I Is the new Ampère exactly the same as the old Ampère?

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The new definition of the Ampère aligns with the flow of 1/(1.602 176 634 × 10-19) elementary charges per second, while the previous definition was based on the force between parallel conductors. Both definitions yield similar measurements within the margin of error, ensuring consistency in electric current measurements. However, the introduction of "conventional" units in 1990, based on the Josephson junction, allowed for more precise voltage measurements, creating a distinction from the new SI units. The redefinition of the electromagnetic base unit has led to significant deviations between the old and new SI units, with relative changes around 10^-10. Quantum methods for defining electromagnetic quantities remain in use for realizing the Ampère through derived units.
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The new BIPM/SI definition of the unit of electric current reads:

1 A (Ampère) is the electric current corresponding to the
flow of 1/(1.602 176 634 × 10-19) elementary charges per second.

The old definition (until 2019) was:

1 A (Ampère) 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 × 10-7 MKS unit of force [Newton] per metre of length.*

Is the new one identical to the old one, in the sense that when we speak of "I measured an electric current with this amperemeter and found 1,2 A" do we have the same flow of charge inside?
 
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Yes, the new Ampere is within the margin of error of the old Ampere. Similarly with all of the derived electrical units.

However, in 1990 the so-called "conventional" units were introduced, based on the Josephson junction. These allowed much more precise measurements of voltage than were possible using the SI volt. Those became the de-facto standard in electrical metrology from 1990 until the most recent revision of the SI. The new SI electrical units are not equal to the "conventional" electrical units.
 
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In fact the redefinition of the electromagnetic base unit from defining ##\mu_0## to defining ##e## leads to the largest deviations between the "old" and the "new" SI units, valid since 2019. The order of the relative changes are about ##10^{-10}##.

Of course the above mentioned quantum methods to define the various electromagnetic quantities are still in use to realize the Ampere via the derived units like Volt, Farad, Ohm, etc. For details, see the Mise en pratique for the Ampere:

https://www.bipm.org/utils/en/pdf/si-mep/SI-App2-ampere.pdf
 
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