# Electrical Standards

### Electric Current

**ampere, A:** The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10^{–7} newton per metre of length.

The definition of the ampere effectively defines μ0 (a magnetic constant, the permeability of free space) to be 4π x 10^{-7}. Since c^{2}=ε0μ0 and the speed of light is defined by the definition of the metre, the electrostatic constant ε0(the permittivity of free space) is also defined. As with other SI definitions the ampere requires a more practical realisation because a direct interpretation of the definition is experimentally difficult, perhaps only as accurate as a part in 10^{7}. The practical realisation of electrical standards is instead based on two Nobel Prize winning discoveries.

Josephson in 1962, predicted a peculiar quantum physical effect in which a sandwich of superconducting material immersed in radio waves would produce a dc voltage proportional to the frequency of the waves. The generated voltage is

where e is the charge of the electron, h is Planck’s constant, ν is the frequency and n is an integer. The best measurements of the two constants (based on SI definitions) have been used to assign a value to K_{J} of 483 597.9 GHz/V. This enables the volt to be realised in terms of the second, which can be realised to be very high accuracy. Unfortunately it is a very low voltage, so thousands of junctions have to be connected together to generate a useful voltage. At present a practical realisation of the volt using this technique is good to about 1 part in 10^{10}. The development of the Josephson junction arrays has enabled about a 100 times improvement in voltage standards, which has lead to a similar improvement in a wide range of electrical measurement instruments, especially high grade digital voltmeters.

In 1980 the German physicist Von Klitzing observed another very strange quantum physical effect when specially designed semiconductors were exposed to strong magnetic fields and very low temperatures. The magnetic field modifies the movement of electrons causing the Hall effect voltage (a voltage generated at right angles to the current) to become quantised and proportional to the current. The possible values of quantised Hall resistance (QHR) are given by an equation very much like that for the Josephson effect.

The quantum Hall effect proves to be a far more precise way of realising resistance standards than via the SI definition. Again the best direct measurements of resistance have been used to assign RK a value of 25 812.807 ohm. This enables a definition of resistance that is at least repeatable to parts in 10^{10}.

If two quantum physics effects are not extraordinary enough, there are a couple of techniques under development at several national laboratories that enable electrons to be counted. If the accuracy can be improved we will have all three corners of Ohm’s law (voltage, resistance, and current) defined in terms of quantum mechanical effects. MSL has research projects investigating improved techniques for transferring the QHR to real resistances, switching Josephson arrays quickly to generate accurate ac voltages and theoretical investigations into the quantum current sources.