Lab Report 6

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University of Illinois, Urbana Champaign *

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Course

212

Subject

Electrical Engineering

Date

Feb 20, 2024

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pdf

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5

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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 5% Actual resistor: 9.84 kΩ 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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