Electric and Electronic Measurements

Lecture-3: Units and Dimensions

Dr. Omar A. Hafez

Electrical Engineering Department

Faculty of Engineering & Islamic Architecture Umm Al-Qura University

oahafez@uqu.edu.sa

Electric and Electronic Measurements

At the end of this Lecture, students should be able to:

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Discuss the fundamental of mechanical units in the SI system and derived units.

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Define the dimensions of various quantities.

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Define and explain the types of measurement errors.

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Explain and apply measurement terms.

Learning Outcomes

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Before standard systems of measurement were invented, many approximate units were used.

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With the development of science and engineering, more accurate units had to be devised.

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It is necessary to establish a single system of units of measurement that would be acceptable internationally because of the increase of world trade and exchange of scientific information.

Introduction

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Units of measurement define the definite magnitude of physical quantity which adopt convention and law.

➢

e.g. Unit for physical quantity length is metre

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The International System of units (SI unit) is a form of metric system and divided in 3 classes:

➢

^{Base units}

➢

Derived units

➢

Supplementary units

Units

In the past, the systems of units most commonly used were the English and metric.

Note that while the English system is based on a single standard, the metric is subdivided into two interrelated standards: the MKS and the CGS.

The MKS and CGS systems draw their names from the units of measurement used with each system; the MKS system uses Meters, Kilograms, and Seconds, while the CGS

system uses Centimeters, Grams, and Seconds.

SYSTEMS OF UNITS

English

Units

• SI stands for System International Units, i.e. the International System of Units. SI is the abbreviation used in all languages to indicate the system.

• The SI is constructed from seven base units, which are defined in physical terms.

• By combining these units in accordance with simple geometrical and physical laws, we can arrive at the derived units.

• In principle, the SI covers all application areas, although certain units outside SI are so useful that they are accepted for general use together with the SI (e.g degree, hour, day, minute).

SI System

▪ Fundamental unit refers to quantity

NAME SYMBOL QUANTITY

Kilogram kg Mass

Second s Time

Meter m Length

Ampere A Electrical current

Kelvin K Temperature

Mole mol Amount of substance

Candela cd Luminous intensity

By combining these units in accordance with simple geometrical and physical laws, we can arrive at the derived units.

Base Units (seven base units)

Derived Units

▪ Derivation/further ext./combination . unit of base unit

Derived quantity Derived unit Symbol

Area Square meter m²

Volume Cubic meter m³

Speed, velocity Meter per second m/s

Acceleration Meter per second square m/s²

Angular velocity Radian per second Rad/s

Angular acceleration Radian per second square Rad/s²

Density Kilogram per cubic meter Kg/m³

Magnetic field intensity, (Linear current density)

Ampere per meter A/m

Derived Units

Derived quantity SI derived unit name

Symbol In SI units

In SI base units

Frequency Hertz Hz 1/s

Force Newton N m·kg/s²

Pressure, stress Pascal Pa N/m² kg/m·s²

Energy, work, heat quantity Joule J N/m m² ·kg/s²

Power, radiant flux Watt W J/s m² ·kg /s³

Electric charge Coulomb C s · A

Electric potential difference Volt V W/A m² ·kg /s³ · A Electric capacitance farad F C/V s⁴ · A²/m² ·kg

Electric resistance ohm V/A m² ·kg/ s³ · A²

Electric conductance Siemens S A/V s³ · A²/m² ·kg

Supplementary Units

▪ Unit outside of SI but accepted

Quantity Unit Symbol Value in SI units

Time Minute, hour, day Min, h, d 1 min = 60 s

1 h = 60 min = 3600s

1 day = 24 h = 1440 min = 86400 s

Plane angle Degree, minute,

second, grad

̊

’

”

gon

1 ̊ = (π/180) rad

1’ = (1/60) ̊ = (π/10 800) rad 1” = (1/60) ’ =(π/648 000) rad 1 gon = (π/200) rad ;

400 gon = 360 ̊

Volume litre l, L 1 l = 1 dm³ = 10^-3 m³

Mass Metric tonne t 1 t = 103 kg

Pressure in air, fluid bar bar 1 bar = 105 Pa

TABLE:

Comparison of the English and metric systems of units.

SI Mechanical Units

▪

Unit of Force: Newton (N)

➢

Force which will give a mass of 1 kg an acceleration of 1 meter per second.

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Work: Joule (J)

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The work done in moving a body is the product of the force and the distance through which the body is moved in the direction of the force.

SI Mechanical Units

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^Energy

➢

The capacity for doing work.

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Energy is measured in the same units as work.

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Power: Watt (W)

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The time rate of work done

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If a certain amount of work W is to be done in a time t, the power required is

SI Electrical Units

▪ Units of Current and Charge

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Current is the quantity of electricity that passes a given point in a conductor during a time of 1 s.

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^Voltage

➢

The potential difference between two points on a conductor carrying a constant current of 1 ampere when the power dissipated between these points is 1 watt.

SI Electrical Units

▪ Resistance and Conductance

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Conductance is the reverse of resistance.

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Unit : Siemens (S)

Prefixes

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Parameter or measurement

used to describe some relevant characteristic of an object.

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Dimensions is describing the size or spatial characteristic of an object: length, width, and height .

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Also for other physical

parameters such as the mass

and electric charge of an object. 3-Dimension of gear system

Dimensions

Dimensions

▪ Uses symbol M (mass), L (length), T (time) – known as mech.

unit, Q (e’ charge), I - or A (current)

▪ A derived unit of physical quantity

▪ Example 1;

- Dimension of physical quantity SPEED is L/T (or in units m/s, km/h, mph)

QUANTITY UNIT DIMENSION

SPEED m/s L/T

Dimensions

▪

Dimension of a physical quantity is the total of all units attached to it.

▪For example, speed is given as distance x time;

meters/second (m/s) MKS and centimeters/second (cm/s) in CGS system.

▪Dimension of measurement of speed ,

▪ [v] = [L]/[T]

Example

Velocity = length/time [v] = [L]/[T] = [LT^-1]

• Acceleration = velocity/time

[a] = [v]/[T] = [LT^-1]/[T¹] = [LT^-2]

• Force = mass × acceleration [F] = [M] • [LT^-2] = [MLT^-2]

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Determine the dimensions of velocity, acceleration and force.

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^Solution:

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Dr. Omar A. Hafez

Class homepage http://uqu.edu.sa/oahafez

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