INTRODUCTION

0.1 Tables of quantities

The names in English of the most important quantities within the field of this document are given together with their symbols and, in most cases, their definitions. The definitions are given for identification of the quantities in the International System of Quantities (ISQ), listed in Table 1; they are not intended to be complete.

The scalar, vectorial or tensorial character of quantities is pointed out, especially when this is needed for the definitions.

In most cases, only one name and only one symbol for the quantity are given; where two or more names or two or more symbols are given for one quantity and no special distinction is made, they are on an equal footing. When two types of italic letters exist (for example as with ϑ and θ; φ and φ; a and a; g and g) only one of these is given. This does not mean that the other is not equally acceptable. It is recommended that such variants should not be given different meanings. A symbol within parenthesis implies that it is an alternative symbol, to be used when, in a particular context, the main symbol is in use with a different meaning.

0.2 Units

0.2.1 General

The names of units for the corresponding quantities are given together with the international symbols and the definitions. These unit names are language-dependent, but the symbols are international and the same in all languages. For further information, see the SI Brochure (9^th edition 2019) from BIPM and ISO 80000‑1.

The units are arranged in the following way:

a) The base SI units are given first. The SI units have been adopted by the General Conference on Weights and Measures (Conférence Générale des Poids et Mesures, CGPM). The use of base SI units, and their decimal multiples and submultiples formed with the SI prefixes are recommended, although the decimal multiples and submultiples are not explicitly mentioned. The order of the units is kg, m, s, A, K, mol, cd.
b) Some non-SI units are then given, being those accepted by the International Committee for Weights and Measures (Comité International des Poids et Mesures, CIPM), or by the International Organization of Legal Metrology (Organisation Internationale de Métrologie Légale, OIML), or by ISO and IEC, for use with the SI.
c) Non-SI units that are not recommended are given only in annexes in some parts of ISO 80000 and IEC 80000. These annexes are informative, in the first place for the conversion factors, and are not integral parts of the standard. These deprecated units are arranged in two groups:
1. 1) units in the CGS system with special names, see Annex A;
2. 2) units based on the foot, pound, and some other related units.

0.2.2 Remark on units for quantities of dimension one, or dimensionless quantities

The coherent unit for any quantity of dimension one, also called a dimensionless quantity, is the number one, symbol 1. When the value of such a quantity is expressed, the unit symbol 1 is generally not written out explicitly.

EXAMPLE

Refractive index Refractive index n = 1,53 × 1 = 1,53

Prefixes shall not be used to form multiples or submultiples of this unit. Instead of prefixes, powers of 10 are recommended.

EXAMPLE

Refractive index Reynolds number Re = 1,32 × 10 3

Considering that plane angle is generally expressed as the ratio of two lengths and solid angle as the ratio of two areas, in 1995 the CGPM specified that, in the SI, the radian, symbol rad, and steradian, symbol sr, are dimensionless derived units. This implies that the quantities plane angle and solid angle are considered as derived quantities of dimension one. The units radian and steradian are thus equal to one; they may either be omitted, or they may be used in expressions for derived units to facilitate distinction between quantities of different kinds, but having the same dimension.

0.3 Numerical statements in this document

The sign = is used to denote "is exactly equal to" and the sign ≈ is used to denote "is approximately equal to".

Numerical values of physical quantities that have been experimentally determined always have an associated measurement uncertainty. This uncertainty should always be specified. In this document, the magnitude of the uncertainty is represented as in the following example.

EXAMPLE

l = 2,347 82(32) m

In this example, l = a(b) m, the numerical value of the uncertainty b indicated in parentheses is assumed to apply to the last (and least significant) digits of the numerical value a of the length l. This notation is used when b represents one standard uncertainty (estimated standard deviation) in the last digits of a. The numerical example given above can be interpreted to mean that the best estimate of the numerical value of the length l, when l is expressed in the unit metre, is 2,347 82 and that the unknown value of l is believed to lie between (2,347 82 −0,000 32) m and (2,347 82 +0,000 32) m with a probability determined by the standard uncertainty 0,000 32 m and the probability distribution of the values of l.

0.4 Special remarks

0.4.1 General

The items given in IEC 80000‑6 are generally in conformity with the International Electrotechnical Vocabulary (IEV), especially IEC 60050‑121 and IEC 60050‑131. For each quantity, the reference to IEV is given in the form: "See IEC 60050‑121:20XX, 121‑xx‑xxx.".

The font used for text is sans serif; that used for quantities is serif.

0.4.2 System of quantities

For electromagnetism, several different systems of quantities have been developed and used depending on the number and the choice of base quantities on which the system is based. However, in electromagnetism and electrical engineering, only the International System of Quantities, ISQ, and the associated International System of Units, SI, are acknowledged and are reflected in the standards of ISO and IEC. The SI has seven base units, among them are the kilogram (kg), the metre (m), the second (s), and the ampere (A).

0.4.3 Sinusoidal quantities

For quantities that vary sinusoidally with time, and for their complex representations, the IEC has standardized two ways to build symbols. Capital and lowercase letters are generally used for electric current (item 6-1) and for voltage (item 6-11.3), and additional symbols for other quantities. These are given in IEC 60027‑1.

EXAMPLE 1

The sinusoidal variation with time of an electric current (item 6-1) can be expressed in real representation as

i = 2 I cos ( ω t − φ )

and its complex representation (termed phasor) is expressed as

i = I e − j φ

where i is the instantaneous value of the current, I, is its root-mean-square (RMS) value (see 0.4.4), (ωt − φ) is the phase, φ is the initial phase, and j is the imaginary unit (j² = −1), in mathematics often denoted by i.

EXAMPLE 2

The sinusoidal variation with time of a magnetic flux (item 6-22.1) can be expressed in real representation as

Φ = Φ ^ cos ( ω t − ϕ ) = 2 Φ eff cos ( ω t − ϕ )

where Φ is the instantaneous value of the flux, Φ ^ is its peak value and Φ_eff is its RMS value.

0.4.4 Root-mean-square value, RMS value

For a time-depending quantity a, the positive square root of the mean value of the square of the quantity taken over a given time interval is called root-mean-square value, i.e.

1 T ∫ 0 T a 2 d t

The root-mean-square value of a periodic quantity is usually taken over an integration interval, the range of which is the period multiplied by a natural number. For a sinusoidal quantity a ( t ) = A ^ cos ( ω t + φ ) , the root-mean-square value is A ^ / 2 .

The root-mean-square value of a quantity may be denoted by adding one of the subscripts "eff" or "RMS" to the symbol of the quantity. In electrical technology, the root-mean-square values of electric current i(t) and voltage u(t) are usually denoted I and U, respectively.

BS EN IEC 80000-6:2022

Quantities and units - Electromagnetism

Current

Published:

31 Jan 2023