Lab 4 Worksheet

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Worcester Polytechnic Institute *

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1120

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Physics

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Feb 20, 2024

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Worcester Polytechnic Institute Department of Physics Worksheet for Lab 4: Kirchoff’s Laws Name: Taylor Hamilton Section: PH1120-1121-B23 Partner: Ekta Patel and Efthymia Date: 12/6/23 Use this sheet to enter and submit your answers to the questions asked in the gray boxes on the Lab Instructions document. When you have completed this worksheet, save this file as a .pdf and upload the pdf to the canvas assignment associated with this lab. If you have any trouble converting to a pdf, please ask your Lab Instructor or Lab Assistant. Remember to use complete sentences and that these text boxes will increase in size as you add more content. Based on the data that you took today, write and answer the questions in the following sections. Remember that even though you will have the same data as your partner, the writing in these sections should be done individually. Tables and Raw Data Create tables for your data, use the tables that are included in the lab handout as a template for what columns to include. Table 1: Circuit 1 with calculated Voltage and Uncertainty Resistor Resistor uncertainty band Theoretical Voltage across that component Theoretical voltage uncertainty across that component 2V xx xx xx R1 = 51 Ω 2.55 1.363 V ± 0.01 R2 = 51 Ω 2.55 1.234 ± 0.01 R3 = 68 Ω 3.4 0.6782 ± 0.01 R4 = 68 Ω 3.4 0.3477 ± 0.01 Table 2: Circuit 1 with measured Voltage and Uncertainty Resistor Resistor uncertainty band Measured Voltage across that component Measured voltage uncertainty across that component 2V xx xx xx R1 = 51 Ω 2.55 1.215 ± 0.004692

Worcester Polytechnic Institute Department of Physics R2 = 51 Ω 2.55 0.8881 ± 0.004571 R3 = 68 Ω 3.4 0.4346 ± 0.004914 R4 = 68 Ω 3.4 0.4473 ± 0.004727 Table 3: Circuit 2 with calculated Voltage and Uncertainty Resistor Resistor uncertainty band Theoretical Voltage across that component Theoretical voltage uncertainty across that component 2V xx xx xx R1 = 51 Ω 2.55 1.0325 ± 0.01 R2 = 51 Ω 2.55 1.0046 ± 0.01 R3 = 68 Ω 3.4 0.4501 ± 0.01 R4 = 68 Ω 3.4 0.3335 ± 0.01 R5 = 10 Ω 0.5 0.05987 ± 0.01 Table 4: Circuit 2 with measured Voltage and Uncertainty Resistor Resistor uncertainty band (ohm) Measured Voltage across that component Measured voltage uncertainty across that component The voltage across the DC power supply 2V xx xx xx R1 = 51 Ω 2.55 1.161 ± 0.004508 R2 = 51 Ω 2.55 0.8503 ± 0.005187 R3 = 68 Ω 3.4 0.4051 ± 0.004061 R4 = 68 Ω 3.4 0.3921 ± 0.004530 R5 = 10 Ω 0.5 0.05133 ± 0.004201 Experimental Method 1. Redraw Figure 9: Why: A clear and accurate circuit diagram is crucial for understanding and replicating the experimental setup. It helps in visualizing the connections, ensuring correct assembly, and identifying the components involved. 2. Connect the Circuit as Shown in Figure 9: Why: Proper circuit connection is fundamental to the success of the experiment. Incorrect connections can lead to inaccurate readings, potential damage to equipment, or unsafe conditions. Following the diagram ensures the circuit functions as intended. 3. Adjust Power Supply to Output 2.0 Volts: Why: Setting a specific voltage is essential for controlled experimentation. It allows for standardized conditions and facilitates the measurement of voltage across resistors. Controlling the voltage helps in understanding the behavior of the circuit under specific parameters. 4. Measure Voltage Across Each Resistor: Why: The primary goal of the experiment is to measure voltage across specific resistors. This step provides valuable data for analysis. Recording the mean and standard deviation helps in assessing the variability and reliability of the measurements. 5. Repeat the Process for the Second Circuit (Figure 10): Why: Repetition enhances the reliability and validity of the experiment. Running the same procedure with a different circuit helps confirm the consistency of results and identifies any systematic errors or trends. It also allows for broader conclusions and generalizations. Data Analysis:

Worcester Polytechnic Institute Department of Physics Results Comparing theoretical calculations for each loop in the first circuit with Kirchhoff's Loop Laws, it's crucial to consider the consistency of the results with these fundamental principles. Kirchhoff's Voltage Law (KVL) states that the sum of electromotive forces and potential drops within any closed loop is zero. Therefore, when performing loop analysis, the calculated sum of voltages should align with this principle. Similarly, Kirchhoff's Current Law (KCL) asserts that the total current entering a junction must equal the total current leaving the junction. In the context of the circuit, theoretical calculations at junctions should adhere to this current conservation principle. If the theoretical calculations match the expectations set by Kirchhoff's Laws, it signifies a successful and accurate circuit analysis, reflecting the conservation of energy and charge. Any discrepancies between theoretical calculations and Kirchhoff's Laws would prompt a careful review of the circuit model, measurement techniques, or calculation methodology to ensure the accuracy and validity of the analysis. Conclusion 1. The theoretical calculations for each loop in the first circuit do not match Kirchhoff's Loop Laws or differ from the measured values, potential issues need attention. Errors in the circuit model, inaccuracies in measurements due to calibration problems or equipment limitations, uncertainties in component values and fluctuations in the power supply can all contribute to discrepancies. It's crucial to review the circuit model, validate component values, scrutinize measurement procedures, and ensure the validity of assumptions. Additionally, considering uncertainties in both theoretical calculations and measurements is important. Calibration of equipment and a thorough analysis of potential sources of error are essential steps to improve the accuracy of theoretical predictions and enhance the reliability of the experimental setup. 2. To address differences between theoretical and measured values in the circuit experiment, use more accurate tools, verify component values, and calibrate instruments regularly. Check wiring issues, experiment multiple times to identify consistent results, and explore different circuit setups. Refine the theoretical model by comparing it with alternative methods. Collaborate with peers or seek external input through peer review for valuable insights. These steps aim to improve experiment accuracy, refine models, and enhance overall understanding.

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