• June 22, 2021

### What is the difference between fundamental and derived quantities?

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## What is the difference between fundamental and derived quantities?

The study of nature and its laws is how one can define physics. It is expected that every event that occurs in nature, has some basic law according to which it happens. Physics is the study of observation and revelation of such natural laws and phenomenon. A simple explanation of what Physics aims to do, is the Newton and Apple story. The apple falling from a tree is not something extra ordinary, but this gained prominence with Newton explaining the law of gravitation that dictates why an apple fell off the tree, down to the ground! Physics concerns itself with all the rules that are applicable to all walks of life, thus, critical knowledge and understanding of physics is essential as it is applied to every known domain of learning.

These laws give rise to physical parameters that are used for measurement. If one talks about gravity, then one needs to understand the quantity and quality of this gravitational force and how it can be expressed, making it distinct from other parameters. This is where the concept of fundamental and derived quantities comes into play. This led to the development of standard units. Thes units are defined by a  body  named  ConférenceGénérale  des  Poids  et  Mesures  or  CGPM  also  known as  General  Conference  on  Weight  and  Measures  in English. This body has been given the authority to decide the units by international agreement.

As one is aware, a huge number of physical quantities is measured. Every of these quantities needs a defined unit. However, it is not necessary that these quantities are independent of one another. Consider take a simple example of speed. This unit is dependent on the unit of length (meters) and the unit of time (second), to yield a unit for speed that is meter per second.

Thus, there needs to be a segregation of units that are independent and those units which are dependent. This is where the concept of Fundamental units /quantity and Derived units or quantity comes into play.

A fundamental quantity can be defined as follows:

• Every identified fundamental quantity must be independent of each other
• All the other quantities may be defined with respect to these fundamental quantities.

As per the international body, there are only seven fundamental quantities. All the other physical quantities that are known to us and expressed by us, are derived quantities, which means that these quantities are derived from fundamental quantities. Thus, taking the example above, it can be concluded that length and time are two distinct fundamental quantities, having distinct fundamental units, however speed is a derived quantity which depends on these two fundamental quantities.

There are several systems prevalent in the world and every system has its own fundamental quantities, such as SI units, FPS units, CGS units etc. Most prevalent are SI Units as they have international acceptance. As explained before, the units defined for fundamental quantities are called as fundamental units. In many physics texts, fundamental quantities are defined as Base quantities having their own Base unit. Any fundamental or base unit should have the properties of Invariability and Availability.

As stated, there are seven fundamental quantities, which are described as below.

1. Length, having fundamental unit of meter (m)
2. Mass, having fundamental unit of Kilogram (kg)
3. Time, having fundamental unit of second (s)
4. Electric current, with fundamental unit of Ampere (A)
5. Thermodynamic temperature, with fundamental unit of Kelvin (K)
6. Amount of substance, having fundamental unit of Mole, (mol)
7. Luminous intensity with fundamental unit Candela (cd)

Besides these, there exists two other units called supplementary units.

2. Solid angle with unit steradian (sr)

Each of these fundamental units can be defined as per the CGPM body.

1. Second: It is the time that makes the  unperturbed  ground  state  hyperfine  transition  frequency  to  be9192631770  when  expressed  in  the  unit .
2. Meter: It is the length that makes the speed of lighting vacuum to be 299792458 when expressed in the unit ms‑1
3. Kilogram: It is  the  mass  that  makes the Planck’s constant h to be 6.62607015 x 10^- 34 when expressed  in the unit J-s
4. Ampere: Ampere is the current which makes the elementary charge e to be  1.602176634 x 10^-19  when expressed in the unit C
5. Kelvin: Kelvin is the temperature that makes the Boltzmann constant to  be   1.380649 x 10^-23  when expressed in the unit J/K.
6. Mole: 1 mole of a substance is defined to contain 6.02214076 x 1-^23 elementary entities.
7. Candela: It is the SI unit of luminous intensity, which makes the luminous efficacy of a monochromatic radiation of frequency 540 x 10^12 Hz to 683 when expressed in lm/W.

All the other quantities that exist are called derives quantities such as speed, volume, density, efficacy, voltage, resistance etc.

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