ME348_S24_Lab2 (1)

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Pennsylvania State University *

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Feb 20, 2024

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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

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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