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SECTION 1
UNITS, SYMBOLS,
CONSTANTS, DEFINITIONS,
AND CONVERSION FACTORS
H. Wayne Beaty
Editor, Standard Handbook for Electrical Engineers;
Senior Member, Institute of Electrical and Electronics Engineers,
Technical assistance provided by Barry N. Taylor,
National Institute of Standards and Technology
CONTENTS
1.1 THE SI UNITS................................. 1-
1.2 CGPM BASE QUANTITIES....................... 1-
1.3 SUPPLEMENTARY SI UNITS..................... 1-
1.4 DERIVED SI UNITS............................ 1-
1.5 SI DECIMAL PREFIXES......................... 1-
1.6 USAGE OF SI UNITS, SYMBOLS, AND PREFIXES... 1-
1.7 OTHER SI UNITS............................... 1-
1.8 CGS SYSTEMS OF UNITS....................... 1-
1.9 PRACTICAL UNITS (ISU)........................ 1-
1.10 DEFINITIONS OF ELECTRICAL QUANTITIES...... 1-
1.11 DEFINITIONS OF QUANTITIES OF
RADIATION AND LIGHT....................... 1-
1.12 LETTER SYMBOLS............................ 1-
1.13 GRAPHIC SYMBOLS.......................... 1-
1.14 PHYSICAL CONSTANTS....................... 1-
1.15 NUMERICAL VALUES......................... 1-
1.16 CONVERSION FACTORS....................... 1-
BIBLIOGRAPHY................................... 1-
1.1 THE SI UNITS
The units of the quantities most commonly used in electrical engineering (volts, amperes, watts,
ohms, etc.) are those of the metric system. They are embodied in the International System of Units
( Système International d’Unités , abbreviated SI ). The SI units are used throughout this handbook, in
accordance with the established practice of electrical engineering publications throughout the world.
Other units, notably the cgs (centimeter-gram-second) units, may have been used in citations in the
earlier literature. The cgs electrical units are listed in Table 1-9 with conversion factors to the SI
units.
The SI electrical units are based on the mksa (meter-kilogram-second-ampere) system. They have
been adopted by the standardization bodies of the world, including the International Electrotechnical
Commission (IEC), the American National Standards Institute (ANSI), and the Standards Board of
the Institute of Electrical and Electronics Engineers (IEEE). The United States is the only industri-
alized nation in the world that does not mandate the use of the SI system. Although the U.S. Congress
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Source: STANDARD HANDBOOK FOR ELECTRICAL ENGINEERS
has the constitutional right to establish measuring units, it has never enforced any system. The met-
ric system (now SI) was legalized by Congress in 1866 and is the only legal measuring system, but
other non-SI units are legal as well.
Other English-speaking countries adopted the SI system in the 1960s and 1970s. A few major
industries converted, but many people resisted—some for very irrational reasons, denouncing it as
“un-American.” Progressive businesses and educational institutions urged Congress to mandate SI.
As a result, in the 1988 Omnibus Trade and Competitiveness Act, Congress established SI as the
preferred system for U.S. trade and commerce and urged all federal agencies to adopt it by the end
of 1992 (or as quickly as possible without undue hardship). SI remains voluntary for private U.S.
business. An excellent book, Metric in Minutes (Brownridge, 1994) , is a comprehensive resource for
learning and teaching the metric system (SI).
1.2 CGPM BASE QUANTITIES
Seven quantities have been adopted by the General Conference on Weights and Measures (CGPM†)
as base quantities , that is, quantities that are not derived from other quantities. The base quantities are
length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous
intensity. Table 1-1 lists these quantities, the
name of the SI unit for each, and the standard
letter symbol by which each is expressed in
the International System (SI).
The units of the base quantities have
been defined by the CGPM as follows:
meter. The length equal to 1 650 763.
wavelengths in vacuum of the radiation cor-
responding to the transition between the
levels 2 p 10 and 5 d 5 of the krypton-86 atom
(CGPM).
kilogram. The unit of mass; it is equal
to the mass of the international prototype of
the kilogram (CGPM).
EDITOR ’S NOTE : The prototype is a platinum-iridium cylinder maintained at the International Bureau of Weights and Measures, near Paris. The kilogram is approximately equal to the mass of 1000 cubic cen- timeters of water at its temperature of maximum density.
second. The duration of 9 192 631 770 periods of the radiation corresponding to the transition
between the two hyperfine levels of the ground state of the cesium 133 atoms (CGPM).
ampere. The constant current that if maintained in two straight parallel conductors of infinite
length, of negligible circular cross section, and placed 1 meter apart in vacuum would produce
between these conductors a force equal to 2 × 10 –7^ newton per meter of length (CGPM).
kelvin. The unit of thermodynamic temperature is the fraction 1/273.16 of the thermodynamic
temperature of the triple point of water (CGPM).
EDITOR ’S NOTE: The zero of the Celsius scale (the freezing point of water) is defined as 0.01 K below the triple point, that is, 273.15 K. See Table 1-27.
mole. That amount of substance of a system that contains as many elementary entities as there
are atoms in 0.012 kilogram of carbon-12 (CGPM).
1-2 SECTION ONE
TABLE 1-1 SI Base Units
Quantity Unit Symbol
Length meter m Mass kilogram kg Time second s Electric current ampere A Thermodynamic temperature∗^ kelvin K Amount of substance mole mol Luminous intensity candela cd ∗Celsius temperature is, in general, expressed in degrees Celsius (symbol ∗C).
†From the initials of its French name, Conference G´ene´rale des Poids et Mesures.
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weber. The magnetic flux whose decrease to zero when linked with a single turn induces in the
turn a voltage whose time integral is 1 volt-second.
tesla. The magnetic induction equal to 1 weber per square meter.
henry. The inductance for which the induced voltage in volts is numerically equal to the rate
of change of current in amperes per second.
1-4 SECTION ONE
TABLE 1-4 Examples of SI Derived Units of General Application in Engineering
SI unit
Quantity Name Symbol
Angular velocity radian per second rad/s Angular acceleration radian per second squared rad/s^2 Radiant intensity watt per steradian W/sr Radiance watt per square meter steradian W m–2^ sr– Area square meter m^2 Volume cubic meter m 3 Velocity meter per second m/s Acceleration meter per second squared m/s 2 Wavenumber 1 per meter m – Density, mass kilogram per cubic meter kg/m^3 Concentration (of amount of substance) mole per cubic meter mol/m 3 Specific volume cubic meter per kilogram m^3 /kg Luminance candela per square meter cd/m^2
TABLE 1-3 SI Derived Units in Electrical Engineering
SI unit
Expression Expression in terms of in terms of Quantity Name Symbol other units SI base units
Frequency (of a periodic phenomenon) hertz Hz 1/s s– Force newton N m kg s– Pressure, stress pascal Pa N/m^2 m–1^ kg s– Energy, work, quantity of heat joule J N m m^2 kg s– Power, radiant flux watt W J/s m 2 kg s– Quantity of electricity, electric charge coulomb C A s s A Potential difference, electric potential, volt V W/A m^2 kg s–3^ A– electromotive force Electric capacitance farad F C/V m–2^ kg–1^ s^4 A^2 Electric resistance ohm Ω V/A m^2 kg s–3^ A– Conductance siemens S A/V m –2^ kg–1^ s^3 A^2 Magnetic flux weber Wb V s m^2 kg s–2^ A– Magnetic flux density tesla T Wb/m^2 kg s–2^ A– Celsius temperature degree Celsius °C K Inductance henry H Wb/A m^2 kg s–2^ A– Luminous flux lumen lm cd sr∗ Illuminance lux lx lm/m^2 m–2^ cd sr∗ Activity (of radionuclides) becquerel Bq I/s s– Absorbed dose gray Gy J/kg m 2 s– Dose equivalent sievert Sv J/kg m 2 s– ∗In this expression, the steradian (sr) is treated as a base unit. See Table 1-2.
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lumen. The flux through a unit solid angle (steradian) from a uniform point source of 1 candela;
the flux on a unit surface all points of which are at a unit distance from a uniform point source of
1 candela.
lux. The illumination on a surface of 1 square meter on which there is uniformly distributed a
flux of 1 lumen; the illumination produced at a surface all points of which are 1 meter away from a
uniform point source of 1 candela.
Table 1-4 lists other quantities and the SI derived unit names and symbols useful in engineering
applications. Table 1-5 lists additional quantities and the SI derived units and symbols used in
mechanics, heat, and electricity.
1.5 SI DECIMAL PREFIXES
All SI units may have affixed to them standard prefixes which multiply the indicated quantity by
a power of 10. Table 1-6 lists the standard prefixes and their symbols. A substantial part of the
extensive range (10 36 ) covered by these prefixes is in common use in electrical engineering
(e.g., gigawatt, gigahertz, nanosecond, and picofarad). The practice of compounding a prefix
(e.g., micromicrofarad) is deprecated (the correct term is picofarad).
1.6 USAGE OF SI UNITS, SYMBOLS, AND PREFIXES
Care must be exercised in using the SI symbols and prefixes to follow exactly the capital-letter and
lowercase-letter usage prescribed in Tables 1-1 through 1-8, inclusive. Otherwise, serious confusion
UNITS, SYMBOLS, CONSTANTS, DEFINITIONS, AND CONVERSION FACTORS 1-
TABLE 1-5 Examples of SI Derived Units Used in Mechanics, Heat, and Electricity
SI unit
Expression in terms of Quantity Name Symbol SI base units
Viscosity, dynamic pascal second Pa s m–1^ kg s– Moment of force newton meter N m m^2 kg s– Surface tension newton per meter N/m kg s– Heat flux density, irradiance watt per square meter W/m^2 kg s– Heat capacity joule per kelvin J/K m^2 kg s–2^ K– Specific heat capacity, joule per kilogram kelvin J/(kg K) m^2 s–2^ K– specific entropy Specific energy joule per kilogram J/kg m^2 s– Thermal conductivity watt per meter kelvin W/(m K) m kg s–3^ K– Energy density joule per cubic meter J/m^3 m–1^ kg s– Electric field strength volt per meter V/m m kg s–3^ A– Electric charge density coulomb per cubic meter C/m^3 m–3^ s A Electric flux density coulomb per square meter C/m^2 m–2^ s A Permittivity farad per meter F/m m–3^ kg–1^ s^4 A^2 Current density ampere per square meter A/m^2 Magnetic field strength ampere per meter A/m Permeability henry per meter H/m m kg s–2^ A– Molar energy joule per mole J/mol m^2 kg s–2^ mol – Molar entropy, molar joule per mole kelvin J/(mol K) m^2 kg s–2^ K–1mol – heat capacity
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Luminous Intensity. The SI unit of luminous intensity has been given the name candela , and
further use of the old name candle is deprecated. Use of the term candle-power , either as the name
of a quantity or as the name of a unit, is deprecated.
Luminous Flux Density. The common British-American unit of luminous flux density is the
lumen per square foot. The name footcandle , which has been used for this unit in the United States,
is deprecated.
micrometer and micron. The names micron for micrometer and millimicron for nanometer are
deprecated.
gigaelectronvolt (GeV). Because billion means a thousand million in the United States but a
million million in most other countries, its use should be avoided in technical writing. The term billion
electronvolts is deprecated; use gigaelectronvolts instead.
British-American Units. In principle, the number of British-American units in use should be
reduced as rapidly as possible. Quantities are not to be expressed in mixed units. For example, mass
should be expressed as 12.75 lb, rather than 12 lb or 12 oz. As a start toward implementing this
recommendation, the following should be abandoned:
1. British thermal unit (for conversion factors, see Table 1-25).
2. horsepower (see Table 1-26).
3. Rankine temperature scale (see Table 1-27).
4. U.S. dry quart, U.S. liquid quart, and U.K. (Imperial) quart, together with their various multiples
and subdivisions. If it is absolutely necessary to express volume in British-American units, the
cubic inch or cubic foot should be used (for conversion factors, see Table 1-17).
5. footlambert. If it is absolutely necessary to express luminance in British-American units, the candela
per square foot or lumen per steradian square foot should be used (see Table 1-28A).
6. inch of mercury (see Table 1-23C).
1.7 OTHER SI UNITS
Table 1-8 lists units used in the SI system whose values are not derived from the base quantities but
from experiment. The definitions of these units, given in the IEEE Standard Dictionary (ANSI/IEEE
Std 100-1988) are
electronvolt. The kinetic energy acquired by an
electron in passing through a potential difference of 1 volt
in vacuum.
NOTE : The electronvolt is equal to 1.60218 × 10 – joule, approximately (see Table 1-25B).
unified atomic mass unit. The fraction 1 / 2 of the mass
of an atom of the nuclide 12 C.
NOTE: u is equal to 1.660 54 × 10 –27^ kg, approximately.
astronomical unit. The length of the radius of the unperturbed circular orbit of a body of neg-
ligible mass moving around the sun with a sidereal angular velocity of 0.017 202 098 950 radian per
day of 86 400 ephemeris seconds.
NOTE : The International Astronomical Union has adopted a value for 1 AU equal to 1.496 × 1011 meters (see Table 1-15C).
UNITS, SYMBOLS, CONSTANTS, DEFINITIONS, AND CONVERSION FACTORS 1-
TABLE 1-8 Units Used with the SI System Whose Values Are Obtained Experimentally
Name Symbol
electronvolt eV unified atomic mass unit u astronomical unit∗ parsec pc ∗The astronomical unit does not have an international symbol. AU is customarily used in English, UA in French.
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parsec. The distance at which 1 astronomical unit subtends an angle of 1 second of arc. 1 pc
206 264.8 AU 30 857 × 1012 m, approximately (see Table 1-15C).
1.8 CGS SYSTEMS OF UNITS
The units most commonly used in physics and electrical science, from their establishment in 1873 until
their virtual abandonment in 1948, are based on the centimeter-gram-second (cgs) electromagnetic and
electrostatic systems. They have been used primarily in theoretical work, as contrasted with the SI units
(and their “practical unit” predecessors, see Sec. 1.9) used in engineering. Table 1-9 lists the principal
cgs electrical quantities and their units, symbols, and equivalent values in SI units. Use of these units
in electrical engineering publications has been officially deprecated by the IEEE since 1966.
The cgs units have not been used to any great extent in electrical engineering, since many of the
units are of inconvenient size compared with quantities used in practice. For example, the cgs electro-
magnetic unit of capacitance is the gigafarad.
1.9 PRACTICAL UNITS (ISU)
The shortcomings of the cgs systems were overcome by adopting the volt, ampere, ohm, farad,
coulomb, henry, joule, and watt as “practical units,” each being an exact decimal multiple of the corre-
sponding electromagnetic cgs unit (see Table 1-9). From 1908 to 1948, the practical electrical units
were embodied in the International System Units (ISU, not to be confused with the SI units). During
these years, precise formulation of the units in terms of mass, length, and time was impractical because
of imprecision in the measurements of the three basic quantities. As an alternative, the units were stan-
dardized by comparison with apparatus, called prototype standards. By 1948, advances in the mea-
surement of the basic quantities permitted precise standardization by reference to the definitions of the
1-8 SECTION ONE
TABLE 1-9 CGS Units and Equivalents
Quantity Name Symbol Correspondence with SI unit
Electromagnetic system
Current abampere abA 10 amperes (exactly) Voltage abvolt abV 10 –8^ volt (exactly) Capacitance abfarad abF 10 9 farads (exactly) Inductance abhenry abH 10 –9^ henry (exactly) Resistance abohm abΩ 10 –9^ ohm (exactly) Magnetic flux maxwell Mx 10 –8^ weber (exactly) Magnetic field strength oersted Oe 79.577 4 amperes per meter Magnetic flux density gauss G 10 –4^ tesla (exactly) Magnetomotive force gilbert Gb 0.795 774 ampere Electrostatic system
Current statampere statA 3.335 641 × 10 –10^ ampere Voltage statvolt statV 299.792 46 volts Capacitance statfarad statF 1.112 650 × 10 –12^ farad Inductance stathenry statH 8.987 554 × 10 11 henrys Resistance statohm statΩ 8.987 554 × 10 11 ohms Mechanical units
(equally applicable to the electrostatic and electromagnetic systems) Work/energy erg erg 10 –7^ joule (exactly) Force dyne dyn 10 –5^ newton (exactly)
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Elastance (S). Elastance is the reciprocal of capacitance.
Electric Charge, Quantity of Electricity (Q). Electric charge is a fundamentally assumed con-
cept required by the existence of forces measurable experimentally. It has two forms known as pos-
itive and negative. The electric charge on (or in) a body or within a closed surface is the excess of
one form of electricity over the other.
Electric Constant, Permittivity of Vacuum ( Γ e). The electric constant pertinent to any system of
units is the scalar which in that system relates the electric flux density D in vacuum, to E , the elec-
tric field strength ( D Γ eE ). It also relates the mechanical force between two charges in vacuum to
their magnitudes and separation. Thus, in the equation F Γ rQ 1 Q 2 /4 Γ er^2 , the force F between
charges Q 1 and Q 2 separated by a distance r Γ e is the electric constant, and Γ r is a dimensionless
factor which is unity in a rationalized system and 4 in an unrationalized system.
NOTE : In the cgs electrostatic system, Γ e is assigned measure unity and the dimension “numeric.” In the cgs electromagnetic system, the measure of Γ e is that of 1/ c^2 , and the dimension is [ L –2 T^2 ]. In the International System, the measure of Γ e is 10 7 /4 c^2 , and the dimension is [ L –3 M –1 T^4 I^2 ]. Here, c is the speed of light expressed in the appropriate system of units (see Table 1-12).
Electric Field Strength ( E ). The electric field strength at a given point in an electric field is the
vector limit of the quotient of the force that a small stationary charge at that point will experience,
by virtue of its charge, as the charge approaches zero.
Electric Flux ( Ψ ). The electric flux through a surface is the surface integral of the normal com-
ponent of the electric flux density over the surface.
Electric Flux Density, Electric Displacement ( D ). The electric flux density is a quantity
related to the charge displaced within a dielectric by application of an electric field. Electric flux
density at any point in an isotropic dielectric is a vector which has the same direction as the elec-
tric field strength, and a magnitude equal to the product of the electric field strength and the per-
mittivity . In a nonisotropic medium, may be represented by a tensor and D is not necessarily
parallel to E.
Electric Polarization ( P ). The electric polarization is the vector quantity defined by the equation
P ( D - Γ e E )/Γ r , where D is the electric flux density, Γ e is the electric constant, E is the electric field
strength, and Γ r is a coefficient that is set equal to unity in a rationalized system and to 4 in an unra-
tionalized system.
Electric Susceptibility (ce). Electric susceptibility is the quantity defined by ce ( r 1)/Γ r ,
where r is the relative permittivity and Γ r is a coefficient that is set equal to unity in a rationalized
system and to 4 in an unrationalized system.
Electrization ( E i). The electrization is the electric polarization divided by the electric constant
of the system of units used.
Electrostatic Potential (V). The electrostatic potential at any point is the potential difference
between that point and an agreed-on reference point, usually the point at infinity.
Electrostatic Potential Difference (V). The electrostatic potential difference between two points
is the scalar-product line integral of the electric field strength along any path from one point to the
other in an electric field, resulting from a static distribution of electric charge.
Impedance (Z). An impedance of a linear constant-parameter system is the ratio of the phasor
equivalent of a steady-state sine-wave voltage or voltage-like quantity (driving force) to the phasor
equivalent of a steady-state sine-wave current or current-like quantity (response). In electromagnetic
radiation, electric field strength is considered the driving force and magnetic field strength the
response. In mechanical systems, mechanical force is always considered as a driving force and
velocity as a response. In a general sense, the dimension (and unit) of impedance in a given appli-
cation may be whatever results from the ratio of the dimensions of the quantity chosen as the driving
force to the dimensions of the quantity chosen as the response. However, in the types of systems cited
above, any deviation from the usual convention should be noted.
Mutual Impedance. Mutual impedance between two loops (meshes) is the factor by which the
phasor equivalent of the steady-state sine-wave current in one loop must be multiplied to give the
phasor equivalent of the steady-state sine-wave voltage in the other loop caused by the current in
the first loop.
1-10 SECTION ONE
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Self-impedance. Self-impedance of a loop (mesh) is the impedance of a passive loop with all
other loops of the open-circuited network.
Transfer Impedance. A transfer impedance is the impedance obtained when the response is
determined at a point other than that at which the driving force is applied.
NOTE : In the case of an electric circuit, the response may be determined in any branch except that which contains the driving force.
Logarithmic Decrement ( Λ ). If F is a function of time given by
F A exp (– dt ) sin (2 t / T )
then the logarithmic decrement Λ Td.
Magnetic Constant, Permeability of Vacuum ( Γ m). The magnetic constant pertinent to any sys-
tem of units is the scalar which in that system relates the mechanical force between two currents in
vacuum to their magnitudes and geometric configurations. For example, the equation for the force F
on a length l of two parallel straight conductors of infinite length and negligible circular cross section,
carrying constant currents I 1 and I 2 and separated by a distance r in vacuum, is F Γ m Γ rI 12 l /2 r ,
where Γ m is the magnetic constant and Γ r is a coefficient set equal to unity in a rationalized system
and to 4 in an unrationalized system.
NOTE: In the cgs electromagnetic system, Γ m is assigned the magnitude unity and the dimension “numeric.” In the cgs electrostatic system, the magnitude of Γ m is that of 1/ c^2 , and the dimension is [ L –2 T^2 ]. In the International System, Γ m is assigned the magnitude 4 × 10 –7^ and has the dimension [ LMT –2 I –2].
Magnetic Field Strength ( H ). Magnetic field strength is that vector point function whose curl is
the current density and which is proportional to magnetic flux density in regions free of magnetized
matter.
Magnetic Flux ( Φ ). The magnetic flux through a surface is the surface integral of the normal
component of the magnetic flux density over the surface.
Magnetic Flux Density, Magnetic Induction ( B ). Magnetic flux density is that vector quantity
which produces a torque on a plane current loop in accordance with the relation T IA n × B , where
n is the positive normal to the loop and A is its area. The concept of flux density is extended to a
point inside a solid body by defining the flux density at such a point as that which would be mea-
sured in a thin disk-shaped cavity in the body centered at that point, the axis of the cavity being in
the direction of the flux density.
Magnetic Moment ( m ). The magnetic moment of a magnetized body is the volume integral of
the magnetization. The magnetic moment of a loop carrying current I is m (1/2)∫ r × d r , where r
is the radius vector from an arbitrary origin to a point on the loop, and where the path of integration
is taken around the entire loop.
NOTE : The magnitude of the moment of a plane current loop is IA , where A is the area of the loop. The reference direction for the current in the loop indicates a clockwise rotation when the observer is looking through the loop in the direction of the positive normal.
Magnetic Polarization, Intrinsic Magnetic Flux density ( J, Bi ). The magnetic polarization is the
vector quantity defined by the equation J ( B Γ mH )/Γ r , where B is the magnetic flux density, Γ m
is the magnetic constant, H is the magnetic field strength, and Γ r is a coefficient that is set equal to
unity in a rationalized system and to 4 in an unrationalized system.
Magnetic Susceptibility ( χ m ). Magnetic susceptibility is the quantity defined by χ m ( μr 1)/Γ r ,
where μr is the relative permeability and Γ r is a coefficient that is set equal to unity in a rationalized
system and to 4 in an unrationalized system.
Magnetic Vector Potential ( A ). The magnetic vector potential is a vector point function charac-
terized by the relation that its curl is equal to the magnetic flux density and its divergence vanishes.
UNITS, SYMBOLS, CONSTANTS, DEFINITIONS, AND CONVERSION FACTORS 1-
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Resistance (R)
1. The resistance of an element, device, branch, network, or system is the factor by which the mean-
square conduction current must be multiplied to give the corresponding power lost by dissipation
as heat or as other permanent radiation or as electromagnetic energy from the circuit.
2. Resistance is the real part of impedance.
Resistivity (r). The resistivity of a material is a factor such that the conduction current density
is equal to the electric field strength in the material divided by the resistivity.
Self-inductance (L)
1. Self-inductance is the quotient of the flux linkage of a circuit divided by the current in that same
circuit which induces the flux linkage. If voltage induced, d ( Li )/ dt.
2. Self-inductance is the factor L in the 1 / 2 Li^2 if the latter gives the energy stored in the magnetic field
as a result of the current i.
NOTE : Definitions 1 and 2 are not equivalent except when L is constant. In all other cases, the defini- tion being used must be specified. The two definitions are restricted to relatively slow changes in i , that is, to low frequencies, but by analogy with the definitions, equivalent inductances often may be evolved in high-frequency applications such as resonators and waveguide equivalent circuits. Such “inductances,” when used, must be specified. The two definitions are restricted to cases in which the branches are small in physical size when compared with a wavelength, whatever the frequency. Thus, in the case of a uni- form 2-wire transmission line it may be necessary even at low frequencies to consider the parameters as “distributed” rather than to have one inductance for the entire line.
Susceptance (B). Susceptance is the imaginary part of admittance.
Transfer Function (H). A transfer function is that function of frequency which is the ratio of a
phasor output to a phasor input in a linear system.
Transfer Ratio (H). A transfer ratio is a dimensionless transfer function.
Voltage, Electromotive Force (V). The voltage along a specified path in an electric field is the
dot product line integral of the electric field strength along this path. As defined, here voltage is syn-
onymous with potential difference only in an electrostatic field.
1.11 DEFINITIONS OF QUANTITIES OF RADIATION AND LIGHT
The following definitions are based on the principal meanings listed in the IEEE Standard Dictionary
(ANSI/IEEE Std 100-1988), which should be consulted for extended meanings, compound terms, and
related definitions. The symbols shown in parentheses are from Table 1-10.
Candlepower. Candlepower is luminous intensity expressed in candelas (term deprecated by IEEE).
Emissivity, Total Emissivity (). The total emissivity of an element of surface of a temperature
radiator is the ratio of its radiant flux density (radiant exitance) to that of a blackbody at the same
temperature.
Spectral Emissivity, ( λ ). The spectral emissivity of an element of surface of a temperature radi-
ator at any wavelength is the ratio of its radiant flux density per unit wavelength interval (spectral
radiant exitance) at that wavelength to that of a blackbody at the same temperature.
Light. For the purposes of illuminating engineering, light is visually evaluated radiant energy.
NOTE 1: Light is psychophysical, neither purely physical nor purely psychological. Light is not syn- onymous with radiant energy, however restricted, nor is it merely sensation. In a general nonspecialized sense, light is the aspect of radiant energy of which a human observer is aware through the stimulation of the retina of the eye.
NOTE 2: Radiant energy outside the visible portion of the spectrum must not be discussed using the quan- tities and units of light; it is nonsense to refer to “ultraviolet light” or to express infrared flux in lumens.
UNITS, SYMBOLS, CONSTANTS, DEFINITIONS, AND CONVERSION FACTORS 1-
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Luminance (Photometric Brightness) (L). Luminance in a direction, at a point on the surface
of a source, or of a receiver, or on any other real or virtual surface is the quotient of the luminous
flux (Φ) leaving, passing through, or arriving at a surface element surrounding the point, propagated
in directions defined by an elementary cone containing the given direction, divided by the product
of the solid angle of the cone ( dw ) and the area of the orthogonal projection of the surface element
on a plane perpendicular to the given direction ( dA cos q ). L d^2 Φ/[ dw ( da cos q )] dI /( dA cos q ).
In the defining equation, q is the angle between the direction of observation and the normal to the
surface.
In common usage, the term brightness usually refers to the intensity of sensation which
results from viewing surfaces or spaces from which light comes to the eye. This sensation is
determined in part by the definitely measurable luminance defined above and in part by condi-
tions of observation such as the state of adaptation of the eye. In much of the literature, the term
brightness, used alone, refers to both luminance and sensation. The context usually indicates
which meaning is intended.
Luminous Efficacy of Radiant Flux. The luminous efficacy of radiant flux is the quotient of the
total luminous flux divided by the total radiant flux. It is expressed in lumens per watt.
Spectral Luminous Efficacy of Radiant Flux, K( λ ). Spectral luminous efficacy of radiant flux is
the quotient of the luminous flux at a given wavelength divided by the radiant flux at the wavelength.
It is expressed in lumens per watt.
Spectral Luminous Efficiency of Radiant Flux. Spectral luminous efficiency of radiant flux is
the ratio of the luminous efficacy for a given wavelength to the value at the wavelength of maximum
luminous efficacy. It is a numeric.
NOTE : The term spectral luminous efficiency replaces the previously used terms relative luminosity and relative luminosity factor.
Luminous Flux ( Φ ). Luminous flux is the time rate of flow of light.
Luminous Flux Density at a Surface. Luminous flux density at a surface is luminous flux per
unit area of the surface. In referring to flux incident on a surface, this is called illumination (E). The
preferred term for luminous flux leaving a surface is luminous exitance (M) , which has been called
luminous emittance.
Luminous Intensity (I). The luminous intensity of a source of light in a given direction is the
luminous flux proceeding from the source per unit solid angle in the direction considered ( I
d Φ/ dw ).
Quantity of Light (Q). Quantity of light (luminous energy) is the product of the luminous flux
by the time it is maintained, that is, it is the time integral of luminous flux.
Radiance (L). Radiance in a direction, at a point on the surface, of a source, or of a receiver,
or on any other real or virtual surface is the quotient of the radiant flux ( P ) leaving, passing
through, or arriving at a surface element surrounding the point, and propagated in directions
defined by an elementary cone containing the given direction, divided by the product of the solid
angle of the cone ( dw ) and the area of the orthogonal projection of the surface element on a plane
perpendicular to the given direction ( dA cos q ). L d^2 P / dw ( dA cos q ) dI /( dA cos q ). In the
defining equation, q is the angle between the normal to the element of the source and the direc-
tion of observation.
Radiant Density (w). Radiant density is radiant energy per unit volume.
Radiant Energy (W). Radiant energy is energy traveling in the form of electromagnetic waves.
Radiant Flux Density at a Surface. Radiant flux density at a surface is radiant flux per unit area
of the surface. When referring to radiant flux incident on a surface, this is called irradiance (E). The
preferred term for radiant flux leaving a surface is radiant exitance (M) , which has been called
radiant emittance.
Radiant Intensity (I). The radiant intensity of a source in a given direction is the radiant flux
proceeding from the source per unit solid angle in the direction considered ( I dP / dw ).
Radiant Power, Radiant Flux (P). Radiant flux is the time rate of flow of radiant energy.
1-14 SECTION ONE
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1-16 SECTION ONE
TABLE 1-10 Standard Symbols for Quantities
Quantity Unit based on Quantity symbol International System Remarks
Space and time: Angle, plane a , b , g , q , , y radian Other Greek letters are permitted where no conflict results. Angle, solid Ω w steradian Length l meter Breadth, width b meter Height h meter Thickness d , d meter Radius r meter Diameter d meter Length of path line segment s meter Wavelength l meter Wave number s n ~^ reciprocal meter s 1/ l The symbol n ~ is used in spectroscopy. Circular wave number k radian per meter k 2 / l Angular wave number Area A S square meter Volume V , u cubic meter Time t second Period T second Time constant t T second Frequency f n second Speed of rotation n revolution per second Rotational frequency Angular frequency w radian per second w 2 f Angular velocity w radian per second Complex (angular) p s reciprocal second p – d jw frequency Oscillation constant Angular acceleration a radian per second squared Velocity u meter per second Speed of propagation c meter per second In vacuum, c 0 of electromagnetic waves Acceleration (linear) a meter per second squared Acceleration of free fall g meter per second Gravitational acceleration squared Damping coefficient d neper per second Logarithmic decrement Λ (numeric) Attenuation coefficient a neper per meter Phase coefficient b radian per meter Propagation coefficient g reciprocal meter g a jb Mechanics: Mass m kilogram (Mass) density r kilogram per cubic Mass divided by volume meter Momentum p kilogram meter per second Moment of inertia I, J kilogram meter squared
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UNITS, SYMBOLS, CONSTANTS, DEFINITIONS, AND CONVERSION FACTORS 1-
Force F newton Weight W newton Varies with acceleration of free fall Weight density g newton per cubic meter Weight divided by volume Moment of force M newton meter Torque T M newton meter Pressure p newton per square The SI name pascal has been adopted meter for this unit. Normal stress s newton per square meter Shear stress t newton per square meter Stress tensor s newton per square meter Linear strain e (numeric) Shear strain g (numeric) Strain tensor e (numeric) Volume strain q (numeric) Poisson’s ratio μ , n (numeric) Lateral contraction divided by elongation Young’s modulus E newton per square meter E s / e Modulus of elasticity Shear modulus G newton per square meter G t / g Modulus of rigidity Bulk modulus K newton per square meter K p / q Work W joule Energy E, W joule U is recommended in thermodynamics for internal energy and for blackbody radiation. Energy (volume) density w joule per cubic meter Power P watt Efficiency h (numeric) Heat: Thermodynamic temperature T Θ kelvin Temperature t q degree Celsius The word centigrade has been abandoned as Customary temperature the name of a temperature scale. Heat Q joule Internal energy U joule Heat flow rate Φ q watt Heat crossing a surface divided by time Temperature coefficient a reciprocal kelvin Thermal diffusivity a square meter per second Thermal conductivity l k watt per meter kelvin Thermal conductance Gq watt per kelvin Thermal resistivity rq meter kelvin per watt Thermal resistance Rq kelvin per watt Thermal capacitance Cq joule per kelvin Heat capacity Thermal impedance Zq kelvin per watt Specific heat capacity c joule per kelvin Heat capacity divided by mass kilogram Entropy S joule per kelvin Specific entropy s joule per kelvin Entropy divided by mass kilogram Enthalpy H joule Radiation and light: Radiant intensity I I e watt per steradian Radiant power P , Φ Φe watt Radiant flux
TABLE 1-10 Standard Symbols for Quantities ( Continued )
Quantity Unit based on Quantity symbol International System Remarks
( Continued )
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UNITS, SYMBOLS, CONSTANTS, DEFINITIONS, AND CONVERSION FACTORS 1-
Electric susceptibility c e i (numeric) c e r 1 MKSA Electrization E i K i volt per meter E i ( D /Γe) E MKSA Electric polarization P coulomb per square P D Γe E MKSA meter Electric dipole moment p coulomb meter (Electric) current I ampere Current density J S ampere per square meter Linear current density A a ampere per meter Current divided by the breadth of the conducting sheet Magnetic field strength H ampere per meter Magnetic (scalar) potential U , U m ampere Magnetic potential difference Magnetomotive force F , F m ampere Magnetic flux Φ weber Magnetic flux density B tesla Magnetic induction Magnetic flux linkage Λ weber (Magnetic) vector potential A weber per meter Retarded (magnetic) A r weber per meter vector potential Permeability μ henry per meter Of vacuum, μ v Absolute permeability Relative permeability μ r (numeric) Initial (relative) μ o (numeric) permeability Complex relative μ r∗ (numeric) μ r∗ μ ′r jμ ″r permeability μ ″r is positive for lossy materials. The complex absolute permeability μ ∗^ is defined in analogous fashion. Magnetic susceptibility c m μ i (numeric) c m μ r 1 MKSA Reluctivity n meter per henry n 1/ μ Magnetization H i, M ampere per meter H i ( B /Γm) H MKSA Magnetic polarization J , B i tesla J B Γm H MKSA Intrinsic magnetic flux density Magnetic (area) moment m ampere meter squared The vector product m × B is equal to the torque. Capacitance C farad Elastance S reciprocal farad S 1/ C (Self-) inductance L henry Reciprocal inductance Γ reciprocal henry Mutual inductance L (^) ij , Mij henry If only a single mutual inductance is involved, M may be used without subscripts. Coupling coefficient k k (numeric) k Lij ( LiLj )–1/ Leakage coefficient s (numeric) s 1 k^2 Number of turns N, n (numeric) (in a winding) Number of phases m (numeric) Turns ratio n n ∗ (numeric)
TABLE 1-10 Standard Symbols for Quantities ( Continued )
Quantity Unit based on Quantity symbol International System Remarks
( Continued )
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1-20 SECTION ONE
Transformer ratio a (numeric) Square root of the ratio of secondary to primary self-inductance. Where the coefficient of coupling is high, a n ∗. Resistance R ohm Resistivity r ohm meter Volume resistivity Conductance G siemens G Re Y Conductivity g , s siemens per meter g 1/ r The symbol s is used in field theory, as g is there used for the propagation coefficient. Reluctance R , R m reciprocal henry Magnetic potential difference divided by magnetic flux Permeance P , P m henry P m 1/ R m Impedance Z ohm Reactance X ohm Capacitive reactance XC ohm For a pure capacitance, XC – 1/ wC Inductive reactance XL ohm For a pure capacitance, XL wL Quality factor Q (numeric) See Q in Sec. 1.10. Admittance Y siemens Y 1/ Z G + jB Susceptance B siemens B Im Y Loss angle d radian d ( R /| X |) Active power P watt Reactive power Q Pq var Apparent power S Ps voltampere Power factor cos Fp (numeric) Reactive factor sin Fq (numeric) Input power Pi watt Output power P o watt Poynting vector S watt per square meter Characteristic impedance Z o ohm Surge impedance Intrinsic impedance h ohm of a medium Voltage standing-wave ratio S (numeric) Resonance frequency f r hertz Critical frequency f c hertz Cutoff frequency Resonance angular w r radian per second frequency Critical angular frequency w c radian per second Cutoff angular frequency Resonance wavelength l r meter Critical wavelength l c meter Cutoff wavelength Wavelength in a guide l g meter Hysteresis coefficient k h (numeric) Eddy-current coefficient k e (numeric) Phase angle , q radian Phase difference †( l ) is not part of the basic symbol but indicates that the quantity is a function of wavelength.
TABLE 1-10 Standard Symbols for Quantities ( Continued )
Quantity Unit based on Quantity symbol International System Remarks
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