PES 2150 Capacitance Report

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University of Colorado, Colorado Springs *

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2150

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Electrical Engineering

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Apr 3, 2024

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UNIVERSITY OF COLORADO – COLORADO SPRINGS Capacitance Name: Objective Your answer here (erase this!) Data and Calculations Part I: Measuring Capacitance 1.) Record your DMM data for later comparison. Resistance of 100Ω ‘Block’ as read by the meter = 99.31 Ω Value of 100 µ F Capacitor as read by the meter = 115 µ F Value of 330 µ F Capacitor as read by the meter = 347 µ F 2.) Paste an example one of your Voltage vs Time graph with all curve-fit information included. Alexa Dominguez The objective of this laboratory was to determine how to measure the capacitance of a capacitor In addition we need to understand its function Resistance capacitance and applied voltage can influence characteristics such as charge time maximumcurrent and maximum charge stored Understandingequivalent capacitance through the use of capacitors wired in a paralellseries Resistance capacitance and change in capacitance and evaluatingcurrent through the use of a curve fit equation via a circuit board and capstone program

P E S 2 1 5 0 - P H Y S I C S L A B O R A T O R Y I I Capacitors - 2 3.) Record a copy of your V C curve-fit information for several trials. 100 µ F Capacitor Curve-Fit Data Trial # A Value (V) B Value (s -1 ) 1 2.38 92.1 2 2.27 92.2 3 4 5 Average 330 µ F Capacitor Curve-Fit Data Trial # A Value (V) B Value (s -1 ) 1 2 3 2.22 91.2 2 41 92.8 232 91.7 2 32 92 I 2.57 26.9 2 43 2 8

P E S 2 1 5 0 - P H Y S I C S L A B O R A T O R Y I I Capacitors - 3 4 5 Average Part II: Voltage across the capacitor vs. Voltage across the resistor 1.) Record a copy of your V C and V R curve-fit information for one of the trials. Resistance of 100Ω ‘Block’ as read by the meter = Ω Value of 330 µ F Capacitor as read by the meter = µ F Curve fit equation for V c = Curve fit equation for V R = 2.) Attach a copy of your Voltage vs. Time graph with all curve-fit information. 2.50 26.9 2.63 27.0 2 59 26 96 99.31 347 2 5711 e 26.961 0.00 0.0724 2.54 e 1 26.94

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P E S 2 1 5 0 - P H Y S I C S L A B O R A T O R Y I I Capacitors - 4 Results and Questions Part I: Measuring Capacitance 1.) Restate important information for this circuit from fitting ࠵? ࠵? to an inverse exponential. Average value of ‘B’ for 100µF Capacitor = s -1 Average value of ‘B’ for 330µF Capacitor = s -1 Resistance of 100Ω ‘Block’ as read by meter = Ω 2.) Explain how the ‘B’ value from the curve -fitting equation relates to the Capacitance and Resistance. ࠵? ࠵? = ℰ (1 − ࠵? − ࠵? ࠵?࠵? ) from “Background” ࠵? ࠵? = ࠵?(1 − ࠵? −࠵? (࠵?−࠵? ࠵? ) ) + ࠵? from Capstone Curve fit 92 26.96 99.31

P E S 2 1 5 0 - P H Y S I C S L A B O R A T O R Y I I Capacitors - 5 Your answer here (erase this!) 3.) Use this ‘B’ value, from fitting V C to an inverse exponential, to find the capacitance for both capacitors. You will need the measured value of the resistor ‘block’ (in Ohms). Experimental value of 100 µ F Capacitor = µ F Experimental value of 330 µ F Capacitor = µ F 4.) Compare the capacitance from the previous question to the capacitance written on the capacitor with a percent error. Keep in mind that the value written on the capacitor is only guaranteed by the manufacturer to be within ± 20% of the actual value. 100 µ F Capacitor a. What is 20% of 100 µ F? Therefore, what is the ± 20% for the 100 µ F capacitor? ±20% = b. What is the highest value the 100 µ F capacitor could measure? 100 µ F + 20% = c. What is the lowest value the 100 µ F capacitor could measure? 100 µ F - 20% = d. Did your measured value of the 100 µ F capacitor lie within this ± 20% range? Show your work here! B relates to the curve fit equation because B 7 RC If B is known the equation Vlt At.enl Btltc.BA RCc 11RB JAPAN C 1 923 99.32 109.43 C 7 127 99 32 372.91 22 131 87.43

P E S 2 1 5 0 - P H Y S I C S L A B O R A T O R Y I I Capacitors - 6 Your answer here (erase this!) 330 µ F Capacitor a. What is 20% of 330 µ F? Therefore, what is the ± 20% for the 330 µ F capacitor? ±20% = b. What is the highest value the 330 µ F capacitor could measure? 330 µ F + 20% = c. What is the lowest value the 100 µ F capacitor could measure? 330 µ F - 20% = d. Did your measured value of the 330 µ F capacitor lie within this ± 20% range? Your answer here (erase this!) 5.) Discuss why you think the manufacturer might have such large discrepancies. Your answer here (erase this!) 6.) What does the ‘A’ value from fitting V C represent? The measured value ofthe 100 µ F capacitor does lie within the range 74.58 447.91 297.91 The values that were measured by the 330 µ F didlie within the 20 range Manufacturers may have large discrepancies due to outside factors playing a rolein the data Moisture inthe airor the dieleteirconstant can also affect the numbers These effects can lead to large discrepancies in data

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P E S 2 1 5 0 - P H Y S I C S L A B O R A T O R Y I I Capacitors - 7 Your answer here (erase this!) 7.) What should the ‘C’ value from the fitting of V C be equal to according to theory? Does the experimental value of ‘C’ correspond to theory? Hint: This ‘C’ ࠵? ࠵? = ࠵?(1 − ࠵? −࠵? (࠵?−࠵? ࠵? ) ) + ࠵? Your answer here (erase this!) Part II: Voltage across the capacitor vs. Voltage across the resistor Resistance of 100Ω ‘Block’ as read by meter = Ω Value of ‘B’ for ࠵? ࠵? curve = s -1 Value of ‘B’ for ࠵? ࠵? curve = s -1 1.) Use the curve fit to ࠵? ࠵? to an inverse exponential to calculate the capacitance. C = Units? 2.) Use the curve fit to ࠵? ࠵? to a natural exponential to calculate the capacitance. C = Units? 3.) Are these values close to one another? Should they be? Explain. Your answer here (erase this!) A represents the maximum amount of voltage on the capacitor When using the theory it should be equal to zero but experimentally 0.0026 was measured 99.31 27.0 26.8 C 7 27.0 99.31 372.94 µ FM C 1 99.31 26.8 375.72 µ F Yes the values are close to one another due to the fact thatthe voltage stays the same throughout the circuit

P E S 2 1 5 0 - P H Y S I C S L A B O R A T O R Y I I Capacitors - 8 4.) Quantify your result by taking the percent difference between the values. % Difference = Conclusion Your answer here (erase this!) 0.7010 The laboratory objective wasto understand how to measurecapacitance and understand how it works If ftp.otahiasyhdersetapansfgre.si stance capacitance and charge on capacitance and the evaluation of a curve fit equation using a When examining Part 1 B was determined to be an average of 92s Part 2 contained two separate B values The inverse exponential wasan average of26 96 and the natural exponential was found to be 26.9 After conducting 54 11 91 508 Hahahahah that The offginadro the weaptidante tag at os fnethrehEtfme ed compared It was determined that there was a 0.7 difference between them

P E S 2 1 5 0 - P H Y S I C S L A B O R A T O R Y I I Capacitors - 9

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