rc circuits

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School

University of Pennsylvania *

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Course

151

Subject

Electrical Engineering

Date

Apr 3, 2024

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pdf

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Uploaded by SargentExploration17421

Emily Paul, Sophie Goldman, Colin Hall * Data courtesy of Jake Fanale, Cindy Yang, Alexis Powell, because our circuit didn’t work, even after TA verification and switching out the capacitor, the resistors, and the switchboard. We did all of the analysis and the writeup with their data. We later switched to another lab table with functional equipment so we could run an iteration ourselves, and the numbers and plots from that run are attached at the bottom. 1. What are your calculated time constants for charging and discharging? Capacitor capacitance: 26000 MFD = 0.026 F For charging: R = 318.2, C = 0.026 tau = RC = 8.27s For discharging: R = 1241, C = 0.026 tau = RC = 32.27s 2. Attach plots of the charging/discharging curves including fits. Label the resistances for each curve. Run 1 Charging: Resistance = 318.2 Ohms Calculated capacitance = [1/0.1057] / 318.2 = 0.0297320488 Farads Run 1 Discharging: Resistance = 1241 Ohms Capacitance calculation: [1/0.02698] / 1241 = 0.02986663353 Farads 3. What are your new calculated time constants for charging and discharging? Capacitor capacitance: 26000 MFD = 0.026 F For charging:

R = 145.7, C = 0.026 tau = 3.7882s For discharging: R = 1500, C = 0.026 tau = 39.0s 4. Attach plots of the charging/discharging curves including fits. Label the resistances for each curve. Run 2 Charging: Resistance = 145.7 Ohms Calculated capacitance = [1/0.2217] / 145.7 = 0.0309581325 Farads Run 2 Discharging: Resistance = 1500 Ohms Capacitance calculation: [1/0.02229] / 1500 = 0.02990877822 Farads 5. Make a table that lists all of your resistances and your measured values of capacitance C. Resistance (Ohms) Measured Capacitance (F) 318.2 0.0297320488 1241 0.02986663353 145.7 0.0309581325 1500 0.02990877822

6. Do your capacitance values match across all chargings and dischargings? If not, what could be causing the discrepancy? Do your capacitance values match with what is labeled on the side of the capacitor? Yes, they are all very close to each other, with an average of 0.03011 F in comparison to the ground truth of 0.026F. We’re not accounting for the resistance in the wires which is likely causing the discrepancy between the several charges/ discharges. 7. What was the maximum charge 𝑄 )*+ stored on each capacitor? How many electrons does this correspond to? The charge of an electron is 𝑒 = 1.6 × 10^-16 C. The average capacitance value was 0.0301163982625 F. Thus using Q(t) = CV(t) and that the voltage of the battery is 5.18 volts. The maximum charge is 0.15600294299974998 C. This corresponds to 9.74 x 10^17 electrons. 8. In a brief paragraph, summarize this lab. You should include a summation of the major themes of the lab, as well as brief descriptions of your procedures, analytical methods, all relevant quantitative results, and your conclusions. Also check that all graphs are included and your report is in the correct order. The RC Circuits lab explores the dynamics of how capacitors charge and discharge in electrical circuits, emphasizing the role of resistance and capacitance. Throughout the lab, we constructed circuits to observe real-time charge flow in capacitors, employing a voltage source, resistors, and capacitors to set up experiments for charging and discharging phases. Unfortunately, we were unable to form the circuit. We tried to fix it by using different capacitors, light bulbs, switchboards, and the voltmeter, but there was no progress so we were able to use data from a different group. After completing part of the lab with the other group’s data, we were able to use a different set up to calculate values of our own, the graphs of which are listed below this report. The analytical part of the lab involved monitoring voltage across the capacitor using a differential voltage probe and Logger Pro software, from which charge flow patterns were deduced. By fitting exponential curves to the observed voltage-time data, we calculated the RC time constants for different setups, further using these to determine the capacitance of various capacitors. We found with the different resistors that the capacitance did not change much aside from one resistance which may have been due to factors like the resistance in the wires. Quantitative results from these experiments allowed us to understand the relationship between resistance, capacitance, and the rate at which capacitors can store or release charge through the exponential function curves. The lab underscores the practical application of capacitors in circuits, showcasing their ability to store electrical energy and the factors influencing their charging and discharging rates.

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