dimestion and standards, si unit system

Dimensions and Standard

dimensions and standards: Scientific notations and

metric prefixes. SI electrical units, SI temperature scales,

Other unit systems, dimension and standards.

2/3/2017 1NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

Measurements• Measurement involves comparing the value to be measured with

a known value (standard)

• It is impossible to measure without comparison;

• the act of measurement involves reading the value with aninstrument. The instrument makes the comparison of the valuewith standard & gives reading.

• Standard are object or prescription to which all othermeasurements are compared


Types of Measurement• Direct Method: In this method unknown quantity is directly

compared with the standard. Direct method is quite common formeasurement of physical quantities like Length, Mass and Time

• Indirect Methods: Measurement by direct methods are notalways possible or feasible. Also as direct method involveshumans so are less accurate and sensitive. Measurementsystems are indirect methods for measurement

Measurement system consists of a transuding element whichconverts the quantities to be measured in electrical form.Analogous signal is then processed by some intermediate meansand is then fed to the end devices which displays the result.

2/3/2017NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

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Measuring Instruments• Measurement generally involve an “Instrument” as a physical

means for determining a quantity or variable.

• Instrument may be defined as a device for determining a valueor magnitude of a quantity

Types of Instruments:

• Absolute Instruments: Measures the quantity in terms ofphysical constants of the instruments. Ex : TangentGalvanometer

• Secondary Instruments: Quantity being measured is outputdisplayed by instrument. These instruments are calibrated bycomparison with an absolute instrument or another secondaryinstrument of higher accuracy.


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Scientific notations and metric prefixes

Scientific notation also referred to as standard form or standardindex form is the way of expressing numbers that can easily handlevery large numbers or very small number

A quantity written in scientific notation as M x 10n

where

– M is the number in decimal number (for base 10)

– 10 is the base and n is the exponent or power of 10 (base)

Example• 5.45E+6 or 5.45 x 106

• Numbers less than 1 will have a negative exponent.


Scientific notationsExample• 2930000000000 2.93E+12 or 2.93 x 1012

• 293 2.93E+1 or 2.93 x 102

• 00293.00 2.93E+1 or 2.93 x 102

• 0.293 2.93E-1 or 2.93 x 10-1

• 0.00000293 2.93E-6 or 2.93 x 10-6

Scientific notation has two parts• The digits (with the decimal point placed after the first non zero digit)• power part ; multiplied by 10 to a power that puts the decimal point after first non zero digit


SI Unit Prefixes - Part I

Name Symbol Meaning Factor

Yotta Y 1,000,000,000,000,000,000,000,000 1024

Zetta Z 1,000,000,000,000,000,000,000 1021

Exa E 1,000,000,000,000,000,000 1018

Peta P 1,000,000,000,000,000 1015

Tera T 1,000,000,000,000 1012

Giga G 1,000,000,000 109

Mega M 1,000,000 106

kilo k 1,000 103

hecto h 100 102

deka da 10 101

SI Unit Prefixes - Part I

Name Symbol Meaning Factor

deci d 0.1 10-1

centi c 0.01 10-2

mili m 0.001 10-3

micro µ 0.000 001 10-6

nano n 0.000 000 001 10-9

pico p 0.000 000 000 001 10-12

femto f 0.000 000 000 000 001 10-15

atto a 0.000 000 000 000 000 001 10-18

zepto z 0.000 000 000 000 000 000 001 10-21

yocto y 0.000 000 000 000 000 000 000 001 10-24

Measurements Standards


A Comuter Generated Image of the international prototype kilogram (the inch ruler is for scale). The prototype is ofa platinum–iridium alloy and is 39.17 mm in both diameter and height, its edges have a four-angle (22.5°, 45°,67.5° and 79°) chamfer to minimize wear https://en.wikipedia.org/wiki/Kilogram#/media/File:CGKilogram.jpg

STANDARD: thephysical object orrealizable physicalparameter

DIMENSION: what it measures (for example, length or mass or a combination of basic units)

UNIT: the label given tothe standard; whatmeasurements aremeasured in. Ex KGstandard

Each standard has, a unit and a dimension related to it. The unit is the label given to it, and the dimension is what the standard measures.

https://en.wikipedia.org/wiki/Computer-generated_imagery

Standards

The 4 desirable characteristics of a STANDARD

• Universal – is agreed upon by the world

• Easily Available – must be reproducible with relative ease

• Immutable – does not change appreciably over a long period of time

• Precise – the best of the best


Standards

The CIPM (abbreviated from the French Comité international despoids et mesures) consists of eighteen persons from Member Statesof the Metre Convention (Convention du Mètre) of 1875 appointedby the General Conference on Weights and Measures (CGPM)whose principal task is to ensure world-wide uniformity in units ofmeasurement by direct action or by submitting proposals to theCGPM.https://en.wikipedia.org/wiki/International_Committee_for_Weights_and_Measures


Standards


A standard is physical representation of a unit of physical quantity.Standards are used for obtaining the values of physical properties ofother equipments by comparison.

International StandardsMaintained by International Bureau of weights and measure

Primary StandardsMaintained by National Laboratories

Secondary StandardsBasic reference maintained in Industrial reference Laboratories

Working StandardsMajor tools of Measurement Laboratories

The Seven Base SI Units

Basic Physical parameter Unit Symbol

Length meter m

Mass kilogram kg

Time second s

Temperature kelvin K

Electric Current ampere A

Amount of substance mole mol

Luminous Intensity candela cd

Supplementary unitsAngle Radiun rad

Solid Angle Staradian sr

The International System of Units (SI units) is founded on seven SIbase units for seven base quantities assumed to be mutuallyindependent. In addition two supplementary units are added


Metre (m): Length equal to 1650763.73 wavelength in vacuum ofradiation corresponding to transitions between level 2p10 and5ds (orange and red line) of the Krypton 86 atom (exited at triplepoint of nitrogen at 63.15 0K)

Kilogram (Kg): equal to the mass of the international prototypeof the mass. This prototype is a cylinder of Platinum Iridium alloy.

Second (s): is duration of 9192631770 periods of radiationcorresponding to the transition between two hyperfine levels ofground state of Cesium 133 atom


Ampere (A) : Constant current, which if maintained between twoparalle conductors of infinite length of negligible cross sectionand placed one meter apart in vaccum would produce betweenthem a force equal to 2 x 10-7 Newton per meter length

Kelvin (K): is 1/273.15 of thermodynamic temperature of triplepoint of water

Candela (Cd): Luminous intensity in a perpendicular direction ofa surface of 1/600000 square meter of a black body at thetemperature of freezing platinum under a pressure of 101325Newton per square meter.


Mole: is amount of substance of a system which contains asmany elementary entities as there are atoms in 0.012 Kg ofCarbon 12.

Supplementary Units

Radian (rad): Plane angle subtended by an arc of a circle equal inlength to the radius of the circle.

Steradian (sr): solid angle subtended at the centre of a sphere bythe surface whose area is equal to the square of radius of thesphere

Derived Units

Physical parameter Unit Name Symbol Equivalent SI Unit

volume Cubic meter m3

Density Kilogram per cubic meter Kg/m3

speed Meter per second m/s

Force Newton N kg m/s2

pressure Pascal Pa N / m2

Energy Joule J N m

Power Watt W J / s

Derived quantities, are defined in terms of the seven basequantities via a system of quantity equations. The SI derivedunits for these derived quantities are obtained from theseequations and the seven SI base units

SI Electrical Units


Physical parameter Unit Name Symbol Equivalent SI Unit

Power Watt W J / s

Electric Potential Volt V W / A

Frequency Hertz Hz s-1

Electric Charge Coulomb C A s

Electric Resistance Ohm V / A

Capacitance Farad F C/V

Inductance Henry H V s / A

Electric Conductance Siemens S A / V

Magnetic Flux Weber Wb V s

Magnetic Flux Density Tesla T Wb / s2

SI Temperature Scales• The SI unit of temperature is the Kelvin. The Kelvin (K) is the

fraction 1/273.15 of the thermodynamic temperature of thetriple point of water.

• Absolute zero (0 0K) is lowest possible temperature. Absolutezero, in Celsius scale, is approximately -273 0C.

• Scientists discovered absolute zero when they figured that astemperature decreases, the volume of a gas also gets smaller.They graphed this relationship and found that for each substancetested, zero volume for each substance would hypotheticallyoccur around minus 273 0C, the equivalent of absolute zero.


Other Temperature Scales

• Celsius temperature scale and Fahrenheit temperature scale isderived SI unit and is generally used to measure everydaytemperature


From\To 0C 0F 0K

0C 0C 0C*1.8+32 0C+273.15

0F (0F-32)/1.8 0F (0F-32)/1.8 +273.15

0K 0K-273.15 (0K-273.15)*1.8+32 0K

Q . Normal Human temperature of Human body is 98.6 0F. Convert into 0C

Temperature in 0C = (0F-32)/1.8 = (98.6-32)/1.8=66.6/1.8= 37 0C

Units Outside the SI


Certain units are not part of the International System of Units, butare important and widely used. the units in this category that areaccepted for use with the SI are

Name

Sym

bo

l

Value in SI units Name

Sym

bo

l

Value in SI units

minute min 1 min = 60 s liter L 1 L = 1 dm3 = 10-3 m3

hour h 1 h = 60 min = 3600 s metric ton (a) t 1 t = 103 kg

day d 1 d = 24 h = 86 400 s neper Np 1 Np = 1

degree (angle) ° 1° = ( /180) rad bel (b) B 1 B=(1/2) ln 10 Np (c)

minute (angle) 1=(1/60)°=(/10 800) rad electronvolt (d) eV 1 eV=1.60218 x 10-19 J, approx

second (angle) 1=(1/60)=(/648 000) radunified atomic mass unit (e) u 1 u=1.66054 x 10-27 kg, approx

Pascal Pa 1 Pa = 1 N/m2 astronomical unit (f) ua 1 ua=1.49598 x 1011 m, approx

Other unit systems: CGS


• In 1832, German mathematician Carl F. Gauss proposed a system ofthree fundamental units as millimetre, milligram and second

• In 1874, British physicists Maxwell extended it with a set ofelectromagnetic units and the selection of centimetre, gram andsecond and the naming of CGS (Centimetre, Gram, Second) System.

• The sizes of many CGS units turned out to be inconvenient forpractical purposes. For example, everyday objects are hundreds orof centimetres long, such as humans, rooms and buildings.

• CGS system never gained wide use outside the field of science

Other unit systems FPS


Foot–pound–second system

• built on the three fundamental units: foot for length, (avoirdupois)pound for mass and second for time

• Variants of the FPS system were the most common system intechnical publications in English until the middle of the 20thcentury

• 1 Pound (Lb) = 0.453592 Kg• 1 Foot = 0.3048 Meter

Dimension


Every derived unit is recognized by its dimensions which can bedefined as complete algebraic formula for derived unit in terms offundamental units using characteristic notion.

DerivedUnit

sym

bo

l

Relation

Dim

en

sio

n

Derived Unit

sym

bo

l

Relation

Dim

en

sio

n

Velocity v =Displacement/ Time LT-1 Charge Q =Current x Time TI

AccelerationA =Velocity/ Time LT-2 EMF E =Work done/ Charge ML2T-3I-1

Force F =Mass x Acceleration MLT-2 Resistance R =EMF/ Current ML2T-3I-2

Work W =Force x Displacement ML2T-2 Magnetic Flux E=N(d/dt) ML2T-2I-1

Power P =Work/ Time ML2T-3 Flux Density B =flux/ Area MT-2I-1

Energy E =power x Time ML2T-2 Inductance L E=L(dI/dt) ML2T-2I-2

Torque T =Force x distance ML2T-2 Capacitance C =Q/E M-1L-2T4I2

Thanks


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dimestion and standards, si unit system

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