Competitive Exams: Physics: SI Unit System

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Other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units. Examples of such SI derived units are given below, where it should be noted that the symbol 1 for quantities of dimension 1 such as mass fraction is generally omitted.

Examples of SI derived units

Derived quantityNameSymbol
areasquare meterm2
volumecubic meterm3
speed, velocitymeter per secondm/s
accelerationmeter per second squaredm/s2
wave numberreciprocal meterm − 1
mass densitykilogram per cubic meterkg/m3
specific volumecubic meter per kilogramm3/kg
current densityampere per square meterA/m2
magnetic field strengthampere per meterA/m
amount-of-substance concentrationmole per cubic metermol/m3
luminancecandela per square metercd/m2
mass fractionkilogram per kilogram, which may be represented by the number 1kg/kg = 1

SI Derived Units

For ease of understanding and convenience, 22 SI derived units have been given special names and symbols

SI derived units with special names and symbols

Derived quantityNameSymbolExpression in terms of other SI unitsExpression in terms of SI base units
plane angleradian (a)radN/Am x m − 1 = 1 (b)
solid anglesteradian (a)sr (c)N/Am2 × m − 2 = 1 (b)
frequencyhertzHzN/As − 1
forcenewtonNN/Am x kg x s − 2
pressure, stresspascalPaN/m2m − 1 x kg x s − 2
energy, work, quantity of heatjouleJN x mm2 x kg x s − 2
power, radiant fluxwattWJ/sm2 x kg x s − 3
electric charge, quantity of electricitycoulombCN/As x A
electric potential difference, electromotive forcevoltVW/Am2 x kg x s − 3 × A − 1
capacitancefaradFC/Vm − 2 x kg-1 × s4 x A2
electric resistanceohmV/AN/Am2 x kg x s − 3 × A − 2
electric conductancesiemensSA/Vm − 2 x kg-1 × s3 x A2

For ease of understanding and convenience, 22 SI derived units have been given special names and symbols

Derived quantityNameSymbolExpression in terms of other SI unitsExpression in terms of SI base units
magnetic fluxweberWbV x sm2 x kg x s − 2 × A − 1
magnetic flux densityteslaTWb/m2kg x s − 2 × A − 1
inductancehenryHWb/Am2 x kg x s − 2 × A − 2
Celsius temperaturedegree Celsius° CN/AK
luminous fluxlumenlmcd x sr (c)m2 × m − 2 x cd = cd
illuminanceluxlxlm/m2m2 × m − 4 x cd = m − 2 x cd
activity (of a radionuclide)becquerelBqN/As − 1
absorbed dose, specific energy (imparted) , kermagrayGyJ/kgm2 × s − 2
dose equivalent (d)sievertSvJ/kgm2 × s − 2
catalytic activitykatalkatN/As − 1 x mol
  1. The radian and steradian may be used advantageously in expressions for derived units to distinguish between quantities of a different nature but of the same dimension; some examples are given in Table 4.
  2. In practice, the symbols rad and sr are used where appropriate, but the derived unit “1” is generally omitted.
  3. In photometry, the unit name steradian and the unit symbol sr are usually retained in expressions for derived units.
  4. Other quantities expressed in sieverts are ambient dose equivalent, directional dose equivalent, personal dose equivalent, and organ equivalent dose.

Note on Degree Celsius

The derived unit in above table with the special name degree Celsius and special symbol° C deserves comment. Because of the way temperature scales used to be defined, it remains common practice to express a thermodynamic temperature, symbol T, in terms of its difference from the reference temperature T0 = 273.15 K, the ice point. This temperature difference is called a Celsius temperature, symbol t, and is defined by the quantity equation t = T-T0.

The unit of Celsius temperature is the degree Celsius, symbol° C. The numerical value of a Celsius temperature t expressed in degrees Celsius is given by

t/° C = T/K − 273.15.

It follows from the definition of t that the degree Celsius is equal in magnitude to the kelvin, which in turn implies that the numerical value of a given temperature difference or temperature interval whose value is expressed in the unit degree Celsius (° C) is equal to the numerical value of the same difference or interval when its value is expressed in the unit kelvin (K) .

Thus, temperature differences or temperature intervals may be expressed in either the degree Celsius or the kelvin using the same numerical value. For example, the Celsius temperature difference t and the thermodynamic temperature difference T between the melting point of gallium and the triple point of water may be written as

t = 29.7546° C = T = 29.7546 K.

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