Lab 6

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Northwestern University *

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136

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Electrical Engineering

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Feb 20, 2024

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Page | 1 Interlude: Writing Workshop The purpose of this week is to support the writing of your first full lab report. After this workshop, you should be able to describe features of good and bad lab reports and apply the general lab rubric to the lab that you are documenting. What makes a good and bad lab report? 1.1 (5 points): (Peer discussion) What are elements or characteristics of the best lab report you can imagine? Use this space for recording your individual thoughts, interesting ideas from your lab partner, or notes about the class discussion of this question. 1.2 (5 points): (peer discussion) What are elements or characteristics of the worst lab report you can imagine? Use this space for recording your individual thoughts, interesting ideas from your lab partner, or notes about the class discussion of this question. How to apply the rubric 2.1 (5 points): (Peer discussion) Review the general lab report rubric (you can download it from Canvas). The rubric is written generally so that it applies to all of the labs that you will later turn A great lab report is characterized by clear and cogent writing that effectively communicates the underlying scientific principles. It would have a well-organized structure that guides the reader through the experiment and its outcomes. The report acknowledges all sources of information, ensuring appropriate citations are included. The writing style should be concise and precise, eliminating unnecessary jargon and focusing on the essential details. The report maintains a logical flow, providing clarity on the context and the processes used in the experiment. Lastly, the results are well-documented, with significant figures correctly used, ensuring the data’s accuracy and reliability. This combination of elements contributes to a comprehensive and insightful lab report. A good sign of this would be if someone who reads the lab report can follow it and repeat the experiment. A subpar lab report is characterized by unclear writing that does not effectively communicate the scientific principles at play. It lacks a coherent structure and logical flow, making it difficult for the reader to follow the method used. The report may contain plagiarized content and lack proper citations, undermining its credibility. The writing is often verbose, with extensive explanations that are not concise and include extraneous information. The report does not adhere to a consistent standard of significant figures, compromising the accuracy of the data presented. Furthermore, there is a lack of clarity about the experimental process, leaving the reader unsure about the methodologies employed. These shortcomings result in a lab report that falls short of academic standards.

Page | 2 into lab reports both in this and future quarters. How will these general guidelines and requirements apply to the specific lab that you are documenting? Use the space below for recording your individual thoughts, interesting ideas from your lab partner, or notes about the class discussion of this question. Plagiarism and citation style When you present someone else’s work as your own, you are plagiarizing their work. Plagiarism is a serious case of academic dishonesty. Matters of academic dishonesty are referred to Weinberg College’s Assistant Dean for Academic Integrity for investigation. To avoid being dishonest in this way, you should properly credit (cite) the original author of the work. One big challenge with plagiarism in an academic context is that different fields have different standards about what content needs to be credited and how to credit that previous work. Here’s what those standards are in the context of this physics lab. What should be cited: You should provide credit for work that someone else created and specific facts that aren’t common knowledge . This includes material from lab reports (which were created by your instructional team) but does not include laws of physics such as energy conservation and Newton’s 2 nd Law (which are considered common knowledge). How you should cite: There are many styles of citation: MLA, APA, Chicago, and IEEE to name the most common. If you are comfortable with one of those, you may use it. If you are unfamiliar with all styles of citation, we recommend providing information about the source of the material in a parenthetical as in the example below. For these lab reports, it is perfectly appropriate to cite encyclopedic sources such as Wikipedia as well as your physics textbook. Background information will be the history of Ohm’s law and the purpose would be to analyze real world situations and see if they match ohms law Any further background information -- Methods: Identifying the parts in our setup and how the experiment was planned, what each instrument was and what quantity was measured. The ammeter, voltage source, resistor, LEDs, Pasco Computer Interface and how they were setup to get appropriate readings and test our purpose statement Type of data analysis: plotting on Excel, using z scores and error estimation of -- Results: oexplai why using the results analysis methods we used was the right way to go about it, and describe the results and experimental process Present the Voltage and Current readings int a concise manner Analysis: Use z score to validate or invalidate your results

Page | 3 Example reference 1: Crown glass, for example, has an index of refraction of 1.52 (OpenStax University Physics, Volume 3, Section 1.1). Example reference 2: Figure 3 shows a photo of our experimental setup (Northwestern University PHYS 136-3, Lab 7: Atomic Spectra worksheet). 3.1 (5 points): (Peer discussion) With your lab partner, come up with one example of a situation where you think you would need a citation and one example of a situation where you think you would not need a citation. Record your two examples (as well as whether or not those situations require a citation) in the box below. (You may ask your TA if you are not sure.)

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Page | 4 Lab 6 : Ohm’s Law Introduction: This laboratory exercise embarks on an exploration of Ohm’s Law, a cornerstone of physics, which asserts that the current (I) flowing through a conductor is directly proportional to the voltage (V) across it. The constant of proportionality is the resistance (R), culminating in the equation 𝑉 = 𝐼𝑅 This law, named after the German physicist Georg Ohm 1,2 , was first published in 1827 . Ohm’s groundbreaking work laid the foundation for much of our modern understanding of electricity. The following experiment aims to validate this law by examining the behavior of a resistor and subsequently an incandescent bulb. We will measure the current and voltage across these components at varying input voltages. For the resistor, we anticipate a linear correlation between current and voltage, with the slope equivalent to the specified resistance value. This introductory segment is designed to provide some context and articulate the objectives of our experiment, offering an overview of our experimental apparatus. Methodology: Method I: Observing Potential vs. Current In the initial phase of our experiment, we use a setup consisting of a 1 kΩ resistor, a power supply, an ammeter, and a voltmeter, all connected to form a circuit as depicted in Figure 1(b). The power supply can deliver an adjustable input voltage ranging from -5V to 5V. The ammeter, connected in series with the resistor, measures the resultant circuit current in milliamperes (mA), while the voltmeter, connected in parallel with the resistor, gauges the voltage drop across the resistor terminals in volts (V). The ammeter , voltmeter, and battery voltage are controlled by Pasco’s 85 0 Universal Interface, with the “High Current Sensor” serving as the ammeter (A), the “Voltage Sensor” as the voltmeter (V), and “Output 1” supplying the battery voltage (VB). The experimental procedure for Method I is outlined as follows: 1. Assemble the circuit as illustrated in Figure 1(b), using the schematic from Figure 1(a) and the specified 1 kΩ resistor, power supply, ammeter, and voltmeter. 2. Configure the power supply to deliver an input voltage of -5V.

Page | 5 3. Utilize the voltmeter to measure and document the voltage across the resistor, and the ammeter to measure and document the current flowing through the circuit. 4. Gradually increase the input voltage in 1V increments from -5V to 5V, recording the voltage and current at each increment. 5. Compile the measured voltage and current values, along with the corresponding battery voltage values, in Table 1, located in the results section of this report. 6. Plot the voltage versus current data using the provided “line fit” Excel sheet. 7. Fit the plotted data to a straight line. The slope of this line represents the resistance, as per Ohm’s Law. 8. Compare the calculated slope with the expected resistance value to assess the validity of Ohm’s Law. Figure 1: diagrams of a simple circuit schematic (a) and a representation of the setup for Method I (b) (Northwestern University PHYS 136- 2, Lab 4: Ohm’s Law Lab Worksheet) Method II: Properties of Electric Meter This method aimed to examine the properties of both the electric meters we had present. The methodology for this experiment was bifurcated into two parts. Initially, with the setup as depicted in Figure 1(b), we removed the resistor and documented the readings from both the ammeter and voltmeter. This data was then utilized to infer the resistance of the voltmeter. Subsequently, the second part of the procedure necessitated the reinstallation of the resistor, with the voltmeter connected across the ammeter rather than the resistor. We were then tasked with

Page | 6 recording the voltage across the ammeter and the current flowing through it. Leveraging Ohm’s Law, we were then able to calculate the resistance of the ammeter. Method III: Observing Exceptions to Ohm’s Law We reconfigured the setup to mirror Figure 1(b) once again. This time, however, we substituted the resistor with either an incandescent lamp or a light-emitting diode (LED), making a note of which device is being utilized. With the chosen device installed, we replicated replicate steps 1-6, applying them to the lamp or diode in lieu of the resistor. As with Method 1, we started with a with a Battery voltage of -5V and incrementally increase it by 1V until you attain 5V. Construct a table encapsulating the Voltage across the lamp/diode (V) and the current (mA), along with the corresponding Battery voltage. This table should resemble to Table 2 in the results section of this report.

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Page | 7 Results: Method I: Observing Potential vs. Current The data analysis was conducted with precision and accuracy, adhering to the guidelines provided in the lab manual. The analysis involved determining the relationship between voltage (V) and current (I) for the selected resistor, which in this case was 1 kΩ . To carry out this analysis, we employed Ohm’s Law (V = IR), applying it to the data points recorded for each setting of the battery voltage. For every voltage value, we computed the corresponding current by rearranging the equation to I = V/R, where R is the resistance of the 1 kΩ resistor. The experimental results, encompassing both the directly measured and calculated values, are systematically presented in Table 1 below: Table 1: Potential difference vs. electric current observer for an electric resistor Battery voltage (V) Voltage across resistor (V) Current (A) -5.00 -4.95 -0.00488 -4.00 -3.97 -0.00389 -3.00 -2.97 -0.00290 -2.00 -1.99 -0.00191 -1.00 -0.99 -0.00092 1.00 0.99 0.00108 2.00 1.98 0.00207 3.00 2.96 0.00305 4.00 3.96 0.00404 5.00 4.943 0.00503 The above results were then plotted in a Excel, to obtain a distribution of results as well as a line of best fit.

Page | 8 Figure 2: Graph of Voltage (y-axis) vs Current (x-axis) Figure 2 shows a plot of the data in the table with a linear fit. The distribution of points shows a linear positive distribution, with a consistent gradient, which explains why the line of best fit intersects all the points. Ohm’s law states that the voltage equals the current times resistance (V= IR), with V and I being the Y and X values respectively and R being the slope of the graph. Plotting a linear graph would be assuming that the resistance is independent of current and voltage and that the voltage is proportional to the current with the proportionality constant being the resistance. Given all this, the graph does reflect Ohm’s law. This is because the slope is 997.52 ( Ω ) with an uncertainty of ±8.62 Ω which is convincingly close to 1kΩ . Determining that as per Method I, the Resistor is an Ohmic device (i.e., a device that follows Ohm’s law).

Page | 9 Method II: Properties of Electric Meter We utilized the setup outlined in Method 2, Part 1 to determine the resistance of the voltmeter. With the resistor removed and an input voltage of 5V, we observed an output voltage and an output current as follows: Table 2: Measuring Voltage and Current for a Voltmeter Input Voltage (V) Voltage Across (V) Current (A) 5.000 4.988 0.0009 This led us to using Ohm’s Law to calculate the resistance of the Voltmeter. Which was calculated as follows, manipulating V = IR to calculate the resistance: 𝑅 = 𝑉 𝐼 = 4.988 0.0009 ≈ 55𝑘Ω This result aligns with our expectations, as voltmeters typically exhibit high resistance, which would prevent much current from passing through and deliver accurate results for measuring potential differences. The calculated resistance of 55 𝑘Ω confirms this characteristic. Next, we aimed to find the resistance of the ammeter using the setup described in Method 2. Table 3 represents the results found: Table 3: Measuring Voltage and Current for an Ammeter Input Voltage (V) Voltage Across (V) Current (A) 5.000 0.045 0.005 With an input voltage of 5V, we recorded an output voltage of 0.0045V and an output current of 10.04 mA. Again, using Ohm’s law, we calculated the resistance as: 𝑅 = 𝑉 𝐼 = 0.045 0.005 ≈ 9Ω This result is also consistent with our expectations, as ammeters generally have a very low resistance, which is useful while trying to measure accurate current. The calculated resistance of 9Ω supports this understanding. Thus, our experiment successfully determined the resistances of a voltmeter and an ammeter, providing practical reinforcement of theoretical principles.

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Page | 10 Method III: Observing Exceptions to Ohm’s Law In Method 3 of our experiment, we substituted the resistor with an incandescent lamp and replicated the steps from Method 1. The results of our experiment are in Table 4 and Figure 3. Table 4: Potential difference vs. electric current observed for an Incandescent Bulb. Battery voltage (V) Voltage across resistor (V) Current (A) -5.00 -3.84 -0.118 -4.00 -3.01 -0.103 -3.00 -2.18 -0.086 -2.00 -1.37 -0.067 -1.00 -0.59 -0.044 1.00 0.58 0.044 2.00 1.36 0.067 3.00 2.17 0.086 4.00 3.00 0.103 5.00 3.83 0.118 Figure 3: Graph of Voltage (y-axis) vs Current (x-axis)

Page | 11 As depicted in the table and Figure 3, we observed a nonlinear relationship between the voltage across the lamp and the current, in fact, the shape of the points looks cubic on a purely observational level . This data does not appear to conform to Ohm’s law, as the distribution of points indicates a clear non-linear relationship between voltage and current. This is a deviation from the results of Method 1, where we used a resistor and observed a linear relationship. The non-linearity observed when the resistor was replaced with an incandescent lamp can be due to the differing electrical properties and behaviors of the lamp compared to a simple resistor. The main reason for this difference is that incandescent lamps exhibit non-Ohmic behavior. Unlike a typical resistor, where Ohm’s Law (V = IR) assumes that the resistance (R) remains constant over a wide range of voltages, the resistance of incandescent lamps varies with temperature, as is common physics knowledge. As current passes through the lamp, it heats up, causing its resistance to change. This variation in resistance with temperature is the key factor contributing to the non-linear relationship observed in our experiment. Thus, our experiment successfully demonstrated the non-Ohmic behavior of an incandescent lamp, providing a practical demonstration of this important electrical property.

Page | 12 Discussion: Method I: Method 1 Our experimental results align with the anticipations delineated in the introduction. We discerned a linear correlation between voltage and current for the resistor, as foreseen by Ohm’s law. The slope of 997 ± 8.62 V/mA corresponds to the specified resistance of 1 kilo ohm within uncertainties. This quantitative concurrence substantiates the applicability of Ohm’s law for this resistor over our measurement range of -5 V to 5 V. This is further corroborated by the extremely low Z-score value of 0.0 5 that we obtained, which suggests our slope is consistent with Ohm’s law as our Z-score is lower than 2. There are several potential sources of systematic error that could influence our measurements. The meters likely possess some internal resistance that modifies the actual circuit resistance. Any discrepancies in connecting the meters to the appropriate points in the circuit topology could also introduce errors. Resistance from the wires and connections in the breadboard may induce additional voltage drops. Fluctuations in contact resistance each time a connection is altered could lead to inconsistencies. Manufacturing tolerances on the resistor value directly affect the expected slope. The 5% tolerance on the 1 kilo ohm resistor dominates the uncertainty in the expected slope. The minor mismatch between observed and expected slope of 997 V/mA versus 1000 V/mA is only about 0.3%, well within the resistor tolerance. This indicates that the systematic effects are minor relative to the resistor uncertainty for this experiment. In future experiments with more precise reference components, these systematic factors would become the limiting errors. To enhance the experiment, we could employ higher precision meters and calibrate them to quantify their internal resistances. Measuring a set of standard resistors spanning a wide range of resistances would characterize any issues stemming from the breadboard and connections. Repeated trials would identify inconsistencies from contact resistance variations. Incorporating multiple trials into the analysis could reduce the statistical uncertainty. Modifying the circuit topology could potentially minimize voltage drops from unwanted resistances. These modifications would allow testing Ohm’s law to much higher precision. Method 2: To gain a deeper understanding of the potential uncertainty introduced by the internal resistance of the meters, which could alter the actual circuit resistance, we employed Method 2. This method allowed us to calculate the internal resistance of both the voltmeter and the ammeter. As anticipated, we found a relatively high resistance for the voltmeter and a comparatively low resistance for the ammeter. These findings not only align with our expectations but also enhance our understanding of the accuracy of our results in Methods 1 and 3.

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Page | 13 Like Method 1, potential sources of error in this method could stem from the internal resistance of the wires and the breadboard, which could have influenced the resistance values we calculated. By acknowledging these potential sources of error, we can better interpret our results and understand the limitations of our experimental setup. This awareness is crucial for the accurate analysis and interpretation of our findings. Method 2: When we substituted the resistor with an incandescent lamp. Initially, as per the introduction, we anticipated a linear relationship between voltage and current, in accordance with Ohm’s Law (V = IR). However, our observations with the incandescent lamp deviated from this expectation. This deviation was substantiated by the numerical results. The nonlinearity marked a clear divergence from the behavior predicted by Ohm’s Law. As we increased the voltage, the lamp’s resistance did not remain constant, leading to a departure from the expected linear trend and the trend observed in Method 1. The non-linearity observed in our experiment with the incandescent lamp can be ascribed to several systematic errors stemming from the experimental design. A key source of systematic error is the temperature- dependent resistance of the lamp’s filament. As the lamp heats up due to the passage of current, its resistance alters. This change in resistance with temperature introduces a systematic effect that disrupts the expected linear relationship. The systematic effect, resulting from the temperature-dependent resistance of the incandescent lamp, significantly modifies the outcome of our experiment. As the lamp’s temperature rises, its resistance increases, leading to a modification in the voltage-current relationship. This effect was clearly manifested in our data, as the lamp’s resistance varied with temperature, causing a non - linear response, as clearly depicted in Figure 3. To alleviate the sources of systematic error identified in our experiment, it would be necessary to consider alternative components or setups that do not exhibit temperature-dependent resistance. An improvement could involve using more specialized resistive elements designed to maintain a consistent resistance over a wide range of temperatures. Additionally, employing digital components with well-defined characteristics could minimize the impact of temperature variations on the resistance, thereby producing a more linear relationship between voltage and current.