EET-117 LAB 1 F21 Aaron Brillantes

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Centennial College ELECTRICAL ENGINEERING TECHNICIAN & TECHNOLOGY Course: EET-117 Name Aaron Brillantes Student Number 301074732 Date Sept 10, 2023 Lab #1 Metric Prefixes, Scientific Notation, and Graphing Based on Experiments in Basic Circuits by David Buchla OBJECTIVES: 1. Convert standard form numbers to scientific and engineering notation, use metric prefixes. 2. Use proper graphing techniques to plot experimental data. SUMMARY OF THEORY: Persons working in the electrical field need to be able to make concise statements about measured quantities. The basic electrical quantities encompass a very large range of numbers- from the very large to the very small. For example, the frequency of an FM radio station can be over 100 million hertz (Hz) and a capacitor can have a value of 10 billionths of a farad (F). To express very large and very small numbers, scientific (powers of 10) notation and metric prefixes are used. Metric prefixes are based on the decimal system and stand for powers of 10. They are widely used to indicate a multiple or sub-multiple of a measurement unit. Scientific notation is a means of writing any quantity as a number between 1 and 10 times a power of 10. The power of 10 is called the exponent. It simply shows how many places the decimal point must be shifted to express the number in its standard form. If the exponent is positive, the decimal point must be shifted to the right to write the number in standard form. If the exponent is negative, the decimal point must be shifted to the left. Note that 10° = 1, so multiplying by a power of 10 with an exponent of zero does not change the original number. Exponents that are a multiple of 3 are much more widely used in electrical and electronics work than exponents that are not multiples of 3. Numbers expressed with an exponent that is a multiple of 3 are said to be expressed in engineering notation. Engineering notation is particularly useful in the electrical field because of its relationship to the most widely used metric prefixes. Some examples of numbers written in standard form, scientific notation, and engineering notation are shown below (Table 1). Table 1 1

Numbers expressed in engineering notation can be simplified by using metric prefixes to indicate the appropriate power of 10. In addition, prefixes can simplify calculations. You can perform arithmetic operations on the significant figures of a problem and determine the answer's prefix from those used in the problem. For example, 4.7 kΩ + 1.5 kΩ = 6.2 kΩ. The common metric prefixes used in electricity and their abbreviations are shown in Table 2. The metric prefixes representing engineering notation are shown. Table 2 Any n u mber can be converted from one prefi x to ano th er (or no prefix) u s ing the table . Write th e num b er to be converted on the line with the decimal u n d er t h e metric prefix that appear s with the n um b er . The decimal point i s then moved directly under any other line , and the me t ric prefix immediate l y above the li n e i s used . The number can also be r ead in engineer i ng nota t ion by u s ing the power of 10 s hown immediate l y abo v e the line. Example 1: Example 2: 2

SIGNI F ICANT DIGITS: When a measurement contains approximate data, those digits known to be correct are called significant digits . Zeros that are used only for locating the decimal place are not significant, but those that are part of mea s ured quantity are significant . When reporting a measured value, the least significant uncertain digits m ay be retained, but all other uncertain digits should b e discarded. It is not correct to show either too many o r too few digits. For example, it is not valid to retain more than three digits when using a met e r that has a three-digit resolution, nor is it proper to discard valid digits, even if they are zeros. For example, if you s et a power supply to the nearest hundredth of a volt, then the recorded voltage should be reported to the h undredth place (3 . 00 V is correct, but 3 V is incorrect). For laboratory work in this course, you should normally be able to measure and retain three significant digits. To find the number of significant digits in a given number, ignore the decimal point and count the number of digits from left to right , st a rting with the first nonzero digit and ending with the last digit to the right. A ll digits counted are significant except zeros at the right end of the number . A zero on the right end of a n umber is significant only if it is to the right of the decimal point; otherwise, it is uncertain. For example, 43 . 00 contains four significant digits. The whole number 4300 may contain two, three, or four significant digits . In the absence of other information, the significance of the right-hand zeros is uncertain, and t hese digit s cannot be assumed to be significant . To avoid confusion, numbers such as these should be reported using scientific notation. For e x ample , the number 2.60 X 10 3 contains three significant figures and t he number 2 . 600 X 10 3 contains four significant figures. Rules for determining if a reported digit is significant are as follows: 1. Nonzero digits are always considered to be significant . 2. Zeros to the left of the first nonzero digit are never significant . 3. Zeros between nonzero digits are always significant . 4. When digits are shown to the right of the decimal point, zeros to the right of the digits are significant . 5. Zeros at the right end of a whole number are uncertain. Whole numbers should be reported in scientific or engineering notation to clarify the significant figures. The rule for multiplication and division: The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer. Example: A= LxW = (3.2 m)(2.8 m) = 8.96 m 2 ={original values had 2 sig. digits}=> 9.0 m 2 Videos: 1. Significant digits https://www.khanacademy.org/math/arithmetic-home/arith-review-decimals/arithmetic- significant-figures-tutorial/v/significant-figures 2. Multiplying and dividing with significant digits https://www.khanacademy.org/math/arithmetic-home/arith-review-decimals/arithmetic- significant-figures-tutorial/v/multiplying-and-dividing-with-significant-figures 3

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G RAPHS: A gr aph is a visual tool that can quickly convey to the reader the relationship between variables. The eye can discern trends in magnitude or slope more easily on a graph than from tabular data . Graphs are widely used i n experimental work to present information because they enable the reader to discern variations in magnitude, slope, and direction between two quantities. In experimental work, you will graph data on many occasions. The following steps will guide you in preparing a graph : 3. Determine the type of scale that will be used. A linear scale is the most frequently used and will be discussed here. Choose a scale factor that enables all of the data to be plotted on the graph without being cramped. The most common scales are multiples of 1, 2 , 5, or 10 units per division . 4. Number the major divisions along each axis. Do not number each small division as it will make the graph appear cluttered. Each division must have equal weight . 5. Label each axis to indicate the quantity being measured and the measurement units. Usually, the measurement units are given in parentheses. 6. Plot the data points with a small dot with a small circle around each point . If additional sets of data are plotted, use other distinctive symbols (such as triangles) to identify each set . 7. Draw a smooth line that represents the data trend. It is normal practice to consider data points but to ignore minor variations due to experimental errors . 8. Title the graph , indicating with the title what the graph represents. The completed graph should be self-explanatory. Figure 1 shows an example of a set of data taken in an experiment where frequency is measured as a function of capacitance. The data is plotted in accordance to the rules given previously. Notice that not every data point lies on the smooth curve drawn to represent the "best - fit" of the data . Also, the scale factors are selected to fit all of the data points onto the graph, and the labels are given to both axes with proper measurement units. Fig. 1 4

Example of how to make a graph (Fig. 1) in Microsoft (MS) Excel: 1. Enter your data into Excel converting to the same prefixes if necessary (e.g. kHz -> MHz): 2. Highlight your data and choose one of the graphs options to make: 3. 'Insert' your desired graph in “Charts” option: a) b) 0 100 200 300 400 500 600 0 0.5 1 1.5 2 2.5 4. Adjust your data's layout and design: 5. Add, change the size of your chart's legend and axis labels: 0 100 200 300 400 500 600 0 0.5 1 1.5 2 2.5 Frequency as a function of Capacitance Capacitance (pF) Frequency (MHz) 6. As stated earlier, you may want to show the data trend (to ignore minor variations due to experimental errors) using the trend option: Note: Please refer to the short video in the Lab 1 folder for your reference: “Video of Graph's example in MS Excel.mp4” 5

PROCEDURE: 1. Rewrite the numbers in Table 3 in scientific notation, engineering notation, and using one of the engineering metric prefixes. The first line has been completed as an example . Table 3 Number Scientific Notation Engineering Notation Metric Value MARKS (3 per line) 0.0829 V 8.29 x 10 -2 V 82.9 x 10 -3 V 82.9 mV - 0.000 020 H 2.0 x 10 -5 H 20 x 10 -6 H 20 µH 45,000 Hz 4.5 x 10 4 Hz 45 x 10 3 Hz 45 kHz 350 000 Ω 3.5 x 10 5 Ω 350 x 10 3 Ω 350 kΩ 5,400,000 Ω 5.4 x 10 6 Ω 5.4 x 10 6 Ω 5.4 MΩ 0.000 000 47 F 4.7 x 10 -7 F 470 x 10 -9 F 470 nF 0.000 033 A 3.3 x 10 -5 A 33 x 10 -6 A 33 µA 8,500 W 8.5 x 10 3 W 8.5 x 10 3 W 8.5 kW Subtotal: / 21 2. Convert the metric values listed in Table 4 into engineering notation. The first line has been completed as an example. Table 4 Metric Value Engineering Notation MARK 100 pF 100 x 10 -12 F - 5.0 MΩ 5.0 x 10 6 Ω 30 mV 30 x 10-3 V 6.2 ns 6.2 x 10 -9 s 2.4 GHz 2.4 x 10 9 Hz 56 kΩ 56 x 10 3 Ω 335 mA 355 x 10 -3 A 500 kW 500 x 10 3 W Subtotal: / 7 3. Using the rules given in the Summary of Theory for significant digits, determine the number of significant digits for each number listed in Table 5. Underline the significant digits and cite the pertinent rule number(s) from the rules given in the Summary of Theory. The first three are completed as examples. Table 5 Number Rule Number(s) MARKS (2 per line) 1.472 1 - 4.09 x 10 6 1,3 - 0.00 150 1,2,4 - 0.0842 1,2 7.00 1,4 0.05 1,2 75.82 1 56 x 10 3 1 6

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Subtotal: /10 7

4. This step is to provide you with practice in graphing and in presenting data. Table 6 lists inductance data for 16 different coils wound on identical iron cores. There are three variables in this problem: the length of the coil (I) given in centimeters (cm), the number of turns , N, and the inductance, L, given in millihenrys (mH). Since there are three variables, we will hold one constant and plot the data using the remaining two variables . This procedure shows how one variable relates to the other. Start by plotting the inductance for coils that have 400 turns (last column) as a function of the length (first column). Inductance should be on the Y axis and length on the X axis in appropriate units. Table 6 5. On the same plot, graph the data for the 400 turn coil, then 300 turn, 200 turn and 100 turn coils. Use a different symbol for each set of data. The resulting graph is a family of curves that 8

gives a quick visual indication of the relationship among the three variables. Tip: you can use MS Excel to create a graph from a table as was shown previously. Marks: / 20 9

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REVIEW QUESTIONS 1. For each metric prefi x and unit shown , write the abbreviation of the metric prefix with the unit symbol . N Unit with metric prefix Abbreviation Mark 0 kilowatt kW - 1 milliampere mA 2 picofarad pF 3 nanosecond ns 4 megohm MΩ 5 microhenry µH Subtotal: /5 2. Write the metric prefix and unit name for each of the abbreviations shown. N Abbreviation Unit with metric prefix Mark 0 MW megawatt - 1 nA nanoampere 2 µJ microjoule 3 ms millisecond 4 kΩ kiloohm 5 GHz gigahertz Subtotal: /5 3. Using your calculator, perfo r m the following multiplications . Express your answer in scientific notation. Apply the rule for multiplication and division with significant digits. N Multiplications Answer in scientific notations Mark (2 per line) 0 (1.0 X 10 2 )(8.8 X 10 -4 ) 8.8 x 10 -2 - 1 (3.6 X 10 4 ) ( 8.8 X 10 - 4 ) 3.2 x 10 1 2 ( - 4 . 0 X 10 - 6 ) (1 . 7 X 10 - 1 ) -6.8 x 10 -7 3 ( - 7.5 X 10 2 )(-2 . 5 X 10 - 5 ) 1.9 x 10 -2 4 (56 X 10 3 )(9.0 X 10 -7 ) 5.0 x 10 -2 Subtotal: /8 4. Using your calculator, perform the following divisions. Express your answer in engineering notation and answer with a metric prefix. Apply the rule for multiplication and division with significant digits. N Divisions Answer in engineering notations Answer with the metric prefix Mark (3 per line) 0 (8.8 X 10 -4 ) ÷ (1.0 X 10 2 ) 8.8 x 10 -6 8.8 µ - 1 (4 . 4 X 10 9 ) ÷ ( - 7 . 0 X 10³) -630 x 10 3 -630 k 2 (3.1 X 10 2 ) ÷ (31 X 10 - 6 ) 1 x 10 6 1 M

3 ( - 2.0 X 10 4 ) ÷ ( - 6.5 X 10 -6 ) 3.1 x 10 -9 3.1 G 4 (0 . 0033 X 10 -3 ) ÷ ( - 15 X 10 -2 ) 22 x 10 -6 22 µ Subtotal: /12 5. Metric prefixes are useful for solving problems without having to key in the exponent in your calculator. For example, when a milli prefix (10 -3 ) is multiplied by a kilo prefix (10 + 3 ), the metric prefixes cancel, and the result has only the unit of measure. As you become proficient with these prefixes, math operations can be simplified and fewer keystrokes are required in solving the problem with a calculator. To practice this, determine the metric prefix for the answer when the operation indicated in Table 7 is performed. The first line is shown as an example. Table 7 N Metric Unit in Operand Mathematical Operation Metric Unit in Operand Metric Unit in Result Mark 0 milli multiplied by milli micro - 1 kilo multiplied by micro milli 2 nano multiplied by kilo micro 3 milli multiplied by kilo 10 0 4 micro divided by nano kilo 5 micro divided by pico mega 6 pico divided by pico 10 0 7 milli divided by mega nano Subtotal: /7 Conclusions. The conclusion summarizes the important points of the laboratory work. You must analyze the examples to add emphasis to significant points. You must also include the features/benefits of each of the examples . Example 1 and 2 both give useful representations of metric prefixes allowing me to understand prefixes and abbreviations more. The example given for creating graphs allowed me to learn more about excel and how to apply data to create and edit graphs. This lab helped me memorize the rules of significant digits. I'm able to solve engineering and scientific notations faster through constant repetition.

Marks: /20

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Rubric-Grading. Criteria Marks Punctuality /10 Procedure /58 Review Questions /37 Conclusion /20 Neatness, Spelling, Grammar, and Sentence Structure /10 Total: /135

EET-117 LAB 1 F21 Aaron Brillantes

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