2.06 Comparing base dimensions and base units

If we use a table to compare base dimensions and base SI units we see that there is not a direct correspondence.

BASE DIMENSION QUANTITY BASE SI UNIT
L Length Metre
T Time Second
M Mass Kilogram
Q Electrical Charge -
Θ Temperature Kelvin
- Electrical current Ampere
- Luminous Intensity Candela
- Amount of substance Mole
(bold = SI base quantity)

For example, consider electrical charge which is a base dimension. Electrical charge is measured in Coulombs, but Coulombs are not base units! This may seem strange at first but the explanation lies in the fact that when choosing suitable SI base units there are other criteria to be met rather than just selecting the units that match each of the base dimensions

  1. It must be possible to devise practical, reliable and accurate procedures to set the standards for each of the base units.
  2. The SI units must be practical to use. i.e. to provide a suitable range of units of measurement of appropriate sizes to allow commonly measured properties to be conveniently expressed.
  3. All other units in the system of measurement must be derived from these base units.

It is criteria 1 and 2 that explain the lack of correspondence between base dimension and base units.

Objectives


The objective of this section is to understand the difference between base dimensions and base units.

Explanation of differences in the table

Electrical charge and electrical current


Electrical charge is a base dimension and it is measured in units called Coulombs. Originally the Coulomb was used as an SI base unit however it was found that a more accurate and reliable measurement standard could be set for defining the Ampere (the unit which is used for measuring electrical current). For this reason the Ampere was preferred over the Coulomb as an SI base unit. So the situation we are left with now is Electrical charge is a base dimension and electrical current is defined in terms of charge. (i.e. current = rate of flow of charge) The unit for measuring current the ampere is one of the base SI units and the unit for measuring charge is derived from the base units of amperes and seconds (i.e. 1 coulomb is the amount of charge that is displaced when 1 amp flows for 1 second)

Luminous intensity


The unit for luminosity is chosen as a base SI unit even though it actually incorporates a combination of different base dimensions! Luminosity is defined as an SI base unit simply because It provides a convenient unit for measuring electromagnetic radiation and there is a reliable procedure which can be used to set the standard which defines the magnitude of the candela.

The mole


The mole is a dimensionless unit and so it obviously has no corresponding base dimension. The mole just measures the number of particles in a system in multiples of approx 6.022 x 1023. The mole is included as an SI base unit because of criteria 2 i.e. it provides a practical and useful unit of measurement when dealing with large quantities of atoms and molecules.

Base quantities
A base quantities is simply a quantity that is measured by one of the seven SI base units rather than a quantity that is one of the five base dimensions. Therefore current is regarded as a base quantity rather than electrical charge