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System of Units

 

A unit is a particular physical quantity, defined and adopted by convention, with which other particular quantities of the same kind are compared to express their value. A physical quantity is a quantity that can be used in the mathematical equations of science and engineering. The value of a physical quantity is the quantitative expression of a particular physical quantity as the product of a number and a unit, the number being its numerical value. Thus, the numerical value of a particular physical quantity depends on the unit in which it is expressed. When making measurements, it is customary to record both the quantity (how much) and the unit (of what). Science and technology depend largely on the unit of measurement. For example, the value of the height h of building is h = 120 m. Here h is the physical quantity, its value expressed in the unit “meter,” unit symbol m, is 120 m, and its numerical value when expressed in meters is 120.

 

 

The SI System of Measurement

 

A system of units is a class of units defined by composition from a base set of units, such that every instance of the class is “standard” unit for a physical dimension and every physical dimension has an associated unit. A measurement of any physical quantity must be expressed as a number followed by a unit. A unit is a standard by which a dimension can be expressed numerically. The units for the fundamental dimensions are called the fundamental or base units.

 

While carrying out engineering calculations, there are several systems of base units that are available. However, they may be broken into two main groups. First, the International System of Units (also called SI, from the French "Système International des Unités")  introduced by Griorgi in 1901, including the meter-kilogram-second-ampere (MKSA) subsystem representing the four fundamental dimensions length, mass, time, and electric current, respectively. Second is the centimeter-gram-second (CGS) system. The units for other dimensions are called secondary or derived units and are based on the above fundamental units.

The International System of Units has seven base units, several derived units with special names, and many derived units with compound names.

 

The seven base units are the building blocks from which the derived units are constructed. Each base unit is defined by a very precise measurement standard that gives the exact value of the unit. The base units are not related to one other, no do they depend on each other for their definition. The complete SI system involves units and other recommendations, one of which is that multiple and submultiples of the MKSA units be set in steps of 103 or 10-3. The base units SI units and abbreviations are listed in Table 1

 

The SI has tremendous advantage over previous systems because it uses a unique unit name for each physical quantity and it assigns a unique symbol for each name. This book employs the SI units that are commonly adhered to by virtually all-engineering professional societies. The SI is the standard system used in today’s scientific literature.

 

 Table 1 The Seven Fundamental SI Units

Quantity

Unit

Abbreviation

Length

Mass

Time

Electric current

Temperature

Luminous intensity

Matter

meter

kilogram

second

ampere

kelvin

candela

mole

m

kg

s

A

K

cd

mol

 

The SI derived units are formed from the previously defined SI base units. Table 2 lists many of the SI derived units used in electric and electronic circuits.

The SI uses the decimal system to relate larger and smaller units to the basic units, and employs prefixes to signify the various powers of 10. A list of prefixes and their symbols is given in Table 3. These prefixes are very important in engineering studies and are worth memorizing.

 

Table 2 SI Derived Units 

Quantity

Symbol

Unit

Unit Symbol

Angle

q

radian

rad

Capacitance

C

farad

F

Conductance

G

siemens

S

Electric charge

Q

coulomb

C

Electromotive force

E

volt

V

Energy, work

W

joule

J

Force

F

newton

N

Frequency

f

hertz

Hz

Inductance

L

henry

H

Power

P

watt

W

Resistance

R

ohm

W

Pressure

p

pascal

Pa

Magnetic Flux

f

weber

Wb

Magnetic Induction

B

tesla

T

Light Flux

L

lumen

lm

 

Table 3 SI Prefixes

Metric Symbol

Metric Prefix

Value

Power of Ten

T

One Trillion

Tera

1012

G

One Billion

Giga

109

M

One Million

Mega

106

K

One Thousand

Kilo

103

m

One Thousandth

Milli

10-3

m

One Millionth

Micro

10-6

n

One Billionth

Nano

10-9

p

One Trillionth

Pico

10-12