Lab Report 1

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Northeastern Illinois University *

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108

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Electrical Engineering

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Apr 3, 2024

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Erin Weisser Sophie Arostegui Shreyas Rajagopalan Tara Pavithran LAB 1 REPORT – AVERAGE JOE’S INTRODUCTION Today’s lab is focused on designing two experiments that will observe and test the relationship of ΔV/R for resistors as well as the Loop Rule. The Loop Rule states that the sum of all ΔV in a circuit is zero. In order to study the behavior of currents in a circuit with different resistors, we will experiment with different voltages and measurements along the circuit. In part one of this lab, we will set up a one loop circuit with two resistors and see how their ΔV/R ratio compares to one another at different voltages. We hypothesized that both resistors would have the same ΔV/R ratio because they are attached to the same circuit. For the second part of this experiment, we will test the Loop Rule Hypothesis by setting up a Two-Loop Circuit and record the ΔV at different resistors to test if they will add to zero. METHODS Introductory Lab: 1. Insert one end of a wire into the IOLab device into the A7 sensor, this will be used to read the voltage of the circuit at different points. 2. Using the IOLab software, change the DAC voltage to test different current strengths within the circuit. 3. In your bread board, place two resistors and connect them in the circuit by putting one end of both resistors next to the other within the same row, to ensure the flow of electricity is continuous. 4. Connect one red wire into the DAC sensor of the IOLab and connect the opposite end by clipping it to one end of one of the resistors. 5. Connect one black wire into the GND sensor of the IOLab and connect the opposite end by clipping it to one end of the other resistor to complete the circuit. a. For the purposes of this experiment, we assumed GND is set to zero volts. 6. Find the ratio of ΔV/R for each resistor. 7. Calculate the average ΔV/R ratio using the sensor data from the IOLab software.
Part 2: 1. In part 2 of the lab, we will be testing the hypothesis of the Loop Rule which states that the sum of voltage differences around a circuit is equal to 0. 2. We will collect our ΔV/R values by testing different resistors within a Two-Loop Circuit by following steps 3-7 from the introductory lab methods. a. Since resistors were verified to be accurate in the first part of lab, they are assumed to be accurate here too, and were not checked again. 3. Adjust the DAC voltage using the IOLab software. 4. Collect voltage data within the IOLab software. 5. Collect the data again with a voltmeter.
RESULTS Lab 1 IOLab Data Table Checking resistances: Resistance Observed Resistance ( kΩ) 33.3 33 *1 14.8 15 * 1 DAC Voltage (V) Voltage 1 (V) Voltage 2 (V) 15 ( kΩ) Resistor Ratio ( ΔV/R1) Voltage 1 Voltage 2 33 ( kΩ) Ratio ( ΔV/R1) 1.8 1.7896 1.2385 0.037 1.2381 0 0.038 2.1 2.1118 1.4606 0.043 1.4606 0 0.044 3.2 3.1685 2.1915 0.065 2.1916 0 0.066 Average -- -- 0.0483 ± 0.00849 0.0493 ± 0.008571 Lab 2 Data Table Part 2 FIRST LOOP DAC Voltage (V) Resistor 1 Initial (V) Resistor 1 Final (V) Resistor 2 Initial (V) Resistor 2 Final (V) Resistor 3 Initial (V) Resistor 3 Final (V) Sum of ΔV 1.8 1.7900 0.8724 0.8723 0.6096 0.6095 0 -- Difference ΔV (final – initial) iOLab 0.918 0.263 0.609 1.8 Difference ΔV (final – initial) Voltmeter 0.92 V 0.26 V 0.61 V 1.8 SECOND LOOP DAC Voltage (V) Resistor 4 Initial (V) Resistor 4 Final (V) Resistor 5 Initial (V) Resistor 5 Final (V) Resistor 6 Initial (V) Resistor 6 Final (V) Resistor 2 Initial (V) Resistor 2 Final (V) Sum of ΔV 1.8 0.8725 0.7771 0.7774 0.7253 0.7253 0.6095 0.6093 0.8724 -- Difference ( ΔV) – iOLab 0.102 0.0521 0.143 -0.263 0.03
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Difference ( ΔV) – Voltmeter 0.09 0.04 0.11 -0.25 0.01 WHOLE TWO-LOOP CIRCUIT DAC Voltage (V) Resistor 1 Initial (V) Resistor 1 Final (V) Resistor 4 Initial (V) Resistor 4 Final (V) Resistor 5 Initial (V) Resistor 5 Final (V) Resistor 6 Initial (V) Resistor 6 Final (V) Resistor 3 Initial (V) Resistor 3 Final (V) Sum of ΔV 1.8 1.7906 0.8724 0.8723 0.7772 0.7776 0.7253 0.7255 0.6095 0.6093 0 -- Difference ( ΔV) - iOLab 0.918 0.0951 0.0523 0.116 0.6093 1.79 Difference ( ΔV) - Voltmeter 0.92 0.09 0.04 0.11 0.61 1.77
DISCUSSION In the first experiment, the average ratio for the first resistor was 0.0483 V/ kΩ, and the average ratio for the second resistor was 0.0493 V/kΩ. The ratios are approximately the same, with negligible errors. Since they are connected to the same circuit, voltage is constant throughout the conductor. In the second experiment, we analyzed voltages for each individual circuit and then the entire circuit. The hypothesis we formulated was the sum of voltages changes across all elements in a closed circuit is zero. Based on our results, in Loop 1, Loop 2, and the whole loop, the sum of the ΔV read by the IOLab and voltmeter minus the supply voltage was 0. This means that the energy is conserved across the entire circuit and that our results agree with the hypothesis. Uncertainty The standard errors that exist from the data we collected during lab could be the result of small discrepancies between each trial. Some of the factors that may have played a role in these variations could be due to the resistors we had in class, as they have been used multiple times before and may not all function at the same capacity. In the same regard, the battery used in our experiment may be imperfect as well. Both imperfections would lead to a change in observed voltage. In addition, we also consider human error (such as accidentally touching the resistors during data collection) to be a possible source of these deviations. These are all possibilities that could act as a source for potential error. However, although standard error does exist, our data table above supports that our results are significant as they are within the 95% confidence interval. CONCLUSION In the first experiment, we tested the hypothesis that the ratio of voltage to resistance is constant regardless of the value of each resistor and at different voltages. The ratios for each resistor were approximately equal, showing that this is true. The hypothesis that the ΔV/R ratios would be the same is supported by the data collected. In the second experiment, we tested the hypothesis that the sum of all voltages across each circuit totaled to 0. We found that this was the case, which is in accordance with Kirchoff’s Law and supports our initial hypothesis. In future experiments, we could test for differences in voltage with different kinds of batteries or resistors to test how that changes any properties of the circuit. To further improve the experiment, we could run more trials to minimize error.