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ELECTRICAL
FUNDAMENTALS


          TOPIC 1
Fundamental And Derived Units

                                1
Learning Objectives
At the conclusion of this section, students should be
able to:
  Identify the basic units of measurement
  Define and use the SI derived units for force,
    pressure, energy, work, temperature and power
  Convert units to multiple and sub-multiple units
  Transpose a given equation for any variable in the
    equation
  Perform basic calculations of electrical and
    related mechanical quantities given any
    combination of units, multiple units or sub-
    multiple units.



                                                        2
Resources

Hampson & Hanssen, “Electrical Trade Principles – A practical
  approach”
    Pgs 2 – 5, 15 – 25 & 421 including review questions

Chisholm Moodle E Learning




                                                            3
TRANSPOSITION




                4
TRANSPOSITION
addition/subtraction




                       5
TRANSPOSITION
multiply/divide




                  6
TRANSPOSITION –
 multiply/divide




                   7
TRANSPOSITION – mixed
     operations




                        8
TRANSPOSITION – mixed
     operations




                        9
TRANSPOSITION –
 mixed operations




                    10
TRANSPOSITION – roots




                        11
TRANSPOSITION – roots




                        12
Substitution
Take the electrical quantities of: Power (P),
Voltage (V), Current (I) and Resistance (R). There
are two equations that use these quantities, they
are:
 P = V x I and V = I x R
Suppose we want to calculate power when only
current (I) and resistance (R) is known.
Substitution will enable power to be calculated.


                                                 13
Substitution

                V       IR
Substituting IR for V in the power equation,


              P      I R I
                        2
                     I R
                                               14
Base Units
            • The Systeme Internationale’ (SI) is the
                   International Metric System

            There are 6 Base Units in the SI system
                Unit       Symbol                Quantity   Symbol
               Length        l                    Metre       m
                Time         s                   Second       s
                Mass         m                   Kilogram     kg
               Current       I                   Ampere       A
             Temperature     T                    Kelvin      K
                Light        I                   candela      cd

2/17/2012                           Revision02                       15
SI Derived Units
    The six basic units are not sufficient to
        act for all situations that arise in
                   measurement.

    Derived units are used for all non-basic
                   situations.

     Most derived units use the three basic
       units of length, mass and time in
             various combinations.
.
2/17/2012             Revision02              16
SI Derived Units

            The units used can be subdivided
                   into three groups:

      mechanical, electrical and magnetic

       although it must be realised there
      are many more examples than those
                     listed


2/17/2012                 Revision02           17
Derived Quantities
 Velocity (distance traveled in a given time)
 Acceleration (the rate of change in velocity)
 Force (the physical action capable of moving a body)
 Torque (twisting force eg produced by a motor)
 Pressure (force per unit area)
 Electrical charge (1 Amp flowing for 1 second)
 Voltage (electrical pressure)
 Resistance (opposition to current flow)
 Energy (the capacity to do work)
 Work (force acting through a distance)
 Power (rate of doing work)

                                                         18
Derived Mechanical Units

                Unit        Symbol                Quantity   Symbol

                Force         F                   Newton       N

              Pressure        P                    Pascal      Pa

            Energy & Work     W                    Joule       J




2/17/2012                            Revision02                       19
Derived Electrical Units

               Unit       Symbol             Quantity   Symbol

              Power         P                  watt       W

            Frequency       F                 hertz       Hz

             Potential      V                  volt       V

              Charge        Q                coulomb      C

            Capacitance     C                 farad       F




2/17/2012                       Revision02                       20
Multiples And Submultiples
         In practical cases some SI values are
       inconveniently large or small, In order to
     choose values that are convenient to handle,
           multiples or submultiples are used.

    For example, if the resistance of an electrical
    installation is measured at 15 000 000 ohms,
     it is more convenient to refer to this value as
                     15 megohms.

2/17/2012               Revision02                 21
Multiples and Submultiples
                 Tera    1012    T

                 giga    109     G

                mega     106     M

                 kilo    103     k

                 milli   10-3    m

                micro    10-6

                 nano    10-9    n

                 pico    10-12   p




2/17/2012                                22
2/17/2012   Revision02   23
Scientific Notation
• Another method of overcoming cumbersome
  rows of figures is to notate numbers to a
  value between 1 and 10 multiplied by 10 to
  some power.
• For example, 6 800 000 can be expressed as
                      •
                 6.8 x 106 and
             • 1250 as 1.25 x 103
2/17/2012            Revision02                24
Examples:
                    • Given: 1.015 x 10 -8

             – Answer: 0.00000001015 (8 places to left)

            – Negative exponent move decimal to the left

                      – Given: 5.024 x 10 -3

               – Answer: 5,024 (3 places to the right)

            – Positive exponent move decimal to the right

2/17/2012                     Revision02                    25
Examples
• Express in standard form

                     • 1.09 x 10 3

                    • 4.22715 x 10 8

                    • 3.078 x 10 – 4

                    • 9.004 x 10 – 2

                    • 5.1874 x 10 2
2/17/2012                    Revision02   26
To change from scientific notation
        to standard form:

  • Move decimal point to right for positive
              exponent of 10

   • Move decimal point to left for negative
               exponent of 10


2/17/2012            Revision02                27
Express in correct scientific
                     notation

                    0.0000568
                       321
                    64 960 000
                     0.07085
                      61 500
2/17/2012               Revision02          28
PREFIXES




           29
PREFIXES




           30
Abbreviations and Conventions
(shortened names for things)      (agreed standard ways to do or
                                  write things)
1. There should be a space between the
   numeric value and the unit symbol.
     For example five milliamps is written as
            5 mA and not 5mA
(A ‘hard’ space in a typed document will prevent this; 240
     V i.e. the unit symbol appearing on the next line.)


                                                                   31
Abbreviations and Conventions
2. When writing numbers above 999, they
   should be clustered into groups of three.
   For example,
   1 000 or 20 000 or 0.000 006 78
   and not 1000 or 20000 or 0.00000678
   (This reduces the chance of mis-reading a number’s
   size by mis-counting zero’s)


                                                    32
Abbreviations and Conventions
5. A leading zero should precede a decimal value.
    For example
            0.351 and not .351


    (This makes it easier to recognise a missing decimal
    point, for instance, on a well-used drawing 0 351
    would be obvious but 351 could lead to a major
    error!)


                                                       33

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E104 B Topic 1

  • 1. ELECTRICAL FUNDAMENTALS TOPIC 1 Fundamental And Derived Units 1
  • 2. Learning Objectives At the conclusion of this section, students should be able to:  Identify the basic units of measurement  Define and use the SI derived units for force, pressure, energy, work, temperature and power  Convert units to multiple and sub-multiple units  Transpose a given equation for any variable in the equation  Perform basic calculations of electrical and related mechanical quantities given any combination of units, multiple units or sub- multiple units. 2
  • 3. Resources Hampson & Hanssen, “Electrical Trade Principles – A practical approach” Pgs 2 – 5, 15 – 25 & 421 including review questions Chisholm Moodle E Learning 3
  • 8. TRANSPOSITION – mixed operations 8
  • 9. TRANSPOSITION – mixed operations 9
  • 10. TRANSPOSITION – mixed operations 10
  • 13. Substitution Take the electrical quantities of: Power (P), Voltage (V), Current (I) and Resistance (R). There are two equations that use these quantities, they are: P = V x I and V = I x R Suppose we want to calculate power when only current (I) and resistance (R) is known. Substitution will enable power to be calculated. 13
  • 14. Substitution V IR Substituting IR for V in the power equation, P I R I 2 I R 14
  • 15. Base Units • The Systeme Internationale’ (SI) is the International Metric System There are 6 Base Units in the SI system Unit Symbol Quantity Symbol Length l Metre m Time s Second s Mass m Kilogram kg Current I Ampere A Temperature T Kelvin K Light I candela cd 2/17/2012 Revision02 15
  • 16. SI Derived Units The six basic units are not sufficient to act for all situations that arise in measurement. Derived units are used for all non-basic situations. Most derived units use the three basic units of length, mass and time in various combinations. . 2/17/2012 Revision02 16
  • 17. SI Derived Units The units used can be subdivided into three groups: mechanical, electrical and magnetic although it must be realised there are many more examples than those listed 2/17/2012 Revision02 17
  • 18. Derived Quantities  Velocity (distance traveled in a given time)  Acceleration (the rate of change in velocity)  Force (the physical action capable of moving a body)  Torque (twisting force eg produced by a motor)  Pressure (force per unit area)  Electrical charge (1 Amp flowing for 1 second)  Voltage (electrical pressure)  Resistance (opposition to current flow)  Energy (the capacity to do work)  Work (force acting through a distance)  Power (rate of doing work) 18
  • 19. Derived Mechanical Units Unit Symbol Quantity Symbol Force F Newton N Pressure P Pascal Pa Energy & Work W Joule J 2/17/2012 Revision02 19
  • 20. Derived Electrical Units Unit Symbol Quantity Symbol Power P watt W Frequency F hertz Hz Potential V volt V Charge Q coulomb C Capacitance C farad F 2/17/2012 Revision02 20
  • 21. Multiples And Submultiples In practical cases some SI values are inconveniently large or small, In order to choose values that are convenient to handle, multiples or submultiples are used. For example, if the resistance of an electrical installation is measured at 15 000 000 ohms, it is more convenient to refer to this value as 15 megohms. 2/17/2012 Revision02 21
  • 22. Multiples and Submultiples Tera 1012 T giga 109 G mega 106 M kilo 103 k milli 10-3 m micro 10-6 nano 10-9 n pico 10-12 p 2/17/2012 22
  • 23. 2/17/2012 Revision02 23
  • 24. Scientific Notation • Another method of overcoming cumbersome rows of figures is to notate numbers to a value between 1 and 10 multiplied by 10 to some power. • For example, 6 800 000 can be expressed as • 6.8 x 106 and • 1250 as 1.25 x 103 2/17/2012 Revision02 24
  • 25. Examples: • Given: 1.015 x 10 -8 – Answer: 0.00000001015 (8 places to left) – Negative exponent move decimal to the left – Given: 5.024 x 10 -3 – Answer: 5,024 (3 places to the right) – Positive exponent move decimal to the right 2/17/2012 Revision02 25
  • 26. Examples • Express in standard form • 1.09 x 10 3 • 4.22715 x 10 8 • 3.078 x 10 – 4 • 9.004 x 10 – 2 • 5.1874 x 10 2 2/17/2012 Revision02 26
  • 27. To change from scientific notation to standard form: • Move decimal point to right for positive exponent of 10 • Move decimal point to left for negative exponent of 10 2/17/2012 Revision02 27
  • 28. Express in correct scientific notation 0.0000568 321 64 960 000 0.07085 61 500 2/17/2012 Revision02 28
  • 29. PREFIXES 29
  • 30. PREFIXES 30
  • 31. Abbreviations and Conventions (shortened names for things) (agreed standard ways to do or write things) 1. There should be a space between the numeric value and the unit symbol. For example five milliamps is written as 5 mA and not 5mA (A ‘hard’ space in a typed document will prevent this; 240 V i.e. the unit symbol appearing on the next line.) 31
  • 32. Abbreviations and Conventions 2. When writing numbers above 999, they should be clustered into groups of three. For example, 1 000 or 20 000 or 0.000 006 78 and not 1000 or 20000 or 0.00000678 (This reduces the chance of mis-reading a number’s size by mis-counting zero’s) 32
  • 33. Abbreviations and Conventions 5. A leading zero should precede a decimal value. For example 0.351 and not .351 (This makes it easier to recognise a missing decimal point, for instance, on a well-used drawing 0 351 would be obvious but 351 could lead to a major error!) 33