What are the derived SI units?
- Derived SI units are units obtained through equations containing the seven base units
- Thus, they allow any physical quantity to be expressed in terms of SI units
What are the commonly used derived SI units and how are they defined?
Unit
Unit Symbol
Base Measure
Base Units
Definition
Hertz
Hz
Frequency
s−1
The frequency of one cycle per second
Newton
N
Force
kg.m.s−2
The force required to give 1 kilogram an acceleration of 1 metre per second per second
Pascal
Pa
Pressure
N.m−2
The pressure of 1 Newton per square metre
Joule
J
Energy or Work
N.m
The energy expended when the point of application of a force of 1 Newton moves 1 metre in the direction of the force
Watt
W
Power
J.s−1
1 joule per second
Volt
V
Electrical Potential
kg⋅m2⋅s-3⋅A−1
The difference of electrical potential between two points of a conductor carrying a constant current of 1 ampere, when the power dissipated between these points is 1 watt
Ohm
Ω
Electrical Resistance
kg⋅m2⋅s−3⋅A−2
The resistance when one volt is applied across a conductor and produces a current of 1 ampere
Coulomb
Q
Charge
s⋅A
The quantity of electricity transported in one second by a current of 1 ampere
Farad
F
Capacitance
kg−1⋅m−2⋅s4⋅A2
The capacitance if a potential difference of 1 volt is present across its plates, when a charge of 1 coulomb is held by them.
Henry
H
Inductance
kg⋅m2⋅s−2⋅A−2
The inductance in a circuit when an electric current that is changing at 1 ampere per second results in an electromotive force of 1 volt across the inductor:
Weber
Wb
Magnetic Flux
kg⋅s−2⋅A−1
The magnetic flux that, linking a circuit of one turn, would produce in it an electromotive force of 1 volt if it were reduced to zero at a uniform rate in 1 second
Tesla
T
Magnetic Flux Density
kg⋅m2⋅s−2⋅A−1
The magnetic flux density equal to 1 weber per square metre
What are the base SI units and how are they defined?
Unit
Unit Symbol
Base Measure
Physical Constant
Definition
Second
s
Time
Hyperfine transition frequency of caesium (ΔνCs)
The time taken by 9,192,631,770 oscillations of the light emitted by a caesium-133 atom
Metre
m
Length
Speed of light (c)
The length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second
Mole
mol
Amount of Substance
Avagadro's constant - a value of 6.02214076 × 1023
The amount of substance that contains the same number of particles as there are atoms in 0.012 kg (12 g) of carbon-12, which isequal to Avagadro's dumber
Ampere
A
Electric Current
Elementary charge (e) - the charge of a single proton
Defined by taking the elementary charge e to be a fixed numerical value of 1.602176634×10 A⋅s
Candela
cd
Luminous Intensity
Luminous efficacy of monochromatic radiation of frequency 540×1012 Hz (Kcd)
Defined by taking the fixed numerical value of Kcd, to be 683 expressed in the units cd⋅sr⋅kg–1⋅m–2⋅s3
Kilogram
kg
Mass
Plancks Constant (h) - relationship between a photons energy and frequency
Defined by taking Plancks constant (h) to be a fixed numerical value of 6.62607015×10−34 m2⋅kg⋅s–1
Kelvin
K
Temperature
Boltzmann's Constant (k) - relationship between a particles kinetic energy and temperature
Defined by taking the Boltzmann constant k to be a fixed numerical value of 1.380649×10−23 kg⋅m2⋅s–2⋅K–1)