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## Tobias Bergsten

Forskare

Contact TobiasIn 1820, the Danish physicist Hans Christian Ørsted showed that magnetism and electricity are related, by showing that a compass needle deviates from north in the vicinity of an electric current. This is because the current creates a magnetic field around the electrical conductor that affects other magnetic fields nearby, in this case the compass needle’s magnetic field.

Ørsted’s discovery inspired the French mathematician and physicist André-Marie Ampère to further research the connection between electricity and magnetism. He discovered that two current-carrying conductors exert an attractive force on each other if the direction of current is the same in both conductors, and that they repel each other if they have the opposite direction of current.

Over time, the need for a standardised measurement unit system for electricity grew:

- In 1893, the IEC (International Electrical Congress) proposed that the ohm and ampere should be the base units of a common system of units of measurement.
- At the 1921 General Conference on Weights and Measures in Paris, the ampere was formally added as a unit of electric current.
- In 1948, the definition of an ampere was decided, a definition based on André-Marie Ampère's discoveries more than a hundred years earlier.
- In 1960, the ampere officially became one of the base units of the SI International System of Units.

The decision in 1948 meant that 1 ampere was defined as the current which, when it passes through two infinitely long, straight, and parallel conductors, with negligible cross-section and one meter between them, generated a force of 2x10^{-7} newtons per meter between the conductors.

Note that based on this definition it seems impossible to realise, bring into reality, exactly one ampere. It is not possible to manufacture two infinitely long conductors. But the definition still made it possible to make a practical realisation of the ampere through a device known as an ampere balance, where a known mass is balanced against an electromagnetic force from the current in several coils. Through accurate measurements of the dimensions of the coils, the current could be determined with sufficiently small measurement uncertainty.

Formulated by the German scientist Georg Ohm in 1827, Ohm's Law describes the relationship between electric current (amperes), voltage (volts) and resistance (ohms) and is one of the simplest and most useful equations in physics:

I = V / R

where I is the current, V is the voltage and R is the resistance. This means that if two of the values are known, the third can be calculated using the formula. If the voltage and resistance of a circuit are known, the current can be easily calculated.

The three units thus belong together. To understand it, you can make a simple comparison with a water system, where voltage corresponds to the water pressure, the current corresponds to how much water flows in the pipe and the resistance corresponds to the diameter of the pipe. If you know the diameter and the water pressure, it is easy to calculate how much water flows. In the same way, it is easy to calculate the pressure if you know the diameter of the pipe and how much water flows through the pipe.

In the 70's and 80's electrical measuring instruments started to get so good that the ampere balance did not suffice. At the same time, scientific breakthroughs in quantum mechanics made it possible to realise volt and ohm based on natural constants. With the help of Ohm's law, it was then possible to determine ampere with very small measurement uncertainty.

Volt is realised using the Josephson effect and ohm using the quantum hall effect. These quantum mechanical phenomena have both been awarded Nobel Prizes and have changed the way we define and measure these quantities.

The derived units volt and ohm were thus used to realise the ampere. This clearly seems backwards. The idea was that the base units in the SI system would be used as the base for the derived units, not the other way around. The reason for this was that voltage and resistance could be measured with much less measurement uncertainty than electric current. The problem, however, was that this method was not based on the definition of ampere, even though the realisations of volts and ohms are very accurate.

In 2019, the definition of ampere within the SI system was changed. Instead of being based on the force between two infinitely long electrical conductors, the ampere is now defined via the value of the elementary charge e. The elementary charge was also given a fixed value of 1.602 176 634 ∙ 10^{-19} C, where the unit coulomb, C, can be expressed as A∙s, ampere times second. This means that one ampere corresponds to a charge flow of 1 coulomb, i.e., approximately 6.241 509 074 ∙ 10^{18} electrons, per second. Through this redefinition, the realisations of volt and ohm also became correct according to the SI definition.

However, the new definition does not make it easy to realise ampere based on its definition. It requires extremely accurate counting of an incredibly large number of individual electrons. Although possible, the technology is in its infancy and needs further development. In practice, Ohm's law and realisations of volt and ohm through the Josephson effect and the quantum hall effect are therefore still used to realise the ampere. It is this method we use to realise the national standard for ampere at the National Laboratory for Electrical Quantities here at RISE.