Lesson 2: System of Measurement and Calculation

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Overview

This lesson covers the knowledge, skills, and proper attitude in self-checking and correcting numerical computations’ accuracy; obtaining accurate measurements; identifying and converting systems of measurements; and measuring work pieces according to job requirements.

Learning Objectives

At the end of this lesson, you should be able to:

Cognitive Domain

Identify and convert systems of measurement according to job requirement.
Identify the theory of Ohm’s Law

Affective Domain

Practice proper and accurate measurements according to job requirements.
Practice solving for resistance, voltage and current.

Psychomotor Domain

Measure work pieces according to job requirements.
Perform solving using ohm’s law and conduct test.

Watch the following videos and accomplish learning activities given!

Now, it’s time for you to apply what have you’ve learned!

Learning Activity 1

Instruction: Answer the following questions that are given on the document provided and submit your answer through Google Drive Link below.

The File Name of your output shall always be in this suggested format:

SurnameFNMI_LearningActivityNo.

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Learning Activity 1

Module 3 Lesson 2 Activity Sheet.pdf

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Learning Activity 2

Click here: https://forms.gle/nRJq23Fs7o5K6srXA

It’s time to further concrete your knowledge! Read and analyze the content discussion, and try to answer the activity based on your previous knowledge and current learning.

System of Measurement

The two (2) systems of measurements are: the English and the Metric System. The English system originated in England also known as the U.S. customary system of measurement while the Metric System was developed in France and also known as the S. I. (International Standard).

Common units of measurement used in making layout and installation of electrical materials:

A. Linear Measurement

English system provides the creative way on how people can measure by themselves. For example, people measure shorter distance on the ground with their feet. They measure long distances by their palms which is equal to a yard.

Inch
Yard
Miles

Metric system is a decimalized system of measurement. It exists in several variations with different choices of base units. Metric units are widely used around the world for personal, commercial and scientific purpose.

Millimeter
Centimeter
Decimeter
Meter

B. English units and each equivalent

12 inches = foot(ft)
1 foot = 3yard (yd)
1 yard = 36 inches

C. Metric units and each equivalent

10millimeter (mm) = 1centimeter (cm)
10centimeter = 1decimeter (dm)
10 decimeter = 1meter

D. English to metric equivalent

1 inch = 2.54 cm
1 foot = 30.48 cm
1 yard = 91.44 cm

E. The centimeter graduation

How to read the cm graduation:

1. First graduation is .5 mm

2. Second graduation is 1mm

3. Third graduation is 1.5mm

4. Fourth graduation is 2mm

F. The inch graduation

How to read the inch graduation:

1. First graduation is 1/16

2. Second graduation is 18

3. Third graduation is 3/16

4. Fourth graduation is 1/4 then follows the given scale above.

Reading of Measurement

I. Reading the inch

The inch is divided into segments called graduations. Each graduation represents a measurement in form of a proper fraction. The inch can be divided into 16, 8, 4 and 2, equal parts.

Note: The illustration is not the actual length of an inch.

II. Reading the centimeter and millimeter

CONVERTING FRACTION TO DECIMAL

In converting fractions to decimals, divide the numerator by its denominator whether it is proper, improper or mixed fraction.

CONVERTING UNITS OF MEASURE

Sample Solutions in Conversion

I. Foot to inches

3 ft = _________ inches (Solution: Multiply 3ft by 12 inches / ft = 36 inches)

II. Inch to feet

48 inches = ________ Feet (Solution: Divide 48 inches by 12 inches / feet = 4feet)

III. Centimeter to millimeter

22 cm = ________ millimeters (Solution: Multiply 22 cm by 10 mm / cm = 220mm)

IV. Inch to centimeter

6 inches = _______ centimeter (Solution: Multiply 6 inches by 2.54 cm / inch = 15.24 cm)

Electric Unit of Measure

Electrical Units of Measurement are used to express standard electrical units along with their prefixes when the units are too small or too large to express as a base unit

The standard units of electrical measurement used for the expression of voltage, current and resistance are the Volt [ V ], Ampere [ A ] and Ohm [ Ω ] respectively.

These electrical units of measurement are based on the International (metric) System, also known as the SI System with other commonly used electrical units being derived from SI base units.

Sometimes in electrical or electronic circuits and systems it is necessary to use multiples or sub-multiples (fractions) of these standard electrical measuring units when the quantities being measured are very large or very small.

The following table gives a list of some of the standard electrical units of measure used in electrical formulas and component values.

Standard Electrical Units of Measure

Multiples and Sub-multiple

There is a huge range of values encountered in electrical and electronic engineering between a maximum value and a minimum value of a standard electrical unit. For example, resistance can be lower than 0.01Ω or higher than 1,000,000Ω. By using multiples and submultiple’s of the standard unit we can avoid having to write too many zero’s to define the position of the decimal point. The table below gives their names and abbreviations.

So to display the units or multiples of units for Resistance, Current or Voltage we would use as an example:

- - - - 1kV = 1 kilo-volt – which is equal to 1,000 Volts.
      - 1mA = 1 milli-amp – which is equal to one thousandths (1/1000) of an Ampere.
      - 47kΩ = 47 kilo-ohms – which is equal to 47 thousand Ohms.
      - 100uF = 100 micro-farads– which is equal to 100 millionths (100/1,000,000) of a Farad.
      - 1kW = 1 kilo-watt – which is equal to 1,000 Watts.
      - 1MHz = 1 mega-hertz –which is equal to one million Hertz.

To convert from one prefix to another it is necessary to either multiply or divide by the difference between the two values. For example, convert 1MHz into kHz.

Well we know from above that 1MHz is equal to one million (1,000,000) hertz and that 1kHz is equal to one thousand (1,000) hertz, so one 1MHz is one thousand times bigger than 1kHz. Then to convert Mega-hertz into Kilo-hertz we need to multiply mega-hertz by one thousand, as 1MHz is equal to 1000 kHz.

Ohm's Law

Ohm’s law states the relationship between electric current and potential difference. The current that flows through most conductors is directly proportional to the voltage applied to it. Georg Simon Ohm, a German physicist was the first to verify Ohm’s law experimentally.

Ohm’s Law Explanation

One of the most basic and important laws of electric circuits is Ohm’s law.

Ohm’s law states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperature remain constant.

Mathematically, this current-voltage relationship can be written as,

In the equation, the constant of proportionality, R is Resistance and has units of ohms, with symbol Ω.

The same formula can be rewritten in order to calculate the current and resistance respectively as follows:

Ohm’s law only holds true if the provided temperature and the other physical factors remain constant. In certain components, increasing the current raises the temperature. An example of this is the filament of a light bulb, in which the temperature rises as the current is increased. In this case, Ohm’s law cannot be applied. The lightbulb filament violates Ohm’s Law.

Ohm’s Law Statement: Ohm’s law states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperature, remain constant.

Ohm’s Law Equation: V = IR, where V is the voltage across the conductor, I is the current flowing through the conductor and R is the resistance provided by the conductor to the flow of current.

Relationship between Voltage, Current and Resistance

Analyzing row 1,2 and 3, we come to understand that doubling and tripling the voltage leads to doubling and a tripling of the current in the circuit. Likewise, when we compare rows 1 and 4 and rows 2 and 5, we come to understand that doubling the total resistance serves to halve the current in the circuit.

Water Pipe Analogy for Ohm’s Law

Ohm’s Law describes the current flow through a resistance when different electric potentials (voltage) are applied at each end of the resistance. Since we can’t see electrons, the water-pipe analogy helps us understand the electric circuits better. Water flowing through pipes is a good mechanical system that is analogous to an electrical circuit.

Here, the voltage is analogous to water pressure, the current is the amount of water flowing through the pipe, and the resistance is the size of the pipe. More water will flow through the pipe (current) when more pressure is applied (voltage) and the bigger the pipe, (lower the resistance).

Experimental Verification of Ohm’s Law

Ohm’s Law can be easily verified by the following experiment:

Apparatus Required:

Resistor *Ammeter *Voltmeter
Battery *Plug Key *Rheostat

Circuit Diagram:

Procedure:

Initially, the key K is closed and the rheostat is adjusted to get the minimum reading in Ammeter A and voltmeter.
The current in the circuit is increased gradually by moving the sliding terminal of the rheostat. During the process, the current flowing in the circuit and the corresponding value of potential difference across the resistance wire R is recorded.
This way different set of values of voltage and current are obtained.
For each set of values of V and I, the ratio of V/I is calculated.
When you calculate the ratio V/I for each case, you will come to notice that it is almost the same. So V/I = R, which is a constant.
Plot a graph of the current against the potential difference, it will be a straight line. This shows that the current is proportional to the potential difference.

Ohm’s Law Magic Triangle

You can make use of the Ohm’s law magic triangle to remember the different equations for Ohm’s law used to solve for different variables(V, I, R).

Circuit Diagram:

If the value of voltage is asked and the values of the current and resistance are given, then to calculate voltage simply cover V at the top. So, we are left with the I and R or I X R. So, the equation for Voltage is Current multiplied by Resistance. Examples of how the magic triangle is employed to determine the voltage using Ohm’s law is given below.

Ohm’s Law Solved Problems

Example 1: If the resistance of an electric iron is 50 Ω and a current of 3.2 A flows through the resistance. Find the voltage between two points.

Solution:

If we are asked to calculate the value of voltage with the value of current and resistance given to us, then cover V in the triangle. Now, we are left with I and R or more precisely I × R.

Therefore, we use the following formula to calculate the value of V:

V = I × R

Substituting the values in the equation, we get

V = 3.2 A × 50 ÷ = 160 V

V = 160 V

Example 2: An EMF source of 8.0 V is connected to a purely resistive electrical appliance (a light bulb). An electric current of 2.0 A flows through it. Consider the conducting wires to be resistance-free. Calculate the resistance offered by the electrical appliance.

Solution:

When we are asked to find out the value of resistance when the values of voltage and current are given, then we cover R in the triangle. This leaves us with only V and I, more precisely V ÷ I.

Substituting the values in the equation, we get

R = V ÷ I

R = 8 V ÷ 2 A = 4 Ω

R = 4 Ω

Calculating Electrical Power Using Ohm’s Law

The rate at which energy is converted from the electrical energy of the moving charges to some other form of energy like mechanical energy, heat, magnetic fields or energy stored in electric fields, is known as electric power. The unit of power is the watt. The electrical power can be calculated using the Ohm’s law and by substituting the values of voltage, current and resistance.

Formula to find power

When the values for voltage and current are given,

When the values for voltage and resistance are given,

When the values for current and resistance are given,

What is a Power Triangle?

The power triangle can be employed to determine the value of electric power, voltage and current when the values of the other two parameters are given to us. In the power triangle, the power (P) is on the top and current(I) and voltage (V) are at the bottom.

When the values of current and voltage are given, the formula for finding power is,

When the values of power and voltage is given, the formula for finding current is,

When the values of power and current is given, the formula for finding voltage is,

Ohm’s Law Pie Chart

To better understand the relationship between various parameters, we can take all the equations used to find the voltage, current, resistance and power, and condense them into a simple Ohm’s Law pie chart as shown below.

Ohm’s Law Matrix Table

Like Ohm’s Law Pie Chart shown above, we can condense the individual Ohm’s Law equations into a simple matrix table as shown below for easy reference when calculating an unknown value.

Ohm’s Law Applications

The main applications of Ohm’s law are:

To determine the voltage, resistance or current of an electric circuit.
Ohm’s law is used to maintain the desired voltage drop across the electronic components.
Ohm’s law is also used in DC ammeter and other DC shunts to divert the current.

Limitations of Ohm’s Law

Following are the limitations of Ohm’s law:

Ohm’s law is not applicable for unilateral electrical elements like diodes and transistors as they allow the current to flow through in one direction only.
For non-linear electrical elements with parameters like capacitance, resistance etc the voltage and current won’t be constant with respect to time making it difficult to use Ohm’s law.