frequency-dependent. This is a limitation on its use as a quantum impedance standard. We develop a model for the principal ac losses arising in the QHE device and show how they are responsible for the observed QHR current and frequency coefficients. We believe that losses are mainly caused by dissipative ac charging of the device along its edges. Charging is induced by the passage of the Hall current and by capacitive coupling between an edge and any nearby conductor maintained at an ac potential different to that of the edge, as for example at shield potential. The loss power is proportional to frequency and increases more rapidly than the square of the applied voltage or current. We model losses in terms of in-phase loss currents, which are a function of the amplitude of the ac charge reaching or leaving edges. The QHR frequency coefficient is zero only when the loss current for one portion of the high-potential edge and that for a corresponding portion of the low-potential edge are equal and of opposite sign. We propose a simple method for approaching that balance condition: gates are located under the device edges and their ac potentials adjusted so that the QHR current coefficient, evaluated at a constant frequency, is zero. We report measurements of the residual QHR frequency coefficients obtained after adjustment for GaAs/GaAlAs devices of two different types. For five different devices of the most favourable type, the QHR frequency coefficients do not exceed ±2 parts in 108 per kilohertz.
Since the quantum Hall resistance (QHR) measured with alternating current (ac) has reached the state of an excellent quantum standard of impedance, we have realized a quadrature bridge with two ac QHRs to accurately calibrate capacitance standards in terms of the SI value of the von-Klitzing constant, without the need for any calculable artefact. The advantages of the realized measuring chain, experimental tests of the coaxial ac bridges involved and the achieved relative uncertainty of 6 × 10 −9 (k = 1) are discussed.
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