For Day 2 Homework Cover Sheet Name:_________________________________________________ 1. Read Pages from 19-33, or watch the videos listed below.  Decimal Number System http://www.youtube.com/watch?v=ntpehqS5ejA (12 min)  Natural through Complex Numbers http://www.youtube.com/watch?v=MH946PzUGIg (13 min) 2. Attempt problems on workbook pages 3-6 Summary of the lectures you watched. List any parts of the video lecture (if there are any) that were unclear or you had trouble understanding. Please be specific and do not just say “All of it”. Questions you had difficulty with or felt stuck on- ALEKS topic number from this sheet that you were stuck on- ALEKS topics to be mastered (13 topics) Converting a decimal to a fraction: Basic Expanded form Expanded form with zeros Multiplication by 10, 100, and 1000 Numeral translation: Problem type 1 Numeral translation: Problem type 2 Whole number place value: Problem type 1 Whole number place value: Problem type 2 Writing a decimal and a fraction for a shaded region Writing a signed number for a real-world situation Writing ratios for real-world situations Decimal place value: Hundreds to ten thousandths Decimal place value: Tenths and hundredths

For Day 2 Homework Cover Sheet Name:_________________________________________________ 1. Read Pages from 19-33, or watch the videos listed below.  Decimal Number System http://www.youtube.com/watch?v=ntpehqS5ejA (12 min)  Natural through Complex Numbers http://www.youtube.com/watch?v=MH946PzUGIg (13 min) 2. Attempt problems on workbook pages 3-6 Summary of the lectures you watched. List any parts of the video lecture (if there are any) that were unclear or you had trouble understanding. Please be specific and do not just say “All of it”. Questions you had difficulty with or felt stuck on- ALEKS topic number from this sheet that you were stuck on- ALEKS topics to be mastered (13 topics) Converting a decimal to a fraction: Basic Expanded form Expanded form with zeros Multiplication by 10, 100, and 1000 Numeral translation: Problem type 1 Numeral translation: Problem type 2 Whole number place value: Problem type 1 Whole number place value: Problem type 2 Writing a decimal and a fraction for a shaded region Writing a signed number for a real-world situation Writing ratios for real-world situations Decimal place value: Hundreds to ten thousandths Decimal place value: Tenths and hundredths

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ELEC153 Circuit Theory II M2A3 Lab: AC Series Circuits Introduction Previously you worked with two simple AC series circuits, R-C and R-L circuits. We continue that work in this experiment. Procedure 1. Setup the following circuit in MultiSim.The voltage source is 10 volts peak at 1000 Hz. Figure 1: Circuit for analysis using MultiSim 2. Change R1 to 1 k and C1 to 0.1 uF. Connect the oscilloscope to measure both the source voltage and the voltage across the resistor.You should have the following arrangement. Figure 2: Circuit of figure 1 connected to oscilloscope To color the wires, right click the desired wire and select “Color Segment…” and follow the instructions. Start the simulation and open the oscilloscope. You should get the following plot: Figure 3: Source voltage (red) and the voltage (blue) across the resistor The red signal is the voltage of the source and the blue is the voltage across the resistor. The colors correspond to the colors of the wires from the oscilloscope. 3. From the resulting analysis plotdetermine the peak current. To determine the peak current measure the peak voltage across the resistor and divide by the value of the resistor (1000 Ohms). Record it here. Measured Peak Current 4. Determine the peak current by calculation. Record it here. Does it match the measured peak current? Explain. Calculated Peak Current 5 Determine the phase shift between the current in the circuit and the source voltage. We look at the time between zero crossings to determine the phase shift between two waveforms. In our plot, the blue waveform (representing the circuit current or the voltage across the resistor) crosses zero before the red waveform (the circuit voltage). So, current is leading voltage in this circuit. This is exactly what should happen when we have a capacitive circuit. 6. To determine the phase shift, we first have to measure the time between zero crossings on the red and blue waveforms. This is done by moving the oscillator probes to the two zero crossing as is shown in the following figure Figure 4: Determining the phase shift between the two voltage waveforms We can see from the figure that the zero crossing difference (T2 – T1) is approximately 134 us. The ratio of the zero-crossing time difference to the period of the waveform determines the phase shift, as follows: Using our time values, we have: How do we know if this phase shift is correct? In step 4 when you did your manual calculations to find the peak current, you had to find the total impedance of the circuit, which was: Now, the current will be: Here, the positive angle on the current indicates it is leading the circuit voltage. 7. Change the frequency of the voltage source to 5000 Hz. Estimulate and perform a Transient Analysis to find the new circuit current and phase angle. Measure them and record them here: Measured Current Measured Phase Shift 8. Perform the manual calculations needed to find the circuit current and phase shift. Record the calculated values here. Do they match the measured values within reason? What has happened to the circuit with an increase in frequency? Calculated Current Calculated Phase Shift Writeup and Submission In general, for each lab you do, you will be asked to setup certain circuits, simulate them, record the results, verify the results are correct by hand, and then discuss the solution. Your lab write-up should contain a one page, single spaced discussion of the lab experiment, what went right for you, what you had difficulty with, what you learned from the experiment, how it applies to our coursework, and any other comment you can think of. In addition, you should include screen shots from the MultiSim software and any other figure, table, or diagram as necessary.

ELEC153 Circuit Theory II M2A3 Lab: AC Series Circuits Introduction Previously you worked with two simple AC series circuits, R-C and R-L circuits. We continue that work in this experiment. Procedure 1. Setup the following circuit in MultiSim.The voltage source is 10 volts peak at 1000 Hz. Figure 1: Circuit for analysis using MultiSim 2. Change R1 to 1 k and C1 to 0.1 uF. Connect the oscilloscope to measure both the source voltage and the voltage across the resistor.You should have the following arrangement. Figure 2: Circuit of figure 1 connected to oscilloscope To color the wires, right click the desired wire and select “Color Segment…” and follow the instructions. Start the simulation and open the oscilloscope. You should get the following plot: Figure 3: Source voltage (red) and the voltage (blue) across the resistor The red signal is the voltage of the source and the blue is the voltage across the resistor. The colors correspond to the colors of the wires from the oscilloscope. 3. From the resulting analysis plotdetermine the peak current. To determine the peak current measure the peak voltage across the resistor and divide by the value of the resistor (1000 Ohms). Record it here. Measured Peak Current 4. Determine the peak current by calculation. Record it here. Does it match the measured peak current? Explain. Calculated Peak Current 5 Determine the phase shift between the current in the circuit and the source voltage. We look at the time between zero crossings to determine the phase shift between two waveforms. In our plot, the blue waveform (representing the circuit current or the voltage across the resistor) crosses zero before the red waveform (the circuit voltage). So, current is leading voltage in this circuit. This is exactly what should happen when we have a capacitive circuit. 6. To determine the phase shift, we first have to measure the time between zero crossings on the red and blue waveforms. This is done by moving the oscillator probes to the two zero crossing as is shown in the following figure Figure 4: Determining the phase shift between the two voltage waveforms We can see from the figure that the zero crossing difference (T2 – T1) is approximately 134 us. The ratio of the zero-crossing time difference to the period of the waveform determines the phase shift, as follows: Using our time values, we have: How do we know if this phase shift is correct? In step 4 when you did your manual calculations to find the peak current, you had to find the total impedance of the circuit, which was: Now, the current will be: Here, the positive angle on the current indicates it is leading the circuit voltage. 7. Change the frequency of the voltage source to 5000 Hz. Estimulate and perform a Transient Analysis to find the new circuit current and phase angle. Measure them and record them here: Measured Current Measured Phase Shift 8. Perform the manual calculations needed to find the circuit current and phase shift. Record the calculated values here. Do they match the measured values within reason? What has happened to the circuit with an increase in frequency? Calculated Current Calculated Phase Shift Writeup and Submission In general, for each lab you do, you will be asked to setup certain circuits, simulate them, record the results, verify the results are correct by hand, and then discuss the solution. Your lab write-up should contain a one page, single spaced discussion of the lab experiment, what went right for you, what you had difficulty with, what you learned from the experiment, how it applies to our coursework, and any other comment you can think of. In addition, you should include screen shots from the MultiSim software and any other figure, table, or diagram as necessary.

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Chapter 03 Reading Questions Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Chapter 3 Reading Quiz Question 1 Part A Isotopes of an element differ from each other by the _____. ANSWER: Correct Chapter 3 Reading Quiz Question 2 Part A Which one of the following statements about pH is correct? ANSWER: Correct Lemon juice is an acid. Chapter 3 Reading Quiz Question 17 Part A In which form are water molecules most closely bonded to each other? ANSWER: number of electrons number of neutrons types of electrons number of protons Stomach acid has more OH- ions than H+ ions. Baking soda has more H+ ions than OH- ions. Lemon juice has more H+ ions than OH- ions. Seawater is slightly acidic. Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 9 5/21/2014 7:58 PM Correct Chapter 3 Reading Quiz Question 16 Part A Which one of the following is a molecule but NOT a compound? ANSWER: Correct Oxygen is a molecule made up of just one element. Therefore, it is not a compound. Chapter 3 Reading Quiz Question 3 Part A Which one of the following is a carbohydrate and one of Earth’s most abundant organic molecule? ANSWER: Correct equally closely bonded in water vapor and ice solid ice forming part of an Antarctic sheet liquid water a few degrees above the freezing point water vapor above a boiling pot of water CH4 O2 CO2 H2O oil protein cellulose DNA Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 9 5/21/2014 7:58 PM Chapter 3 Reading Quiz Question 4 Part A Which one of the following is a protein that functions as a catalyst? ANSWER: Correct Chapter 3 Reading Quiz Question 18 Part A The process of translation involves the use of _____. ANSWER: Chapter 3 Reading Quiz Question 5 Part A The cooling effect of sweating best represents _____. ANSWER: glucose cellulose enzyme RNA proteins to make lipids lipids to make carbohydrates carbohydrates to make proteins nucleic acids to make proteins latent heat transfer conduction radiation convection Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 9 5/21/2014 7:58 PM Correct Chapter 3 Reading Quiz Question 6 Part A When plants use sunlight in photosynthesis, the plants are using a form of _____. ANSWER: Correct Chapter 3 Reading Quiz Question 8 Part A Which of the following converts mass to energy? ANSWER: Correct Chapter 3 Reading Quiz Question 19 Part A When a windmill turns to generate electricity, the amount of kinetic energy input _____. ANSWER: chemical energy in sunlight nuclear fission electromagnetic radiation conduction conduction the breaking of chemical bonds nuclear fission photosynthesis Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 9 5/21/2014 7:58 PM Correct Chapter 3 Reading Quiz Question 20 Part A Which of the following best represents kinetic energy? ANSWER: Correct Chapter 3 Reading Quiz Question 21 Part A Which of the following processes reduces entropy? ANSWER: Correct Chapter 3 Reading Quiz Question 9 is unrelated to the amount of electrical energy produced is more than the amount of electrical energy produced equals the amount of electrical energy produced is less than the amount of electrical energy produced a charged battery gunpowder in a bullet the energy in the wax molecules of a candle a hot burner on a stove burning gasoline in an automobile engine photosynthesis in a leaf a person walking up a flight of stairs cell respiration in a leaf Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 9 5/21/2014 7:58 PM Part A Which one of the following planets is a gas giant? ANSWER: Correct Chapter 3 Reading Quiz Question 10 Part A What is the main driving force that causes Earth’s tectonic plates to drift? ANSWER: Correct Chapter 3 Reading Quiz Question 23 Part A In which of the following locations would you expect to find large quantities of young rocks? ANSWER: Venus Jupiter Mars Mercury Heat from Earth’s core causes the mantle rock to circulate. The weight of the tectonic plates causes them to sink and melt. Currents of magma from the core of Earth circulate just beneath the tectonic plates. Electromagnetic radiation from the sun heats the tectonic plates, causing them to expand. the Appalachian Mountains the Himalayas deep in the central parts of India the Mid-Atlantic Ridge Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 9 5/21/2014 7:58 PM Chapter 3 Reading Quiz Question 12 Part A The oxygen-rich atmosphere of Earth is mainly the result of _____. ANSWER: Correct Chapter 3 Reading Quiz Question 13 Part A A scientist working on the chemical reactions in the ozone layer is studying the _____. ANSWER: Correct Chapter 3 Reading Quiz Question 24 Part A The total amount of moisture in the air is highest when relative humidity is _____. ANSWER: volcanic activity chemical reactions between the early Earth atmosphere and iron photosynthetic organisms erosion of rocks into soil troposphere thermosphere stratosphere mesosphere Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 9 5/21/2014 7:58 PM Chapter 3 Reading Quiz Question 15 Part A You are enjoying a spring day but expect a storm to arrive soon . As the storm arrives and the rain begins to fall, you notice that the temperature drops dramatically. Most likely, you have just experienced the arrival of a _____. ANSWER: Correct Chapter 3 Reading Quiz Question 25 Part A Every day tremendous amounts of the sun’s energy strikes Earth. Why doesn’t Earth overheat? ANSWER: Correct Earth’s energy budget is balanced. Over the course of a year, the energy input is equal to the energy output. Chapter 3 Reading Quiz Question 7 low and temperatures are low high and temperatures are high high and temperatures are low low and temperatures are high cold front Hadley cell intertropical convergence stratospheric event The energy is ultimately radiated back to space. Much of the heat melts rocks, forming lava deep inside of Earth. Most of the energy is used in photosynthesis to help plants grow and survive. The energy mostly is absorbed in various weather systems. Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 9 5/21/2014 7:58 PM Part A How many calories are required to heat up 1,000 grams of liquid water (about 1 liter) from 20 °C to 70 °C? ANSWER: Correct Chapter 3 Reading Quiz Question 14 Part A Hadley cells near the Equator consist of _____. ANSWER: Correct Score Summary: Your score on this assignment is 85.5%. You received 19.67 out of a possible total of 23 points. 100 1,000 5,000 50,000 rising dry air associated with deserts and falling moist air that produces precipitation and rainforests rising moist air that produces precipitation and rainforests, and falling dry air associated with deserts warm, moist air rising up the sides of mountains and cool, dry air descending on the leeward sides cool, dry air rising up the sides of mountains and warm, moist air descending on the leeward sides Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 9 of 9 5/21/2014 7:58 PM

Chapter 03 Reading Questions Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Chapter 3 Reading Quiz Question 1 Part A Isotopes of an element differ from each other by the _____. ANSWER: Correct Chapter 3 Reading Quiz Question 2 Part A Which one of the following statements about pH is correct? ANSWER: Correct Lemon juice is an acid. Chapter 3 Reading Quiz Question 17 Part A In which form are water molecules most closely bonded to each other? ANSWER: number of electrons number of neutrons types of electrons number of protons Stomach acid has more OH- ions than H+ ions. Baking soda has more H+ ions than OH- ions. Lemon juice has more H+ ions than OH- ions. Seawater is slightly acidic. Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 9 5/21/2014 7:58 PM Correct Chapter 3 Reading Quiz Question 16 Part A Which one of the following is a molecule but NOT a compound? ANSWER: Correct Oxygen is a molecule made up of just one element. Therefore, it is not a compound. Chapter 3 Reading Quiz Question 3 Part A Which one of the following is a carbohydrate and one of Earth’s most abundant organic molecule? ANSWER: Correct equally closely bonded in water vapor and ice solid ice forming part of an Antarctic sheet liquid water a few degrees above the freezing point water vapor above a boiling pot of water CH4 O2 CO2 H2O oil protein cellulose DNA Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 9 5/21/2014 7:58 PM Chapter 3 Reading Quiz Question 4 Part A Which one of the following is a protein that functions as a catalyst? ANSWER: Correct Chapter 3 Reading Quiz Question 18 Part A The process of translation involves the use of _____. ANSWER: Chapter 3 Reading Quiz Question 5 Part A The cooling effect of sweating best represents _____. ANSWER: glucose cellulose enzyme RNA proteins to make lipids lipids to make carbohydrates carbohydrates to make proteins nucleic acids to make proteins latent heat transfer conduction radiation convection Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 9 5/21/2014 7:58 PM Correct Chapter 3 Reading Quiz Question 6 Part A When plants use sunlight in photosynthesis, the plants are using a form of _____. ANSWER: Correct Chapter 3 Reading Quiz Question 8 Part A Which of the following converts mass to energy? ANSWER: Correct Chapter 3 Reading Quiz Question 19 Part A When a windmill turns to generate electricity, the amount of kinetic energy input _____. ANSWER: chemical energy in sunlight nuclear fission electromagnetic radiation conduction conduction the breaking of chemical bonds nuclear fission photosynthesis Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 9 5/21/2014 7:58 PM Correct Chapter 3 Reading Quiz Question 20 Part A Which of the following best represents kinetic energy? ANSWER: Correct Chapter 3 Reading Quiz Question 21 Part A Which of the following processes reduces entropy? ANSWER: Correct Chapter 3 Reading Quiz Question 9 is unrelated to the amount of electrical energy produced is more than the amount of electrical energy produced equals the amount of electrical energy produced is less than the amount of electrical energy produced a charged battery gunpowder in a bullet the energy in the wax molecules of a candle a hot burner on a stove burning gasoline in an automobile engine photosynthesis in a leaf a person walking up a flight of stairs cell respiration in a leaf Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 9 5/21/2014 7:58 PM Part A Which one of the following planets is a gas giant? ANSWER: Correct Chapter 3 Reading Quiz Question 10 Part A What is the main driving force that causes Earth’s tectonic plates to drift? ANSWER: Correct Chapter 3 Reading Quiz Question 23 Part A In which of the following locations would you expect to find large quantities of young rocks? ANSWER: Venus Jupiter Mars Mercury Heat from Earth’s core causes the mantle rock to circulate. The weight of the tectonic plates causes them to sink and melt. Currents of magma from the core of Earth circulate just beneath the tectonic plates. Electromagnetic radiation from the sun heats the tectonic plates, causing them to expand. the Appalachian Mountains the Himalayas deep in the central parts of India the Mid-Atlantic Ridge Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 9 5/21/2014 7:58 PM Chapter 3 Reading Quiz Question 12 Part A The oxygen-rich atmosphere of Earth is mainly the result of _____. ANSWER: Correct Chapter 3 Reading Quiz Question 13 Part A A scientist working on the chemical reactions in the ozone layer is studying the _____. ANSWER: Correct Chapter 3 Reading Quiz Question 24 Part A The total amount of moisture in the air is highest when relative humidity is _____. ANSWER: volcanic activity chemical reactions between the early Earth atmosphere and iron photosynthetic organisms erosion of rocks into soil troposphere thermosphere stratosphere mesosphere Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 9 5/21/2014 7:58 PM Chapter 3 Reading Quiz Question 15 Part A You are enjoying a spring day but expect a storm to arrive soon . As the storm arrives and the rain begins to fall, you notice that the temperature drops dramatically. Most likely, you have just experienced the arrival of a _____. ANSWER: Correct Chapter 3 Reading Quiz Question 25 Part A Every day tremendous amounts of the sun’s energy strikes Earth. Why doesn’t Earth overheat? ANSWER: Correct Earth’s energy budget is balanced. Over the course of a year, the energy input is equal to the energy output. Chapter 3 Reading Quiz Question 7 low and temperatures are low high and temperatures are high high and temperatures are low low and temperatures are high cold front Hadley cell intertropical convergence stratospheric event The energy is ultimately radiated back to space. Much of the heat melts rocks, forming lava deep inside of Earth. Most of the energy is used in photosynthesis to help plants grow and survive. The energy mostly is absorbed in various weather systems. Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 9 5/21/2014 7:58 PM Part A How many calories are required to heat up 1,000 grams of liquid water (about 1 liter) from 20 °C to 70 °C? ANSWER: Correct Chapter 3 Reading Quiz Question 14 Part A Hadley cells near the Equator consist of _____. ANSWER: Correct Score Summary: Your score on this assignment is 85.5%. You received 19.67 out of a possible total of 23 points. 100 1,000 5,000 50,000 rising dry air associated with deserts and falling moist air that produces precipitation and rainforests rising moist air that produces precipitation and rainforests, and falling dry air associated with deserts warm, moist air rising up the sides of mountains and cool, dry air descending on the leeward sides cool, dry air rising up the sides of mountains and warm, moist air descending on the leeward sides Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 9 of 9 5/21/2014 7:58 PM

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1 Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 3.1 Laboratory Objective The objective of this laboratory is to understand the basic properties of sinusoids and sinusoid measurements. 3.2 Educational Objectives After performing this experiment, students should be able to: 1. Understand the properties of sinusoids. 2. Understand sinusoidal manipulation 3. Use a function generator 4. Obtain measurements using an oscilloscope 3.3 Background Sinusoids are sine or cosine waveforms that can describe many engineering phenomena. Any oscillatory motion can be described using sinusoids. Many types of electrical signals such as square, triangle, and sawtooth waves are modeled using sinusoids. Their manipulation incurs the understanding of certain quantities that describe sinusoidal behavior. These quantities are described below. 3.3.1 Sinusoid Characteristics Amplitude The amplitude A of a sine wave describes the height of the hills and valleys of a sinusoid. It carries the physical units of what the sinusoid is describing (volts, amps, meters, etc.). Frequency There are two types of frequencies that can describe a sinusoid. The normal frequency f is how many times the sinusoid repeats per unit time. It has units of cycles per second (s-1) or Hertz (Hz). The angular frequency ω is how many radians pass per second. Consequently, ω has units of radians per second. Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 2 Period The period T is how long a sinusoid takes to repeat one complete cycle. The period is measured in seconds. Phase The phase φ of a sinusoid causes a horizontal shift along the t-axis. The phase has units of radians. TimeShift The time shift ts of a sinusoid is a horizontal shift along the t-axis and is a time measurement of the phase. The time shift has units of seconds. NOTE: A sine wave and a cosine wave only differ by a phase shift of 90° or ?2 radians. In reality, they are the same waveform but with a different φ value. 3.3.2 Sinusoidal Relationships Figure 3.1: Sinusoid The general equation of a sinusoid is given below and refers to Figure 3.1. ?(?) = ????(?? +?) (3.1) The angular frequency is related to the normal frequency by Equation 3.2. ?= 2?? (3.2) The angular frequency is also related to the period by Equation 3.3. ?=2?? (3.3) By inspection, the normal frequency is related to the period by Equation 3.4. ? =1? (3.4) ?? Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 3 The time shift is related to the phase (radians) and the frequency by Equation 3.5. ??= ∅2?? (3.5) 3.3.3 Equipment 3.3.3.1 Inductors Inductors are electrical components that resist a change in the flow of current passing through them. They are essentially coils of wire. Inductors are electromagnets too. They are represented in schematics using the following symbol and physically using the following equipment (with or without exposed wire): Figure 3.2: Symbol and Physical Example for Inductors 3.3.3.2 Capacitors Capacitors are electrical components that store energy. This enables engineers to store electrical energy from an input source such as a battery. Some capacitors are polarized and therefore have a negative and positive plate. One plate is straight, representing the positive terminal on the device, and the other is curved, representing the negative one. Polarized capacitors are represented in schematics using the following symbol and physically using the following equipment: Figure 3.3: Symbol and Physical Example for Capacitors 3.3.3.3 Function Generator A function generator is used to create different types of electrical waveforms over a wide range of frequencies. It generates standard sine, square, and triangle waveforms and uses the analog output channel. 3.3.3.5 Oscilloscope An oscilloscope is a type of electronic test instrument that allows observation of constantly varying voltages, usually as a two-dimensional plot of one or more signals as a function of time. It displays voltage data over time for the analysis of one or two voltage measurements taken from the analog input channels of the Oscilloscope. The observed waveform can be analyzed for amplitude, frequency, time interval and more. Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 4 3.4 Procedure Follow the steps outlined below after the instructor has explained how to use the laboratory equipment 3.4.1 Sinusoidal Measurements 1. Connect the output channel of the Function Generator to the channel one of the Oscilloscope. 2. Complete Table 3.1 using the given values for voltage and frequency. Table 3.1: Sinusoid Measurements Function Generator Oscilloscope (Measured) Calculated Voltage Amplitude, A (V ) Frequency (Hz) 2*A (Vp−p ) f (Hz) T (sec) ω (rad/sec) T (sec) 2.5 1000 3 5000 3.4.2 Circuit Measurements 1. Connect the circuit in figure 3.4 below with the given resistor and capacitor NOTE: Vs from the circuit comes from the Function Generator using a BNC connector. Figure 3.4: RC Circuit Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 5 2. Using the alligator to BNC cables, connect channel one of the Oscilloscope across the capacitor and complete Table 3.2 Table 3.2: Capacitor Sinusoid Function Generator Oscilloscope (Measured) Calculated Vs (Volts) Frequency (Hz) Vc (volts) f (Hz) T (sec) ω (rad/sec) 2.5 100 3. Disconnect channel one and connect channel two of the oscilloscope across the resistor and complete table 3.3. Table 3.3: Resistor Sinusoid Function Generator Oscilloscope (Measured) Calculated Vs (Volts) Frequency (Hz) VR (volts) f (Hz) T (sec) ω (rad/sec) 2.5 100 4. Leaving channel two connected across the resistor, clip the positive lead to the positive side of the capacitor and complete table 3.4 Table 3.4: Phase Difference Function Generator Oscilloscope (Measured) Calculated Vs (volts) Frequency (Hz) Divisions Time/Div (sec) ts (sec) ɸ (rad) ɸ (degrees) 2.5 100 5. Using the data from Tables 3.2, 3.3, and 3.4, plot the capacitor sinusoidal equation and the resistor sinusoidal equation on the same graph using MATLAB. HINT: Plot over one period. 6. Kirchoff’s Voltage Law states that ??(?)=??(?)+??(?). Calculate Vs by hand using the following equation and Tables 3.2 and 3.3 ??(?)=√??2+??2???(??−???−1(????)) Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 6 3.5 New MATLAB Commands hold on  This command allows multiple graphs to be placed on the same XY axis and is placed after the first plot statement. legend (’string 1’, ’string2’, ‘string3’)  This command adds a legend to the plot. Strings must be placed in the order as the plots were generated. plot (x, y, ‘line specifiers’)  This command plots the data and uses line specifiers to differentiate between different plots on the same XY axis. In this lab, only use different line styles from the table below. Table 3.5: Line specifiers for the plot() command sqrt(X)  This command produces the square root of the elements of X. NOTE: The “help” command in MATLAB can be used to find a description and example for functions such as input.  For example, type “help input” in the command window to learn more about the input function. NOTE: Refer to section the “MATLAB Commands” sections from prior labs for previously discussed material that you may also need in order to complete this assignment. Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 7 3.6 Lab Report Requirements 1. Complete Tables 3.1, 3.2, 3.3, 3.4 (5 points each) 2. Show hand calculations for all four tables. Insert after this page (5 points each) 3. Draw the two sinusoids by hand from table 3.1. Label amplitude, period, and phase. Insert after this page. (5 points) 4. Insert MATLAB plot of Vc and VR as obtained from data in Tables 3.2 and 3.3 after this page. (5 points each) 5. Show hand calculations for Vs(t). Insert after this page. (5 points) 6. Using the data from the Tables, write: (10 points) a) Vc(t) = b) VR(t) = 7. Also, ???(?)=2.5???(628?). Write your Vs below and give reasons why they are different. (10 points) a) Vs(t) = b) Reasons: 8. Write an executive summary for this lab describing what you have done, and learned. (20 points)

1 Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 3.1 Laboratory Objective The objective of this laboratory is to understand the basic properties of sinusoids and sinusoid measurements. 3.2 Educational Objectives After performing this experiment, students should be able to: 1. Understand the properties of sinusoids. 2. Understand sinusoidal manipulation 3. Use a function generator 4. Obtain measurements using an oscilloscope 3.3 Background Sinusoids are sine or cosine waveforms that can describe many engineering phenomena. Any oscillatory motion can be described using sinusoids. Many types of electrical signals such as square, triangle, and sawtooth waves are modeled using sinusoids. Their manipulation incurs the understanding of certain quantities that describe sinusoidal behavior. These quantities are described below. 3.3.1 Sinusoid Characteristics Amplitude The amplitude A of a sine wave describes the height of the hills and valleys of a sinusoid. It carries the physical units of what the sinusoid is describing (volts, amps, meters, etc.). Frequency There are two types of frequencies that can describe a sinusoid. The normal frequency f is how many times the sinusoid repeats per unit time. It has units of cycles per second (s-1) or Hertz (Hz). The angular frequency ω is how many radians pass per second. Consequently, ω has units of radians per second. Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 2 Period The period T is how long a sinusoid takes to repeat one complete cycle. The period is measured in seconds. Phase The phase φ of a sinusoid causes a horizontal shift along the t-axis. The phase has units of radians. TimeShift The time shift ts of a sinusoid is a horizontal shift along the t-axis and is a time measurement of the phase. The time shift has units of seconds. NOTE: A sine wave and a cosine wave only differ by a phase shift of 90° or ?2 radians. In reality, they are the same waveform but with a different φ value. 3.3.2 Sinusoidal Relationships Figure 3.1: Sinusoid The general equation of a sinusoid is given below and refers to Figure 3.1. ?(?) = ????(?? +?) (3.1) The angular frequency is related to the normal frequency by Equation 3.2. ?= 2?? (3.2) The angular frequency is also related to the period by Equation 3.3. ?=2?? (3.3) By inspection, the normal frequency is related to the period by Equation 3.4. ? =1? (3.4) ?? Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 3 The time shift is related to the phase (radians) and the frequency by Equation 3.5. ??= ∅2?? (3.5) 3.3.3 Equipment 3.3.3.1 Inductors Inductors are electrical components that resist a change in the flow of current passing through them. They are essentially coils of wire. Inductors are electromagnets too. They are represented in schematics using the following symbol and physically using the following equipment (with or without exposed wire): Figure 3.2: Symbol and Physical Example for Inductors 3.3.3.2 Capacitors Capacitors are electrical components that store energy. This enables engineers to store electrical energy from an input source such as a battery. Some capacitors are polarized and therefore have a negative and positive plate. One plate is straight, representing the positive terminal on the device, and the other is curved, representing the negative one. Polarized capacitors are represented in schematics using the following symbol and physically using the following equipment: Figure 3.3: Symbol and Physical Example for Capacitors 3.3.3.3 Function Generator A function generator is used to create different types of electrical waveforms over a wide range of frequencies. It generates standard sine, square, and triangle waveforms and uses the analog output channel. 3.3.3.5 Oscilloscope An oscilloscope is a type of electronic test instrument that allows observation of constantly varying voltages, usually as a two-dimensional plot of one or more signals as a function of time. It displays voltage data over time for the analysis of one or two voltage measurements taken from the analog input channels of the Oscilloscope. The observed waveform can be analyzed for amplitude, frequency, time interval and more. Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 4 3.4 Procedure Follow the steps outlined below after the instructor has explained how to use the laboratory equipment 3.4.1 Sinusoidal Measurements 1. Connect the output channel of the Function Generator to the channel one of the Oscilloscope. 2. Complete Table 3.1 using the given values for voltage and frequency. Table 3.1: Sinusoid Measurements Function Generator Oscilloscope (Measured) Calculated Voltage Amplitude, A (V ) Frequency (Hz) 2*A (Vp−p ) f (Hz) T (sec) ω (rad/sec) T (sec) 2.5 1000 3 5000 3.4.2 Circuit Measurements 1. Connect the circuit in figure 3.4 below with the given resistor and capacitor NOTE: Vs from the circuit comes from the Function Generator using a BNC connector. Figure 3.4: RC Circuit Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 5 2. Using the alligator to BNC cables, connect channel one of the Oscilloscope across the capacitor and complete Table 3.2 Table 3.2: Capacitor Sinusoid Function Generator Oscilloscope (Measured) Calculated Vs (Volts) Frequency (Hz) Vc (volts) f (Hz) T (sec) ω (rad/sec) 2.5 100 3. Disconnect channel one and connect channel two of the oscilloscope across the resistor and complete table 3.3. Table 3.3: Resistor Sinusoid Function Generator Oscilloscope (Measured) Calculated Vs (Volts) Frequency (Hz) VR (volts) f (Hz) T (sec) ω (rad/sec) 2.5 100 4. Leaving channel two connected across the resistor, clip the positive lead to the positive side of the capacitor and complete table 3.4 Table 3.4: Phase Difference Function Generator Oscilloscope (Measured) Calculated Vs (volts) Frequency (Hz) Divisions Time/Div (sec) ts (sec) ɸ (rad) ɸ (degrees) 2.5 100 5. Using the data from Tables 3.2, 3.3, and 3.4, plot the capacitor sinusoidal equation and the resistor sinusoidal equation on the same graph using MATLAB. HINT: Plot over one period. 6. Kirchoff’s Voltage Law states that ??(?)=??(?)+??(?). Calculate Vs by hand using the following equation and Tables 3.2 and 3.3 ??(?)=√??2+??2???(??−???−1(????)) Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 6 3.5 New MATLAB Commands hold on  This command allows multiple graphs to be placed on the same XY axis and is placed after the first plot statement. legend (’string 1’, ’string2’, ‘string3’)  This command adds a legend to the plot. Strings must be placed in the order as the plots were generated. plot (x, y, ‘line specifiers’)  This command plots the data and uses line specifiers to differentiate between different plots on the same XY axis. In this lab, only use different line styles from the table below. Table 3.5: Line specifiers for the plot() command sqrt(X)  This command produces the square root of the elements of X. NOTE: The “help” command in MATLAB can be used to find a description and example for functions such as input.  For example, type “help input” in the command window to learn more about the input function. NOTE: Refer to section the “MATLAB Commands” sections from prior labs for previously discussed material that you may also need in order to complete this assignment. Laboratory 3 – Sinusoids in Engineering: Measurement and Analysis of Harmonic Signals 7 3.6 Lab Report Requirements 1. Complete Tables 3.1, 3.2, 3.3, 3.4 (5 points each) 2. Show hand calculations for all four tables. Insert after this page (5 points each) 3. Draw the two sinusoids by hand from table 3.1. Label amplitude, period, and phase. Insert after this page. (5 points) 4. Insert MATLAB plot of Vc and VR as obtained from data in Tables 3.2 and 3.3 after this page. (5 points each) 5. Show hand calculations for Vs(t). Insert after this page. (5 points) 6. Using the data from the Tables, write: (10 points) a) Vc(t) = b) VR(t) = 7. Also, ???(?)=2.5???(628?). Write your Vs below and give reasons why they are different. (10 points) a) Vs(t) = b) Reasons: 8. Write an executive summary for this lab describing what you have done, and learned. (20 points)

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Task 5 – Learning Outcomes 2.3 Determine heat transfer coefficient using experimental and tabulated data a. In an experimental result showed that air at 300 K and bulk velocity 10 m/s flows over a flat horizontal plate with a temperature of 1000 K at all points on its surface. Given that Nu=0.32Pr1/3 Re½ (Ta/Ts)0.117 Calculate the heat transfer rate from one side over the first 100 mm and the first 200 mm. Ta is the bulk air temperature and Ts is the surface temperature. Given that:

Task 5 – Learning Outcomes 2.3 Determine heat transfer coefficient using experimental and tabulated data a. In an experimental result showed that air at 300 K and bulk velocity 10 m/s flows over a flat horizontal plate with a temperature of 1000 K at all points on its surface. Given that Nu=0.32Pr1/3 Re½ (Ta/Ts)0.117 Calculate the heat transfer rate from one side over the first 100 mm and the first 200 mm. Ta is the bulk air temperature and Ts is the surface temperature. Given that:

Solution   a)   Nu=0.32Pr1/3 Re½ (Ta/Ts)0.117 Pr=0.69 Re1=10/.1*1.788*10e-5 Ta=1000, … Read More...
A company produces bag, each of which could be sold for$150. It has a fixed monthly cost of $13,000 and a variable cost of $20 per bag produced. A. Determine the company monthly total cost function B. determine the company’s monthly revenue function C determine the company’s monthly total profit function D how many bag must the company produce to break even E how many bags must the company produce to generate $26,000 in profit? Compute A log 100 B log 1000 C log2 8 D log5. 25 E log 0.01 F log 1 G loga a

A company produces bag, each of which could be sold for$150. It has a fixed monthly cost of $13,000 and a variable cost of $20 per bag produced. A. Determine the company monthly total cost function B. determine the company’s monthly revenue function C determine the company’s monthly total profit function D how many bag must the company produce to break even E how many bags must the company produce to generate $26,000 in profit? Compute A log 100 B log 1000 C log2 8 D log5. 25 E log 0.01 F log 1 G loga a