Units, Dimensions, and Standards INTRODUCTION

1. Unit of ForceThe SI unit force is the 1 newton (N), defined as that force which will give a mass of 1kilogram an acceleration of 1 meter per second per second.When a body is to be accelerated or decelerated, a force must be applied proportional tothe desired rate of change of velocity, that is, proportional to the acceleration (or deceleration).Force (F) = mass (m) × acceleration (a) (1-1)When the mass is in kilograms and the acceleration is in m/s 2 , the foregoing equationgives the force in newtons. If the body is to be accelerated vertically from the earth’s surface, theacceleration due to gravity (g) must be overcome before any vertical motion is possible. In SIunits:Thus, a mass of 1 kg has a gravitational force of 9.81 N.2. Workg = 9.81 m/s 2 (1-2)When a body is moved, a force is exerted to overcome the body’s resistance to motion.The work done in moving a body is the product of the force and the distance throughwhich the body is moved in the direction of the force.Work (W) = force (F) × distance (d) (1-3)The SI unit of work is the 2 joule (J), defined as the amount of work done when a force of1 newton acts through a distance of 1 meter.Thus, the joule may also be termed a newton-meter. For the equation W = Fd. work isexpressed in joules when F is in newtons and d is in meters.3. EnergyEnergy is defined as the capacity for doing work and measured in the same units as work.4. PowerPower is the time rate of doing work.If a certain amount of work W is to be done in a time t, the power required isPower(P) =work( W )time()t(1-4)The SI unit of power is the 3 watt (W), defined as the power developed when 1 joule ofwork is done in 1 second. For P = W/t, P is in watts when W is in joules and t is in seconds.1. Named for the great English philosopher and mathematician Sir Isaac Newton (1642-1727).2. Named after the English physicist James P. Joule (1818-1899).3. Named after the Scottish engineer and inventor James Watt (1736-1819).2

SCIENTIFIC NOTATION AND METRIC PREFIXES1. Scientific NotationVery large or very small numbers are conveniently written as a number multiplied by 10raised to a power:100 = 1×10×10 = 1×10 210 000 = 1×10×10×10×10 = 1×10 40.001 = 1×10 31500 = 1.5 ×10 30.015 = 1.5 ×10 2Note that in the SI system of units, spaces are used instead of commas when writing largenumbers. Four-numeral numbers are an exception. One thousand is written as 1000, while tenthousand is 10 000.2. Metric PrefixesMetric prefixes and the letter symbols for the various multiples and submultiples of 10 arelisted in Table 1-1, with those most commonly used with electrical units shown in bold type. Theprefixes are employed to simplify the writing of very large and very small quantities. Thus,1000 can be expressed as 1 kilo-ohm, or 1k. Here kilo is the prefix that represents 1000, and kis the symbol for kilo. Similarly, 1×10 3 A can be written as 1 millilampere, or 1 mA.TABLE 1-1 SCIENTIFIC NOTATION AND METRIC PREFIXESValue Scientific Notation Prefix Symbol1 000 000 000 000 10 12 tera T1 000 000 000 10 9 giga G1 000 000 10 6 mega M1 000 10 3 kilo k100 10 2 hecto h10 10 deka da0.1 10 1 deci d0.01 10 2 centi c0.001 10 3 milli m0.000 001 10 6 micro µ0.000 000 001 10 9 nano n0.000 000 000 001 10 12 pico p3. Engineering NotationAs already discussed, 1 k is 1×10 3 , and 1 mA is 1×10 3 A. Note also from Table 1-1that 1×10 6 is expressed as 1 M, and 1×10 6 A can be written as 1 µA. These quantities, and most3

of the metric prefixes in Table 1-1, involve multiples of 10 3 or 10 3 . Quantities that use 10 3 or10 3 are said to be written in engineering notation. A quantity such as 1×10 4 is moreconveniently expressed as 10×10 3 , or 10 k. Also, 47×10 4 A is best written as 4.7×10 3 A, or4.7mA. For electrical calculations, engineering notation is more convenient than ordinaryscientific notation.SI ELECTRICAL UNITS1. Units of Current and ChargeElectric current (I) is a flow of charge carriers. Therefore, current could be defined interms of the quantity of electricity (Q) that passes a given point in a conductor during a time of1s.The 1 coulomb (C) is the unit of electrical charge or quantity of electricity.The coulomb was originally selected as the fundamental electrical unit from which allother units were derived. However, since it is much easier to measure current accurately than it isto measure charge, the unit of current is now the fundamental electrical unit in the SI system.Thus, the coulomb is a derived unit, defined in terms of the unit of electric current.The 2 ampere (A) is the unit of electric current.The ampere is defined as that constant current which, when flowing in each of twoinfinitely long parallel conductors 1 meter apart, exerts a force of 2×10 7 newton per meter oflength on each conductor.The coulomb is defined as that charge which passes a given point in a conductor eachsecond, when a current of 1 ampere flows.These definitions show that the coulomb could be termed an ampere-second. Conversely,the ampere can be described as a coulomb per second:amperes = coulombsseconds(1-5)It has been established experimentally that 1 coulomb is equal to the total charge carriedby 6.24×10 18 electrons. Therefore, the charge carried by one electron is1Q =186.2410= 1.602×10 19 C1. Named after the French physicist Charles Augustin de Coulomb (1736-1806).2. Named after the French physicist and mathematician Andre Marie Ampere (1775-1836).4

2. Emf, Potential Difference, and VoltageThe 1 volt (V) is the unit of electromotive force (emf) and potential difference.The volt (V) is defined as the potential difference between two points on a conductorcarrying a constant current of 1 ampere when the power dissipated between these points is 1 watt.As already noted, the coulomb is the charge carried by 6.24×10 18 electrons. One joule ofwork is done when 6.24×10 18 electrons are moved through a potential difference of 1 V. Oneelectron carries a charge of 1/(6.24×10 18 ) coulomb. If only one electron is moved through 1 V,the energy involved is an electron volt (eV).11 eV =186.2410JThe electron-volt is frequently used in the case of the very small energy levels associatedwith electrons in orbit around the nucleus of an atom.3. Resistance and ConductanceThe 2 ohm is the unit of resistance, and the symbol used for ohms is ; the Greek capitalletter omega.The ohm is defined as that resistance which permits a current flow of 1 ampere when apotential difference of 1 volt is applied to the resistance.The term conductance (G) is applied to the reciprocal of resistance. The 3 siemens (S) isthe unit of conductance.Conductance =1resistance(1-6)4. Magnetic Flux and Flux DensityThe 4 weber (Wb) is the SI unit of magnetic flux.The weber is defined as the magnetic flux which, linking a single-turn coil, produces anemf of 1 V when the flux is reduced to zero at a constant rate in 1 s.The 5 tesla (T) is the SI unit of magnetic flux density.The tesla is the flux density in a magnetic field when 1 weber of flux occurs in a plane of1 square meter; that is, the tesla can be described as 1 Wb/m 2 .1. Named in honor of the Italian physicist Count Alessandro Volta (1745-1827), inventor of the voltaic pile.2. Named after the German physicist Georg Simon Ohm (1787-1854), whose investigations led to his statement of“Ohm’s law of resistance.”3. Named after Sir William Siemens (1823-1883), a British engineer who was born Karl William von Siemens inGermany. The unit of conductance was previously the mho (“ohm” spelled backwards).4. Named after the German physicist Wilhelm Weber (1804-1890).5. Named for the Croatian-American researcher and inventor Nikola Tesla (1856-1943).5

5. InductanceThe SI unit of inductance is the 1 henry (H). The inductance of a circuit is 1 henry, whenan emf of 1 volt is induced by the current changing at the rate of 1 A/s.6. CapacitanceThe 2 farad (F) is the SI unit of capacitance.The farad is the capacitance of a capacitor that contains a charge of 1 coulomb when thepotential difference between its terminals is 1 volt.SI TEMPERATURE SCALESThere are two SI temperature scales, the 3 Celsius scale and the 4 Kelvin scale. The Celsiusscale has 100 equal divisions (or degrees) between the freezing temperature and the boilingtemperature of water. At normal atmospheric pressure, water freezes at 0C (zero degreesCelsius) and boils at 100°C.The Kelvin temperature scale, also known as the absolute scale, commences at absolutezero of temperature, which corresponds to 273.15°C. Therefore, 0°C is equal to 273.15 K, and100°C is the same temperature as 373.15 K. A temperature difference of 1 K is the same as atemperature difference of 1°C.OTHER UNIT SYSTEMSIn the traditional English-language (American and Imperial) systems of measurements,the fundamental mechanical units are the foot for length, the pound for mass, and the second fortime. Other mechanical units derived from these are similar in both systems, with the exceptionof the units for liquid measure. The Imperial gallon equals approximately 1.2 U.S. gallons.Before the SI system was adopted, CGS systems using the centimeter, gram, and secondas fundamental mechanical units were employed for scientific purposes. There were two CGSsystems: an electrostatic system and a magnetic system. Many CGS units were too small or toolarge for practical engineering applications, so practical units were also used.When solving problems, it is sometimes necessary to convert from the traditional unitsystems to SI units. Appendix 1 provides a list of conversion factors for this purpose.1. Named for the American physicist Joseph Henry (1797-1878).2. Named for the English chemist and physicist Michael Faraday (1791-1867).3. Invented by the Swedish astronomer and scientist Anders Celsius (1701-1744).4. Named for the Irish-born scientist and mathematician William Thomson, who became Lord Kelvin (1824-1907).6

Example 1-1A bar magnet with a 1 inch square cross section is said to have a total magnetic flux of500 maxwell. Determine the flux density in tesla.SolutionFrom Appendix 1,total flux, = (500 maxwell) × 10 8 Wb= 5µWbarea, A = (1 in.×1 in.) × (2.54×10 2 ) 2 m 2= 2.54 2 ×10 4 m 2flux density, B 5Wb= = A2 4 22.54 10m= 7.75 mTExample 1-2The normal human body temperature is given as 98.6°F. Determine the equivalentCelsius and Kelvin scale temperatures.SolutionFrom Appendix 1,F 32 98.7 32Celsius temperature = =1.8 1.8= 37°CF 32Kelvin temperature = +273.151.8= 310.15 KSTANDARDS1. Working StandardsElectrical measurement standards are precise resistors, capacitors, inductors, voltagesources, and current sources, which can be used for comparison purposes when measuringelectrical quantities. For example, resistance can be accurately measured by means of aWheatstone bridge which uses a standard resistor. Similarly, standard capacitors and inductorscan be employed in bridge (or other) methods to accurately measure capacitance and inductance.The standard resistors, capacitors, and inductors usually found in an electronicslaboratory are classified as working standards. Working standard resistors are normallyconstructed of manganin or a similar material, which has a very low temperature coefficient.They are available in resistance values ranging from 0.01 to 1 M, with typical accuracies of±0.01% to ±0.1%. A working standard capacitor might be air dielectric type, or might beconstructed of silvered mica. Available capacitance values are 0.001 µF to 1 µF with a typicalaccuracy of ±0.02%.Standard inductors are available in values ranging from 100 µH to 10 H with typicalaccuracies of ±0.1%. Calibrators provide standard voltages and currents for calibratingvoltmeters and ammeters.7

2. Standard ClassificationsMeasurement standards are classified in four levels: international standards, primarystandards, secondary standards and working standards. Thus, the working standards alreadydiscussed are the lowest level of standards.International standards are defined by international agreements, and are maintained atthe International Bureau of Weights and Measures in France. These are as accurate as it isscientifically possible to achieve. They may be used for comparison with primary standards, butare otherwise unavailable for any application.Primary standards are maintained at institutions in various countries around the world,such as the National Bureau of Standards in Washington. They are also constructed for thegreatest possible accuracy, and their main function is checking the accuracy of secondarystandards.Secondary standards are employed in industry as references for calibrating highaccuracyequipment and components, and for verifying the accuracy of working standards.Secondary standards are periodically checked at the institutions that maintain primary standards.In summary, working standards are used as measurement references on a day-today basisin virtually all electronics laboratories. Secondary standards are more accurate than workingstandards, and are used throughout industry for checking working standards, and for calibratinghigh-accuracy equipment. Primary standards are more accurate than secondary standards. Theyare maintained to the highest possible accuracy by national institutions as references forcalibrating secondary standards. International standards are maintained by internationalagreement, and may be used for checking primary standards.PROBLEMS1. Referring to the unit conversion factors in Appendix 1, perform the following conversions:(a) 6215 miles to kilometers. (9,999.9km)(b) 50 miles per hour to kilometers per hour. (80.45km/hr)(c) 12 square feet to square centimeters. (11,149cm 2 )2. Determine how long it takes light to travel to earth from a star 1 million miles away if thespeed of light is 3×10 8 m/s. (5.36s)3. The speed of sound in air is 345 m/s. Calculate the distance in miles from a thunderstormwhen the thunder is heard 5 s after the lightning flash. (1.07miles)4. A 140 lb person has a height of 5 ft 7 in. Convert these measurements into kilograms andcentimeters. (63.5kg, 170.2cm)5. A bar magnet has a cross section of 0.75 in.×0.75 in. and a flux density of 1290 lines persquare inch. Calculate the total flux in webers. (7.26µWb)6. Calculate the Celsius and Kelvin scale equivalents of 80°F. (26.7C, 299.8K)7. A ¼ horsepower electric motor is operated 8 hours per day for 5 days every week. Assuming100% efficiency, calculate the kilowatt-hours of energy consumed in 1 year. (7.46kWh)8

Unit Conversion FactorsThe following factors may be used for conversion between non-SI units and SI units.To Convert To Multiply byArea Unitsacres square meter (m 2 ) 4047acres hectares (ha) 0.4047circular mils square meters (m 2 ) 5.067×10 10square feet square meters (m 2 ) 0.0929square inches square centimeters (cm 2 ) 6.452square miles hectares (ha) 259square miles square kilometers (km 2 ) 2.59square yards square meters (m 2 ) 0.8361Electric and Magnetic Unitsamperes/inch ampere/meter (A/m) 39.37gauses teslas (T) 10 4gilberts ampere (turns)(A) 0.7958line/sq.inch teslas (T) 1.55×10 5Maxwells webers (Wb) 10 8mhos Siemens (S) 1Oersteds amperes/meter 79.577Energy and Work UnitsBtu joules (J) 1054.8Btu kilowatt hours (kW.h) 2.928×10 4ergs joules (J) 10 7ergs kilowatt hours (kW.h) 0.2778×10 13foot-pounds joules (J) 1.356foot-pounds kilogram meters (kgm) 0.1383Force Unitsdynes grams (g) 1.02×10 3dynes newtons (N) 10 5pounds newtons (N) 4.448poundals newtons (N) 0.1383grams newtons (N) 9.807×10 3Pressure Unitsatmospheres kilopascals (kPa) 101.325bars kilopascals (kPa) 100inches of mercury kilopascals (kPa) 3.386pounds/sq.inch kilopascals (kPa) 6.8959

Illumination Unitsfoot-candles lux (lx) 10.764Velocity Unitsmiles/hour (mph) kilometers/hour (km/h) 1.609knots kilometer/hour (km/h) 1.853Power UnitsHorsepower watts (W) 745.7Temperture Unitsdegrees Fahrenheit (F) degrees Celsius (C) (F – 32)/1.8degrees Fahrenheit (F) kelvin (K) 273.15+(F – 32)/1.8Linear Unitsangstroms meters (m) 1×10 10feet meters (m) 0.3048fathoms meters (m) 1.8288inches centimeters (cm) 2.54microns meters (m) 10 6miles (nautical) kilometers (km) 1.853miles (statute) kilometer (km) 1.609mils centimeters (cm) 2.54×10 3yards meters (m) 0.9144Volume Unitsbushels cubic meters (m 3 ) 0.03524cubic feet cubic meters (m 3 ) 0.02832cubic feet liters (l) 28.32cubic inches cubic centimeters (cm 3 ) 16.387cubic inches liters (l) 0.01639cubic yards cubic meters (m 3 ) 0.7646gallons (U.S.) cubic meters (m 3 ) 3.7853×10 3gallons (imperial) cubic meters (m 3 ) 4.546×10 3gallons (U.S.) liters (l) 3.7853gallons (imperial) liters (l) 4.546gills liters (l) 0.1183pints (U.S.) liters (l) 0.4732pints (imperial) liters (l) 0.5683quarts (U.S.) liters (l) 0.9463quarts (imperial) liters (l) 1.137Weight Unitsounces grams (g) 28.35pounds kilograms (kg) 0.45359tons (long) kilograms (kg) 1016tons (short) kilograms (kg) 907.1810