A **base quantity (or basic quantity)** is chosen and arbitrarily defined, rather than being derived from a combination of other physical quantities.

The 7 base quantities are:

Physical quantity | Base SI unit |
---|---|

Mass (m) | Kilogram (Kg) |

Length ($l$) | Metre (m) |

Time (t) | Second (s) |

Current ($\text{I}$) | Ampere (A) |

Temperature (T) | Kelvin (K) |

Amount of sub. (n) | Molar (mol) |

Luminous Intensity (L) | Candela (cd) |

SI units are used as standardised units in all measurements in the world. SI is the short form for “International System of Units”.

### Derived Quantity

A derived quantity is defined based on a combination of base quantities and has a derived unit that is the exponent, product or quotient of these base units.

**Note:**

- Units, such as the joule, newton, volt and ohm, are SI units, but they are not base SI units.
**Dimensional analysis**: The main idea of “deriving” a derived unit is to treat units like algebraic terms, and manipulate them accordingly to get the right derived unit for the quantity. (See example 3 for a walkthrough)

### Practice on Derived Quantity

#### Example 1

An example of derived quantity is energy which has a derived unit of **Joules** which is $\text{kg} \, \text{m}^{2} \, \text{s}^{-2}$ OR $\text{kg} \, \text{m}^{2} / \text{s}^{2}$in **base** SI units.

#### Example 2

Another example of derived quantity is density which has a derived quantity of $\text{kg} \, \text{m}^{-3}$ or $\text{kg}/\text{m}^{3}$ in base SI units.

If you are unclear how to express derived quantity in terms of the base SI units, please study the example below:

#### Example 3

The equation for density is:

$$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$$

Now, you know that the unit for mass is $\text{kg}$, while the unit for volume is $\text{m}^{3}$.

Hence,

$$\begin{aligned} \text{Unit for density} &= \frac{\text{kg}}{\text{m}^{3}} \\ &= \text{kg} / \text{m}^{3} \\ &= \text{kg} \, \text{m}^{-3} \end{aligned}$$

## Homogeneous Equation

When each of the terms in a physical equation has the same base units, the equation is said to be homogeneous. An equation which is not homogeneous must be wrong. However, when a physical equation is homogeneous, it does not necessarily imply that the equation is correct.

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Hi there, I was wondering if you’d spotted the error with the current base unit. I believe it should be charge, as Current = Charge x time (Q=It)

Base quantities are the quantities on the basis of which other quantities are expressed.

AoA.

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