# Units and Measurement

Physical Quantities

Those quantities which can describe the laws of physics are called the physical quantity. A physical quantity is one that can be measured. Thus, length, mass, time, pressure, temperature, current and resistance are considered as physical quantities.

Classification of Physical Quantities-

The physical quantities are classified into

(i) Fundamental quantities or base quantities

(ii) Derived quantities

The physical quantities that are independent of each other are called fundamental quantities. All the other quantities which can be expressed in terms of the fundamental quantities are called the derived quantities.

Units

The reference standard used to measure the physical quantities is called the unit.

Properties of Unit

1. The unit should be of some suitable size
2. The unit must be well-defined
3. The unit should be easily reproducible, i.e., it should not change with place
4. The unit must not change with time
5. The unit should not change with physical conditions like temperature, pressure, etc.
6. The unit must be easily comparable experimentally with similar physical quantities.

Types of Units:-

(i) Fundamental Units

The units defined for the fundamental quantities are called fundamental units.

(ii) Derived Units

The units of all other physical quantities which are derived from the fundamental units are called the derived units.

# FUNDAMENTAL UNITS

The Seven Base Units of Measurement

• Length – Metre (m)

It is defined as the length of the path travelled by light in an interval of exactly

1/299792458

It is based on the fundamental quantity, the speed of light in a vacuum which is c = 299,792,458 m/s.

• Time – Second (s)

It is the time taken by 9,192,631,770 periods of oscillations of the light emitted by a caesium -133 atom corresponding to the transition between two hyper-fine levels of the ground state. This is determined by using highly precise atomic clocks.

• Mass – Kilogram (kg)

It is the mass of a prototype platinum-iridium cylinder kept at the International Bureau of Weights and Measures in Paris, France. Copies of this cylinder are kept by many countries which use them to standardise and compare weights.

• Electric current – Ampere (A)

The constant current which, if maintained in two straight parallel conductors of infinite length and negligible circular cross-section when placed 1 m apart in vacuum, would produce a force equal to 2 x 10-7 newton per metre of length between these conductors. While, it may appear that electric charge should have been used as a base unit, measuring current is far easier and hence is chosen as the standard base unit.

• Temperature – Kelvin (K)

The SI unit of temperature is Kelvin. It is exactly 1/(273.16) of the thermodynamic temperature of the triple point of water. The triple point of water is a fixed temperature and pressure at which the solid, liquid and gaseous states can exist at the same time.

• Amount of a substance – Mole (mol)

The mole is the amount of substance which contains as many entities as there are atoms in 0.012 kg of carbon-12. A mole contains an Avogadro number of entities. Check out our chemistry articles to know more about the Avogadro number.

• Luminous Intensity – Candela (cd)

It is the luminous intensity of a source that emits radiation of a constant frequency of 540 x 1012 Hz with a radiant intensity of 1/683  Watt per steradian in any given direction.

DERIVED UNITS

The units of measurement derived from the seven base units specified by the International System of Units are known as SI derived units. They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation. The names of SI derived units, when written in full, are always in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is “Hz”, but the symbol for metre is “m.” In the table below, we have given a list of derived units.

 Name Symbol Quantity hertz Hz Frequency radian rad angle newton N force, weight farad F electrical capacitance ohm Ω electrical resistance, impedance, reactance weber Wb magnetic flux degree Celsius °C temperature relative to 273.15 K becquerel Bq radioactivity (decays per unit time)

System of Units

(1) FPS System: In this system, the unit of length is foot, the unit of mass is pound, and the unit of time is second.

(2) CGS System: In this system, the units of length, mass and time are centimetre, gram and second, respectively.

(3) MKS System: In this system, the unit of length, mass and time are meter, kilogram and second, respectively.

(4) SI System: This system is widely used in all measurements throughout the world. The system is based on seven basic units and two supplementary units.

 Basic Units Quantity Unit Symbol of the Unit Length metre m Mass kilogram kg Time second s Temperature kelvin K Electric current ampere A Number of particles mole mol Luminous intensity candela cd Supplementary Units Plane angle radian rad Solid angle Steradian sr

Definition of Basic and Supplementary Units

Basic Units

1. Metre (m): One metre is the distance travelled by light in the vacuum during a time interval of (1/299792458) seconds.

2. Kilogram (kg): It is the mass of a platinum-iridium cylinder kept at the National Bureau of Weights and Measurements, Paris.

3. Second (s): The second is the time taken by the light of a specified wavelength emitted by a caesium-133 atom to execute 9192631770 vibrations.

4. Ampere (A): One ampere is that current which, when passed through two straight parallel conductors of infinite length and of negligible cross-section kept at a distance of 1 metre apart in the vacuum, produces between them a force equal to 2 x 10-7 newton per metre length.

5. Kelvin (K): It is the fraction 1/273.6 of the thermodynamic temperature of the triple point of water.

6. Candela (cd): A candela is defined as 1/60 th of the luminous intensity of 1 square centimetre of a perfect black body maintained at the freezing temperature of platinum (1773 0C).

7. Mole (md): One mole is the amount of substance that contains elementary units equal to the number of atoms in 0.012 kg of carbon-12.

Supplementary Units

1. Radian (rad): The radian is the angle subtended at the centre of the circle by the arc whose length is equal to the radius of the circle.

2. Steradian (Sr): The steradian is the solid angle subtended at the centre of a sphere by a spherical surface of an area equal to the square of its radius.