ME348_S24_Lab2 (1)

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ME 348: Circuit Analysis, Instrumentation, and Statistics Lab 2 Circuits II 1. Instructions for Completing this Lab:  Please answer each question completely, showing all work as necessary. Any steps in the lab that require answers from you begin with the number of points in parentheses, highlighted yellow.  You may type your answers into this document, use a tablet to write in your answers, or insert pictures of written work into the spaces provided. The most important thing is that your answers can be easily read/comprehended.  Please follow all the guidelines shown in the formatting guidelines document provided on Canvas.  If pictures are requested, take a picture with your phone and insert it into the space provided if possible. Otherwise, include your picture in a clearly labeled Appendix. Remember to use figure captions.  You need to include properly formatted Excel/MATLAB plots as requested. However, you do not need to include the data used to make these plots unless explicitly requested.  After all the answers have been entered, save this document as a PDF for submission to Canvas. You can delete the Introduction, Background, and Prelab if you desire, but this is not required.  Attach a completed Lab Cover Sheet (provided below) to the front of your submission. Make sure to include all the documents requested, as appropriate.  Only one person (designated by the team on the submission cover sheet) should upload the final submission to Canvas on behalf of the team.  Questions regarding the completion of this lab should be directed towards your lab section TA on Canvas, with the course instructors on the message as well.

2. Activities: 1. Working with Series and Parallel combinations of Resistors 2. Introduction to basic breadboarding: Create a Parallel LED circuit 3. Dual-Source Circuit Analysis 4. Further Examination of Arduino and Arduino IDE 3. Learning Objectives: After completing this lab, students will be able to:  Use a digital multimeter for static measurements of resistance and voltage  Create a simple circuit using a breadboard, and become familiar with wiring electronic components to a breadboard  Program an Arduino Uno to perform simple commands  Understand the difference between the digital and analog I/O (input/output) pins on the Arduino  Build and measure various points in a dual-source circuit for comparison to predicted values of currents and voltages throughout the network 4. Introduction and Background: 4.1 Material for Review from Previous Labs Breadboards – Engineers often use a breadboard to quickly build prototypes of circuits for testing. A breadboard has a series of holes or sockets into which jumper wires are inserted to make electrical connections. The wires are easy to connect and disconnect; thus, circuits wired on a breadboard are quickly and easily modified. Some of the sockets are hard-wired to other sockets, forming a bus . Breadboards have both short buses (typically containing 5 sockets) and long buses (typically running the full length or width of the breadboard and containing many sockets, often also in groups of 5). Short buses are used for component connections, in which two to five wires may be connected to one short bus. Long buses are generally saved for high- usage connections, such as a DC voltage power supply or ground (zero volts). A bus used as ground would, for example, be called a ground bus . Engineers should be familiar with the way the breadboard is internally wired before using the breadboard to create prototype circuits. Components, such as resistors, capacitors, and diodes can be inserted directly into the sockets. An example of how the leads of a resistor can be inserted directly into the breadboard is sketched in Figure ; clusters of 11 short buses are shown on the top and bottom, each containing 5 sockets, aligned Page 2 of 19 A B Short bus R 2 R 1 Figure A: Example of a breadboard with resistors

vertically and indicated by the red rectangle that encircles them. These 5 sockets are connected to each other , but not to any other sockets . A resistor can either straddle two short buses across the empty space, as exemplified by the top resistor on the sketch (right), or cross from one short bus to another within the same cluster of short buses, as exemplified by the bottom resistor on the sketch. The resistor functions properly as long as the two leads of the resistor are inserted into two independent (unconnected) buses. Notice too that from point A to point B on the diagram, these two resistors are in series , since each set of five vertical sockets is a short bus . The equivalent schematic circuit diagram is shown below: In the lab, we sometimes use powered breadboards . A powered breadboard has one or more built-in voltage supplies (in our case -15 V, +5 V, and +15 V DC) in addition to a common ground. Note that some of the powered breadboards in the lab have +/- 18 V rather than +/- 15 V DC power supplies, and some have variable power supplies. The small breadboard in your Arduino kit is NOT powered. Digital and Analog Signals – Data and instruments can be either digital (discrete) or analog (continuous). Because an Arduino itself is a digital device, all measurements it takes are technically digital (discrete). However, Arduino software uses different definitions for the same terms. For an Arduino, a “digital” I/O (input/output) signal consists of either a high (1) or a low (0) value (no other values can beread/written), while an “analog” I/O signal can take many more values. For example, we’ll see in later labs that the analog read on an Arduino outputs integer values between 0 and 1023. This distinction in terminology is very important to keep in mind, especially when we cover digital data acquisition later in the course. For now, this lab will provide a first introduction to this concept. Voltage Divider – As will be discussed in lecture and Lab 1, the voltage divider (schematic to the right) is a simple circuit that “steps-down“ the voltage supply (V in ) to some lower output level (V o ). Based on the choice of values for the two resistors, R 1 & R 2 , the output Vo can be set to a certain value according to the following equation: Page 3 of 19 Figure A: Example of Resistors in Series

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V o = R 2 R 1 + R 2 V ¿ As an example, if a sensor requires a supply voltage of 2 V to function properly and all you have is a 5 V source, you could choose values of R 1 and R 2 such that the potential difference across R 2 (V o ) is 2/5 of the 5 V supply (V in ). Potentiometers - Potentiometers are an extremely important component in both circuit prototyping early in the design process, as well as functional operation of fully-developed circuitry in a given application. They provide the ability to tune/vary resistances in a circuit, useful for situations such as balancing Wheatstone bridge circuits and varying the amount of current supplied to a given component/sensor. As a result, we need to delve a bit deeper into their operation to ensure that you are both comfortable with their use and appreciate their utility. Potentiometers are a three-terminal device, which can lead to some confusion when inserting and connecting them into a circuit. Consider the photo of the potentiometer in the Arduino student kit, as well as the schematic diagram shown to the right. Think of the potentiometer as a device where the resistance between two of the three pins can be smoothly varied from a minimum resistance ( R Min ; often 0 Ω) to a maximum resistance ( R Max ; in our case, 10 kΩ). The resistance across these two pins is some fractional value of the maximum resistance available, which we can refer to as x where x can vary from 0 to 1 (0 x < 1). For the purposes of this discussion related to the potentiometer in the student kit, consider x = 0 to be when the knob is rotated fully counter-clockwise, and x = 1 is when the knob is rotated fully clockwise. There are two different choices of what two pins can be used to function as a variable resistance. Based on the diagram above, pins 1 & 2 result in a resistance where x = 0 corresponds to the minimum resistance condition (0 Ω) and x = 1 is the maximum resistance condition (10 kΩ). Conversely, pins 2 & 3 result in the opposite configuration where x = 0 corresponds to the maximum resistance condition (10 kΩ) and x = 1 is the minimum resistance condition (0 Ω). Mathematically, the resistance between pins 1 & 2 ( R 12 ) and pins 2 & 3 ( R 23 ) as a function of x are as follows: R 12 ( x )= x R Max R 23 ( x ) = 1 − x R Max The resistance across the remaining combination of pins 1 & 3 ( R 13 ) does not vary when the knob is turned and is simply equal to R max . Within the potentiometer, the physical point-of-connection of pin 2 on a resistive element (bar, film, winding, etc.) is being moved as the knob is turned. Based on the relative position of this pin 2 connection point across the entire resistive element (which is connected between pins 1 & 3), this sets Page 4 of 19 Figure B: Example of a voltage divider circuit. Figure C: Left is a 10K potentiometer and right shows the internal circuit.

the value of x in the equations above. Therefore, what we see across either pins 1 & 2 or 2 & 3 are always a fraction of the total resistance range available according to the equations above. When we use a potentiometer in certain circuits such as a Wheatstone bridge, all we may really need is a resistance that varies when we turn the knob. Therefore, we can choose between using either R 12 (pins 1 & 2) or R 23 (pins 2 & 3) based on how we want our circuit to function when the knob is turned in one direction or the other. In these situations where only two of the three pins are necessary to provide the functionality we need, the third pin can be left unconnected. Connecting this third unused pin to any other point in the circuit, including ground, will disrupt the operation of the potentiometer as intended. There are indeed other applications where we may want/need to connect all three pins of a potentiometer to various points of a circuit, such as the voltage divider exercise that used the 10 kΩ potentiometer back in Lab 1. In that case, we needed to utilize both R 12 and R 23 to create a voltage divider. However, in the case of the Wheatstone bridge or others where only one of these two variable resistances is needed, the third terminal on the potentiometer can be left unconnected. 4.2 New Material Required for this Laboratory Light-Emitting Diode (LED) – A type of diode that lights up when electricity passes through it. All diodes (LEDs included) allow electricity to flow in only one direction. LEDs are often used as indicators on electronic devices, inside TVs to display vivid colors, and as energy-efficient lighting in buildings. Dual Source Circuit - Part of this lab will focus on the use of both the 5 V and 3.3 V DC supplies available on the Arduino Uno to construct and measure various voltages and currents in a circuit. In this lab you will use a potentiometer as a variable resistive element, requiring the two-pin type configuration described previously. You will want to review the analysis of these types of circuits via mesh current analysis. Kirchoff’s Current Law (KCL) - Kirchhoff’s current law states that the current entering a given node is equal to the current exiting the same node. Therefore, the net current entering/exiting the node will be zero. For N currents entering/exiting a given node : ∑ k = 1 N i k = 0. An example is also provided with the node labeled in green. One strategy if you are unsure Page 5 of 19 Figure D: LEDS like the ones found in the Arduino kit. Figure E: Example circuit for the KCL law with current evaluated at the green node.

of the current direction is to declare all currents are exiting or entering the nodes. A negative current will mean to change the current direction of the answer. Kirchoff’s Voltage Law (KVL) - For a given loop in an electrical circuit, Kirchhoff’s Voltage law states that the sum of voltage in the closed loop must equal zero. When drawing a voltage loop record your starting node and determine the positive or negative side of each component. When going around the loop if the arrow enters the negative side, then the voltage is negative. If the arrow enters the positive side, then the voltage is positive. Example: − V a + V b + V c + V d = 0 . 5. Lab Safety: You must follow all safety procedures outlined here and in the lab manuals themselves. Safety requirements for all labs include (but are not limited to):  No food or drinks should be in your work area.  Do not wear loose clothing or jewelry. Tie back long hair.  Turn off the power supply to an Arduino or circuit when reconfiguring its wiring.  Do not rest electronics on a conductive table or surface.  Discharge any buildup of static electricity in your body before touching metal components. Avoid workspaces and clothing that are prone to building static charge (e.g., carpeted floor).  Double check the polarities of any connections you make.  Keep a consistent wiring color code. A typical convention would be to use red for power and black for ground, however the ability to use that may depend on the colors/numbers of wires in your kits.  Connect and test one small part at a time as you build complex circuits.  Only work where a functional fire extinguisher is nearby and know where that fire extinguisher is.  Don't put cords where people can trip on them.  Be careful what you touch while troubleshooting. Arduinos usually don't deal with very high voltages, but inductors and capacitors can build up high charges. Be sure to safely discharge any capacitor after use. Page 6 of 19 Figure F: Example KVL circuit with the loop drawn clockwise.

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ME 348: Circuit Analysis, Instrumentation, and Statistics SUBMISSION COVER SHEET: LAB NUMBER _________ DATE COMPLETED _________ TEAM ROSTER SECTION #: _________ TEAM #: ________ MEMBER #1: MEMBER #2: MEMBER #3: TEAM MEMBER UPLOADING FINAL LAB REPORT TO CANVAS IS  ________________________________ Checklist: MUST be completed to receive full credit ¨ ¨ Calculations: o Units included in all calculations o Appropriate number of significant digits reported ¨ Correct spelling and grammar throughout ¨ Tables: o Numbered caption above each table o All columns labeled, including units if appropriate ---------------------------------------------------------------------- ¨ Figures: o Numbered caption below each figure o Data points only connected if appropriate for the context o All axes labeled, including units if appropriate o Legend included if more than one set of data plotted o Axis limits chosen to minimize white space o Reasonable divisions for axis units o Horizontal axis aligned at the bottom of the figure FOR GRADER USE: Lab Participation Grade and Deductions : The instructor or TA reserves the right to deduct points for any of the following, either for all group members or for individual students:   Arriving late to lab or leaving before your lab group is finished  Not participating in the work of your lab group (freeloading)  Causing distractions, arguing, or not paying attention during lab  Not following the rules about formatting plots and tables  Grammatical errors in your lab report  Sloppy or illegible writing or plots (lack of neatness) in your lab report  Other (at the discretion of the instructor or TA) Name Reason for deduction Deduction amount Individual grade Page 7 of 19 TOTAL GRADE _____ / _85 __

Lab #2 Procedures & Questions – ME 348 Part 1: Working with series and parallel combinations of resistors Combo #1: 1. (2) Use your multimeter to identify a 560 Ω and a 220 Ω resistor. Insert a picture of these two resistors connected in parallel on the breadboard and draw the equivalent circuit diagram. Include figure numbers (starting from 1) and caption for this and all following questions. 2. (2) Calculate the equivalent resistance of the two parallel resistors above, based on the nominal values of 560 Ω and 220 Ω. Then, use your multimeter to measure the actual equivalent resistance and calculate the percent error. Combo #2: 3. (2) Use your multimeter to identify two 220 Ω resistors. Insert a picture of these two resistors connected in series on the breadboard and draw the equivalent circuit diagram. 4. (2) Calculate the equivalent resistance of the two series resistors above, based on the nominal values of 220 Ω and 220 Ω. Then, use your multimeter to measure the actual equivalent resistance and calculate the percent error. Combo #3: 5. (2) Use your multimeter to identify two 220 Ω resistors and one 560 Ω resistor. Insert a picture of the series combination of the two 220 Ω resistors connected in parallel with the 560 Ω resistor and draw the equivalent circuit diagram. 6. (2) Calculate the equivalent resistance of the combination in Step 5, based on the nominal values of 220 Ω and 560 Ω. Then, use your multimeter to measure the actual equivalent resistance and calculate the percent error. Combo #4: 7. (2) Using the resistors available in the kit, create an equivalent resistance of 44 Ω. Sketch the schematic of the circuit and include a photo of the breadboarded circuit. 8. (2) Use your multimeter to measure the actual equivalent resistance of the circuit in Step 7 and calculate the percent error. Combo #5: Page 8 of 19

9. (2) Using the resistors available in the kit, create an equivalent resistance of 324 Ω. Sketch the schematic of the circuit and include a photo of the breadboarded circuit. 10. (2) Use your multimeter to measure the actual equivalent resistance of the circuit in Step 9 and calculate the percent error. Part 2: Introduction to basic breadboarding: Parallel LED Circuits 1. Watch this video on circuit schematics ( Circuit Schematics ) to review how to translate between a circuit schematic and a physically breadboarded circuit. 2. Identify a 220 Ω resistor from your hardware kit by reading the resistor code and confirm using a multimeter. 3. (5) Take a picture of the chosen resistor and include it below. Explain how to read the resistor color code. 4. Ensure that your Arduino Project Board (breadboard + Arduino Uno) is NOT CONNECTED to your computer at this time via USB. 5. Using the breadboard and the components in your hardware kit, connect one 220 Ω resistor and an LED (any color) in series . Reference the note below about LEDs to ensure that the shared node between the resistor and the LED is the Anode of the LED. Note: The long lead (or “leg”) of an LED is the anode , and the short leg is the cathode . Make sure you connect them correctly! Note: A resistor, called a ballast resistor, is connected to the LED to limit the current through the LED and to prevent it from burning out. 6. Use a jumper wire to connect the 5 VDC output supply pin from the Arduino Uno to the open connection of the resistor. 7. Use another jumper wire to connect the Cathode of the LED to the ground (GND) pin on the Arduino Uno. 8. Your physical circuit should match the circuit schematic shown in Figure G. The lower-right symbol represents an LED. Double check your circuit to confirm it matches this schematic. Page 9 of 19 Cathode, connect to ground (black) terminal of battery Anode, connect to positive (red) terminal of battery

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Figure G: Example circuit with 220 ohm resistor in series with the LED and the Arduino 9. Connect the Arduino Uno to your computer via USB. The LED should light up. 10. Disconnect the Arduino Uno from your computer. 11. Create a circuit with four LEDs ( all of the same color : IMPORTANT!!!) connected in parallel, the combination of which are in series with a single 220 Ω resistor . The circuit diagram is shown below. Figure H: Example circuit with 4 LEDs in parallel to each other. 12. Connect the Arduino Uno and you should see all four LEDs light up, similar to the photo shown in Figure H. Figure I: Breadboard example of the Arduino and LED. Page 10 of 19

13. (8) If you remove one of the LEDs, what should happen to the brightness of the remaining three LEDs? Explain why (qualitatively), using equations from the lecture to guide your answer. 14. (8) Confirm your intuition (“hypothesis”) by testing this out, removing one LED at a time. Include a photo of your operational circuit for each of the following configurations: 4 LEDs, 3 LEDs, 2 LEDs, 1 LED. (you should have 4 photos in total) Part 3: Dual-Source Circuit Analysis Figure J: For this circuit, 1 end of the 4.7 Kohm, 1 kohm, and 220 ohm resistor should be in the same row on the bread board. The other end of the 220 ohm resistor should connect to ground. 1. (5) Using the techniques discussed in class, analyze the dual source circuit shown above and calculate currents through each of the resistors. Include a picture of your written work with the calculated currents below. 2. Build this same circuit on your Arduino project board. 3. (2) Include a photo of the completed circuit below. 4. Measure the voltage across each of the three resistors. (1) Measured voltage across R1, V R1 = ___________ V (1) Measured voltage across R2, V R2 = ___________ V (1) Measured voltage across R3, V R3 = ___________ V 5. Using the nominal resistances, calculate the current through each of these resistors. (2) Current through R1, i R1 = ___________ A (2) Current through R2, i R2 = ___________ A (2) Current through R3, i R3 = ___________ A Page 11 of 19

6. (3) Compare the currents derived from your measurements to the expected values from step 1. Why do you think these values differ? Part 4: Further Examination of Arduino and Arduino IDE 1. Unplug your Arduino Uno from the computer and clear your breadboard of all the components/wires from Part 1. Then reconnect your Arduino. 2. Be sure to plug the cable all the way in – it’s possible to plug in the cable far enough that the Arduino receives power, but not far enough that it can exchange data with your computer. 3. Open the Arduino IDE . 4. Under Tools , make sure that the following are selected (refer to Lab 1 if you need more details)  Board: Arduino Uno  Port: Select the correct USB port (names may vary by computer) 5. Next, we will set the data rate in bits per second (baud) for serial data transmission to 9600. Do this by clicking on the Serial Monitor icon, then clicking on the dropdown baud menu, and choosing 9600, as shown in the pictures below. Figure K: Example of changing the baud rate in the serial monitor. Note: The baud rate at which your Arduino is sending data needs to match the baud at which Page 12 of 19 Dropdown baud menu Serial Monitor icon.

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your serial monitor is reading data. You can set this for the Arduino at the top of a sketch using the command: Serial.begin(9600) This is shown below. Figure L: Code to set the initial baud rate and allow access to the serial monitor. Serial.begin(xxxx) must match the baud rate in the serial monitor. 6. Remove the USB connection to the Arduino. 7. Now let’s build the circuit below using the Arduino board, 3x 560 Ω resistors (note that if they are 5- band resistors they will look different than in the sketch below), and 3x LEDs (one red, one blue and one green). Connect jumper wires from the anode of each LED to one of digital pins 6, 8, and 12 of the Arduino to create the diagram below. Note that pin 6 supports PWM (discussed below). Use a jumper wire to connect the GND pin on the Arduino to the long bus on the breadboard, which is connected to all the cathodes of the LEDs. Figure M: Three led circuit connected to the PWM pins of the Arduino. Note: Arduino Uno pins are separated into roughly three groups: Power pins, 6 analog input pins, and 14 I/O (input or output) digital ports, of which 6 can be used for Pulse Width Modulation ( PWM ) output. Recall from Lab 1 that digital pins only have two states: On or Off. Page 13 of 19

When used as an output, these can produce a constant output power (when on) or no output power (when off). However, we can switch the pins between these two states very quickly (often at hundreds or thousands of Hz) to achieve an average power output equal to an intermediate value, approximating the behavior of an analog output. The duty cycle is defined as the fraction of one period in which a signal or system is active. For a digital output pin, this is the fraction of time that the pin spends in the “on” state. A greater duty cycle means the pin outputs more average power. Page 14 of 19 14 I/O Digital Pins (~ indicates PWM supported) Power Pins Analog Input Pins

Figure N: Diagram of different Arduino pins along with visualization of PWM. 8. Download the SimDigOut.ino file from Canvas and then open it using the Arduino IDE, plug in your Arduino, and upload the sketch to execute the code on the Arduino. Note: The basics of an Arduino IDE sketch are detailed below. When you open a new Arduino sketch, you will see there are two pre-defined functions as shown below. Page 15 of 19 Upload

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 The setup function will run once any time the Arduino is reset or turns on.  The loop function will run repeatedly . Figure O: Bare minimum Arduino sketch containing both the void setup and void loop functions. Now, look at the structure of the SimDigOut.ino sketch and examine the following: 1. Global variables, which can be accessed anywhere in the program, are declared at the top of the code. In this example, we define which pin numbers are connected to each LED. 2. The setup function is run by the Arduino once, immediately after being reset or powered on. A brief explanation of some of the code in this section is as follows:  Serial.begin(9600) : Sets the baud rate to 9600  pinMode(BluePin, OUTPUT): Defines pin 6 (the “BluePin”) as an output. All digital I/O pin can be used as either an input or output (we saw the former in Lab 1 and are using the latter now). Therefore, we have to define which use we want in the code. 3. The loop function is run continuously. Whenever the Arduino reaches the end of the loop function, it starts again at the top of this function. A brief explanation of some of the code in this section is as follows:  digitalWrite(RedPin, HIGH) : Sets the output value of digital pin 12 (the “RedPin”) to HIGH. We can choose to set the output to HIGH or LOW. HIGH corresponds to a 5V output (or 3.3V on some Arduino boards other than the “Uno” model), and LOW corresponds to a 0 V output (which is essentially off).  Instead of digitialWrite(BluePin, HIGH), analogWrite(BluePin, brightness) can be used instead because PWM is supported on pin 6.  The variable “brightness” is an integer that is programmed using “for” loops to gradually increase from 0 to 225 and then gradually decrease from 255 to zero.  0-255 is the range of integer values that can be input to the analogWrite function.  At 0, the pin is the same as LOW, with a PWM duty cycle of 0%.  At 255, the pin is the same as HIGH, with a PWM duty cycle of 100%.  At intermediate values, the pin has an intermediate PWM duty cycle in proportion to the integer value. The pin is switched between LOW and HIGH hundreds of times per second to approximate an analog output, resulting in an intermediate power output.  delay(10) pauses for 10 milliseconds before increasing or decreasing the brightness Page 16 of 19

Figure P: Sample code which needs to be modified. 9. Modify the code to increase the time delay to 50 ms. 10. Modify the code to keep the Red pin consistently off. 11. (4) Copy and paste your code here. Describe the changes you have made and how/why they have changed the behavior of the circuit. Part 5 Examining RC Box and voltage divider circuits: 1. Construct the circuit below using on your breadboard using one 4.7KΩ resistor, 560Ω resistor, a BLUE LED, the RC Box and use the Arduino’s 5V power pin to power it. Page 17 of 19

The decade resistance box is an adjustable resistor where you adjust the resistance by rotating the appropriate dials. (The decade resistance box below has been set to 1,002,003 Ω). Figure Q: Decade resistance and capacitance both found on the lab table. 2. Set the RC Box to R = 4kΩ, C = 0F. 3. (2) Attach an image of your circuit board with the RC Box shown. 4. Increase the RC Box resistance value by increments of 1kΩ and report on your observations. 5. (2) Explain why you think these observations are taking place as you vary the resistance. 6. (1) Measure the voltage across the RC box and report on the measured voltage. 7. (4) Plug the RC box as in step 2 and determine the RC box resistance that will give a peak output voltage (voltage across the RC box), V out , of 2 V and report the RC resistance value here. Include a picture of your circuit and DMM on the lab table. Page 18 of 19

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Part 6: Clean Up and Check-Out with TA 1. Return all items to your kits (be sure to turn off your multimeter). Ensure all shared equipment, cables, etc. are returned to the original location for the next lab section to use. Turn off all equipment (oscilloscope, function generator, etc.) and log out of the computer. Check out with TA prior to leaving lab. Discussion Questions for Parts 2 and 4: 1. (6) Many old holiday lights in the USA would completely fail if one bulb in the string broke (i.e., if one light became an open circuit all lights would turn off). What does this say about the wiring of the bulbs – were they in series or parallel with each other? Why might the bulbs be connected in this way despite this disadvantage? 2. (6) Although cycling through PWM duty cycles can approximate an analog signal, there is one crucial difference. Explain. (You may use the internet to search if needed but must cite your references.) Page 19 of 19