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Equation 4 · Part 10 · The Last Artefact: Redefining the Kilogram

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KJ=2eh,RK=he2,KJ2RK=4hK_{\mathrm J} = \frac{2e}{h}, \qquad R_{\mathrm K} = \frac{h}{e^{2}}, \qquad K_{\mathrm J}^{2} R_{\mathrm K} = \frac{4}{h}
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

The remaining question is what the electrical quantities are referred to. The current is obtained from a voltage drop across a stable resistor; both voltages are measured against the Josephson constant, taken as KJ = 2e/h, and the resistance against the von Klitzing constant, taken as RK = h/e², so that KJ²RK = 4/h and the mass reduces to h multiplied by an experimental frequency term and divided by the product of local gravity and coil velocity [ 4 ] : KJ=2eh,RK=he2,KJ2RK=4hK_{\mathrm J} = \frac{2e}{h}, \qquad R_{\mathrm K} = \frac{h}{e^{2}}, \qquad K_{\mathrm J}^{2} R_{\mathrm K} = \frac{4}{h}. This is where the quantum electrical standards earn their place. Since 1990 the practical realization of the volt and the ohm had rested on the Josephson and quantum Hall effects, but with conventional values assigned to…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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