## UNIT: ampere

• PID: si:unit:ampere
• Definition: The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634 x 10-19 when expressed in the unit C, which is equal to A s, where the second is defined in terms of ΔνCs.
• Source: SI Brochure 9th Ed. 2019, p 132
• Reference: CGPM Resolution 1 of the 26th CGPM (2018) "On the revision of the International System of Units (SI)"
• Status: Valid
• Valid: 2019-05-20 -
• Notes
1. This definition implies the exact relation $$e = 1.602\:176\:634\:10^{-19} {A\:s}$$. Inverting this relation gives an exact expression for the unit ampere in terms of the defining constants $$e$$ and $$\Delta\nu_{\rm{Cs}}$$: $$1\ {\rm{A}} = (\frac{e}{1.602\:176\:634 \times 10^{-19}}) {\rm{s}}^{-1}$$ which is equal to $$1\ {\rm{A}} = \frac{1}{(9\:192\:631\:770)(1.602\:176\:634 \times 10^{-19})}\Delta\nu_{\rm{Cs}}e \approx 6.789\:687 \times 10^{8}\Delta\nu_{\rm{Cs}}e.$$
2. The effect of this definition is that one ampere is the electric current corresponding to the flow of $$1/(1.602\:176\:634 \times 10^{-19})$$ elementary charges per second.
3. The previous definition of the ampere was based on the force between two current carrying conductors and had the effect of fixing the value of the vacuum magnetic permeability $$\mu_{0}$$ (also known as the magnetic constant) to be exactly $$4\pi \times 10^{-7}\ {H\ m}^{-1} = 4\pi \times 10^{-7}\ {N\ A}^{-2}$$, where $$H$$ and $$N$$ denote the coherent derived units henry and newton, respectively. The new definition of the ampere fixes the value of $$e$$ instead of $$\mu_{0}$$. As a result, $$\mu_{0}$$ must be determined experimentally.
4. It also follows that since the vacuum electric permittivity $$\varepsilon_{0}$$ (also known as the electric constant), the characteristic impedance of vacuum $$Z_{0}$$, and the admittance of vacuum $$Y_{0}$$ are equal to $$1/\mu_{0}c^{2}$$, $$\mu_{0}c$$, and $$1/\mu_{0}c$$, the values of $$\epsilon_{0}$$, $$Z_{0}$$ and $$Y_{0}$$ must now also be determined experimentally, and are affected by the same relative standard uncertainty as $$\mu_{0}$$ since $$c$$ is exactly known. The product $$\varepsilon_{0}\mu_{0} = 1/c^{2}$$ and quotient $$Z_{0}/\mu_{0} = c$$ remain exact. At the time of adopting the present definition of the ampere, $$\mu_{0}$$ was equal to $$4\pi \times 10^{-7}\ {\rm{H\ m^{-1}}}$$ with a relative uncertainty of $$2.3 \times 10^{-10}$$.
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