Capacitance Lab: Analyzing Charge Time & Circuit Behavior

UNIVERSITY OF COLORADO – COLORADO SPRINGS Capacitance Name: Abigail Salberg Objective The purpose of this lab was to determine how the resistance, capacitance and applied voltage affect the charge time, the maximum charge stored on the capacitor and the maximum current in the circuit. In this lab, we also defined capacitance and determined the functioning of a capacitator. Data and Calculations Part I: Measuring Capacitance 1.) Record your DMM data for later comparison. Resistance of 100Ω ‘Block’ as read by the meter = 99.5 Ω Value of 100µF Capacitor as read by the meter = 106.0 µF Value of 330µF Capacitor as read by the meter = 361.0 µF 2.) Paste an example one of your Voltage vs Time graph with all curve-fit information included.

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 3.) Record a copy of your V C curve-fit information for several trials. 100 µF Capacitor Curve-Fit Data Trial # A Value (V) B Value (s -1 ) 1 2.67 91.3 2 2.67 89.3 3 2.67 88.6 4 2.67 87.0 5 2.67 92.9 Average 2.67 89.82 330 µF Capacitor Curve-Fit Data Trial # A Value (V) B Value (s -1 ) 1 2.67 27.3 2 2.67 27.3 3 2.67 26.7 4 2.67 27.0 5 2.67 27.3 Average 2.67 27.12 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 = 99.5 Ω Value of 330µF Capacitor as read by the meter = 361.0 µF Curve fit equation for V c = 2.67(1-e^(-27.3(t+0.00190)))-0.00494 Curve fit equation for V R = 2.52e^(-27.3t)+0.002 2.) Attach a copy of your Voltage vs. Time graph with all curve-fit information. Capacitors - 2

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 Results and Questions Part I: Measuring Capacitance 1.) Restate important information for this circuit from fitting V C to an inverse exponential. Average value of ‘B’ for 100µF Capacitor = 89.82 s -1 Average value of ‘B’ for 330µF Capacitor = 27.12 s -1 Resistance of 100Ω ‘Block’ as read by meter = 99.5 Ω 2.) Explain how the ‘B’ value from the curve-fitting equation relates to the Capacitance and Resistance. Capacitors - 3

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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 V C = E ( 1 − e − t RC ) from “Background” V C = A ( 1 − e − B ( t − t o ) ) + C from Capstone Curve fit The ‘B’ value from the curve fitting equation is the inverse of the time constant. This makes it equal to B=1/RC 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 100µF Capacitor = 112.0 µF Experimental value of 330µF Capacitor = 371.0 µF 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 µF Capacitor a. What is 20% of 100 µF? Therefore, what is the ± 20% for the 100 µF capacitor? ±20% = ±20 µF b. What is the highest value the 100 µF capacitor could measure? 100 µF + 20% = 120 µF c. What is the lowest value the 100 µF capacitor could measure? 100 µF - 20% = 80 µF d. Did your measured value of the 100 µF capacitor lie within this ± 20% range? Yes, it was 112.0 µF, which is in that range Capacitors - 4 B = 1 RC C = 1 RB C = 1 ( 89.82 ) ( 99.5 ) C = 1 ( 27.12 ) ( 99.5 ) C 100 = 1.12 x 10 − 4 C 300 = 3.71 x 10 − 4

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 330 µF Capacitor a. What is 20% of 330 µF? Therefore, what is the ± 20% for the 330 µF capacitor? ±20% = ±66 µF b. What is the highest value the 330 µF capacitor could measure? 330 µF + 20% = 396 µF c. What is the lowest value the 100 µF capacitor could measure? 330 µF - 20% = 264 µF d. Did your measured value of the 330 µF capacitor lie within this ± 20% range? Yes, it was 371.0 µF, which is in that range 5.) Discuss why you think the manufacturer might have such large discrepancies. I think the manufacturer might have such large discrepancies due to the fact that there might be other factors influencing the voltage, so they “made room” for those factors. 6.) What does the ‘A’ value from fitting V C represent? It represents the saturation point of the voltage of the circuit 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’ V C = A ( 1 − e − B ( t − t o ) ) + C According to theory, the ‘C’ value should be zero. The experiment value of C is close to zero, as it is very small, but it is not exact. Part II: Voltage across the capacitor vs. Voltage across the resistor Capacitors - 5

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 Resistance of 100Ω ‘Block’ as read by meter = 99.5 Ω Value of ‘B’ for V C curve = 27.3 s -1 Value of ‘B’ for V R curve = 27.3 s -1 1.) Use the curve fit to V C to an inverse exponential to calculate the capacitance. C = 2.67 µF 2.) Use the curve fit to V R to a natural exponential to calculate the capacitance. C = 0.02 µF 3.) Are these values close to one another? Should they be? Explain. No, but they shouldn’t be because they are an inverse relationship 4.) Quantify your result by taking the percent difference between the values. % Difference = 197.03% Conclusion In conclusion, this lab was difficult , but it overall went well. I learned how the capacitance and resistance are related, as well as how they affect voltage and time. In part 1, the experimental values for the capacitators were within the accepted values. The capacitance values for Part 2 hav e a large percent difference, because they are an inverse relationship. Overall, much was learned. Capacitors - 6

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