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 1
NEC 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 an
instrument. The instrument makes the comparison of the value
with standard & gives reading.
• Standard are object or prescription to which all other
measurements are compared
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Types of Measurement
• Direct Method: In this method unknown quantity is directly
compared with the standard. Direct method is quite common for
measurement of physical quantities like Length, Mass and Time
• Indirect Methods: Measurement by direct methods are not
always possible or feasible. Also as direct method involves
humans so are less accurate and sensitive. Measurement
systems are indirect methods for measurement
Measurement system consists of a transuding element which
converts the quantities to be measured in electrical form.
Analogous signal is then processed by some intermediate means
and is then fed to the end devices which displays the result.
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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 value
or magnitude of a quantity
Types of Instruments:
• Absolute Instruments: Measures the quantity in terms of
physical constants of the instruments. Ex : Tangent
Galvanometer
• Secondary Instruments: Quantity being measured is output
displayed by instrument. These instruments are calibrated by
comparison with an absolute instrument or another secondary
instrument of higher accuracy.
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Scientific notations and metric prefixes
Scientific notation also referred to as standard form or standard
index form is the way of expressing numbers that can easily handle
very 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.
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Scientific notations
Example
• 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
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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
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A Comuter Generated Image of the international prototype kilogram (the inch ruler is for scale). The prototype is of
a 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: the
physical object or
realizable physical
parameter
DIMENSION: what it
measures (for example,
length or mass or a
combination of basic
units)
UNIT: the label given to
the standard; what
measurements are
measured in. Ex KG
standard
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.

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
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Standards
The CIPM (abbreviated from the French Comité international des
poids et mesures) consists of eighteen persons from Member States
of the Metre Convention (Convention du Mètre) of 1875 appointed
by the General Conference on Weights and Measures (CGPM)
whose principal task is to ensure world-wide uniformity in units of
measurement by direct action or by submitting proposals to the
CGPM.
https://en.wikipedia.org/wiki/International_Committee_for_Weights_and_Measures
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Standards
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A standard is physical representation of a unit of physical quantity.
Standards are used for obtaining the values of physical properties of
other equipments by comparison.
International Standards
Maintained by International Bureau of weights and measure
Primary Standards
Maintained by National Laboratories
Secondary Standards
Basic reference maintained in Industrial reference Laboratories
Working Standards
Major 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 units
Angle Radiun rad
Solid Angle Staradian sr
The International System of Units (SI units) is founded on seven SI
base units for seven base quantities assumed to be mutually
independent. In addition two supplementary units are added

Metre (m): Length equal to 1650763.73 wavelength in vacuum of
radiation corresponding to transitions between level 2p10 and
5ds (orange and red line) of the Krypton 86 atom (exited at triple
point of nitrogen at 63.15 0K)
Kilogram (Kg): equal to the mass of the international prototype
of the mass. This prototype is a cylinder of Platinum Iridium alloy.
Second (s): is duration of 9192631770 periods of radiation
corresponding to the transition between two hyperfine levels of
ground state of Cesium 133 atom

Ampere (A) : Constant current, which if maintained between two
paralle conductors of infinite length of negligible cross section
and placed one meter apart in vaccum would produce between
them a force equal to 2 x 10-7 Newton per meter length
Kelvin (K): is 1/273.15 of thermodynamic temperature of triple
point of water
Candela (Cd): Luminous intensity in a perpendicular direction of
a surface of 1/600000 square meter of a black body at the
temperature of freezing platinum under a pressure of 101325
Newton per square meter.

Mole: is amount of substance of a system which contains as
many elementary entities as there are atoms in 0.012 Kg of
Carbon 12.
Supplementary Units
Radian (rad): Plane angle subtended by an arc of a circle equal in
length to the radius of the circle.
Steradian (sr): solid angle subtended at the centre of a sphere by
the surface whose area is equal to the square of radius of the
sphere

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 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

SI Electrical Units
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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 the
triple point of water.
• Absolute zero (0 0K) is lowest possible temperature. Absolute
zero, in Celsius scale, is approximately -273 0C.
• Scientists discovered absolute zero when they figured that as
temperature decreases, the volume of a gas also gets smaller.
They graphed this relationship and found that for each substance
tested, zero volume for each substance would hypothetically
occur around minus 273 0C, the equivalent of absolute zero.
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Other Temperature Scales
• Celsius temperature scale and Fahrenheit temperature scale is
derived SI unit and is generally used to measure everyday
temperature
2/3/2017 20
FromTo 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= 370C

Units Outside the SI
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Certain units are not part of the International System of Units, but
are important and widely used. the units in this category that are
accepted for use with the SI are
Name
Symbol
Value in SI units Name
Symbol
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) rad
unified 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
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• In 1832, German mathematician Carl F. Gauss proposed a system of
three fundamental units as millimetre, milligram and second
• In 1874, British physicists Maxwell extended it with a set of
electromagnetic units and the selection of centimetre, gram and
second and the naming of CGS (Centimetre, Gram, Second) System.
• The sizes of many CGS units turned out to be inconvenient for
practical purposes. For example, everyday objects are hundreds or
of centimetres long, such as humans, rooms and buildings.
• CGS system never gained wide use outside the field of science

Other unit systems FPS
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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 in
technical publications in English until the middle of the 20th
century
• 1 Pound (Lb) = 0.453592 Kg
• 1 Foot = 0.3048 Meter

Dimension
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Every derived unit is recognized by its dimensions which can be
defined as complete algebraic formula for derived unit in terms of
fundamental units using characteristic notion.
Derived
Unit
symbol
Relation
Dimension
Derived Unit
symbol
Relation
Dimension
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
2/3/2017
25

Dimestion and standards, SI Unit system

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