Lab Report 6

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University of Illinois, Urbana Champaign *

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212

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Electrical Engineering

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Feb 20, 2024

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pdf

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Kitchen Sink L4M Names & NetID: Ravyn Edran (redran2), Josh Frye (jcfrye2), Aidan Stahl (ahstahl2), Tuna Tuncer (ttuncer2), & Zhengze Cao (zhengze2) 05 October 2023 LAB REPORT 6 Group Goal: Give more people a chance to perform the experiment & ensure everyone has an understanding of the procedure. Communicate and balance the workload better. Introduction: The goal of this experiment is to study how the labeled capacitance differs from the measured capacitance & determine the uncertainties. We are measuring the uncertainty of the capacitance. We used a multimeter and the IOLab to measure and compare the capacitor to its written value. Methods: We found the voltage before and after the resistor in the circuit. Using 2.5V for the DAC settings, we turned it on to charge the capacitor. We measured the resistance in a 10kΩ resistor using a multimeter to determine the true resistance value. We found the uncertainty of this measurement using the data from the multimeter calibration. Using the graph of the voltage we can calculate the time constant using the difference in two voltages and the time it takes for said voltage drop to occur. This allows us to calculate the capacitance using the time constant and the resistance. The uncertainty in the time measurement was

found from the inverse of the sampling rate of the IO lab halved because it measures two data points at that time. The capacitors & resistors would be the main source of uncertainty, as well as the IOLab. 𝑉(𝑡) = 𝐴𝑒 − 𝑡 τ Charging capacitor: 𝑉 2 = 𝑉 𝑡=∞ (1 − 𝑒 − 𝑡 τ ) Discharging capacitor: 𝑉 2 = 𝑉 𝑡=0 𝑒 − 𝑡 τ τ = 𝑅𝐶 𝑉 1 − 𝑉 2 = 𝐼𝑅 Results: Iolab data, graphs, graph interpretation, uncertainties, results of calculations 22 → 23.25 22→23.252 56 → 59.4 56 → 59.28 𝐶 ± δ𝐶 Raw & calculated data 𝐶 ± δ𝐶 ⇔ δ𝐶 𝐶 = ( δ𝑅 𝑅 ) 2 + ( δτ τ ) 2 Theoretical resistor: 10 kΩ 土 5% Actual resistor: 9.84 kΩ 土 0.1 Theoretical capacitance: 22μF Theoretical capacitance (μF) Actual capacitance (μF) Uncertainty (μF) 1 22 26.26 1.32 2 55 59.37 .61

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Discussion: When we measured the resistance with a multimeter we saw that it was lower than it was supposed to be. When we measured the uncertainty of the multimeter when it comes to resistance we found that it is +/-0.1, we found that our resistance was 9.84 when it should have been 10. This means it was still out of the range that it should be, this does not change our results, however it should still be noted. To find capacitance we measured the voltage drop of our system when the DAC was on and when it was off to see the voltage drop due to the capacitor. This allowed us to determine the time constant. We found the initial voltage once the capacitor was fully charged, then we picked a point at random after the DAC was turned off and the capacitor was discharging. Using the voltage at this random point and the change in time to get to this point we found the time constant. We found the uncertainty in this time constant from the sampling rate constraint of the actual IO lab. We averaged the uncertainties together using the percent uncertainty equation provided. We then found the capacitance using the time constant and the resistance from the resistor in the system. We used this value to change the percent uncertainty into the absolute uncertainty by multiplying our capacitance by the percent uncertainty. The final value for our capacitance for the 22μF was 26.26+/-1.32 and for our 56μF capacitor was 59.37+/-0.61 Conclusion: In this lab, we tested the uncertainty of capacitance across one 22 μF capacitor and one 56 μF capacitor. We did this by measuring the voltage across each capacitor separately when they were in series with a 10,000 Ohm resistor. We then zoomed in on the graph at the point where the capacitor was discharging and we took the time and voltage at the point when it started discharging. Then we found a random point on the discharge graph and took the time and voltage at that point. We used the time constant equation for a discharging capacitor and solved for T (tau). We then used the equation T = RC and divided T by R to find the capacitance. Furthermore, we found the uncertainty of the resistor, the multimeter, and the time constant based on the IOLab’s sampling rate and used the uncertainty equation to average these uncertainties together and calculate the total uncertainty value for each capacitor. Our findings showed that the capacitance that we calculated for both the 22 μF capacitor and the 56 μF

capacitor was higher than the capacitors’ theoretical capacitances. We also found that the uncertainty for the 22 μF capacitor was 1.32 μF and for the 56 μF capacitor was 0.61 μF.