RC decay group results

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George Mason University *

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246

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Electrical Engineering

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Apr 3, 2024

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RESULTS Group Lab Report * Title of Experiment: RC Decay Date: 02/28/2024 Class, Section & Lab group: PHY 246-2D2, Group 10 Recorder (consolidates report and submits into dropbox): Mariam Sabah Group Members PRESENT Rebecca Turcios, Youssef Haddi * Before beginning, save this report on your desktop with the Recorder's last name appended.

1. Predict the time constant τ = RC from the given values of the circuit elements R and C. Note that R is the total circuit resistance. Rv, R1, and C are listed in Table 1. Record the value in your notebook. Req = 10+10=20 Ω T=20M Ω(1.0uF) = 20s 2. Create a graph of the measured voltage values. Plot time on the x-axis and voltage on the y-axis.

3. In your graph insert an excel trendline and display the equation. Determine RC from the trendline

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Equation. V1: RC=1/.043= 23.2558 sec. for V2: RC=1/0.043= 23.2558 sec for V3: RC=1/.044= 22.7272 sec Predicted Value for V1 23.2558 seconds Predicted Value for V2 23.2558 seconds Predicted Value for V3 22.7272 seconds 4. Pick the half-time t1/2 off your graph to calculate the time constant. Use equation 4. V1 RC=23.2558 sec. 27 sec. / 23.2558 sec.= 1.16 for V2: RC=23.2558 sec 27 sec. / 23.2558 sec.= 1.16 for V3: RC=22.7272 sec 27 sec. / 22.7272 sec. = 1.18 5. create a new graph. Plot lnV vs. time. Is the resulting graph linear? Refer to equation 5 and calculate a value for RC from the trendline equation of the graph. Perform a linear regression on the data to determine the uncertainty in RC.

The resulting graph is linear as shown. For trial 1, RC = -1/-0.0431 = 23.20 sec. For trial 2, RC = -1/- 0.0435 = 22.98 sec. For trial 3, RC = -1/-0.044 = 22.73 sec. The uncertainty for RC in trial 1 is 0.02%. For trial 2, the uncertainty is 0.02%. Finally, for trial 3, the uncertainty is 0.01%. 6. You have now determined the time constant RC with different methods. Compare these time

constants. Which method is the most accurate one? The RC value that is the most accurate is the calculation from the average voltage versus the trendline. However, the lnV slope was not that far behind. The Half time calculation was the furthest from the predicted values, therefore, it was the least accurate method to calculate RC. 7. Calculate the uncertainty in the predicted value of the time constant. Assume the uncertainty of Rv to be 1%, of R1 to be 5% and of C to be 5%. Show all steps in the uncertainty calculation. = 1+ 5 +5 = 11% Uncertainty = Sqrt(0.01^2+0.05^2) = 5.099 Total uncertainty = Sqrt(5.099^2+5^2) = 7.14% Error Analysis Inaccuracies might have occurred if the voltmeter readings were not precisely recorded due to human error in this lab. Incorrect circuit assembly and/or connections could have also led to inaccurate readings. Summary and Conclusion In the experiment, the constant for time in an RC circuit was measured to recognize capacitor behavior. The time constant for the circuit was calculated as 20 seconds with the total circuit resistance 20 ohms multiplied by the circuit capacitance, 1.0 uF. With the data provided in the excel a graph was plotted for voltage on the y-axis and time on the x-axis, and the provided trendline equation was used to find RC and time constant. The RC of trial 1 voltage was 23.2558 seconds, and the time constant was 1. 16 . The RC of trial 2 voltage was 23.2558 seconds, and the time constant was 1. 16 . The RC of trial 3 voltage was 22.727 seconds, and the time constant was 1. 16 . A second graph was created plotting ln voltage on the y- axis to time on the x-axis. The graph was linear and had the RC values of 23.2. sec for trial 1, 22.98 sec for trial 2, and 22.73 sec for trial 3. Applying a linear regression to the data determined the RC uncertainty in trial 1 was 0.02%, in trial 2 it was 0.02%, while in trial 3 it was 0.01%. It was concluded the most accurate RC value was the one calculated from the average voltage over the trendline, but both values were very similar. The greatest difference was the half-time calculations which did not reflect the predictions thus making them an inaccurate representation of RC. Finally, with the provided uncertainty values of Rv, R1 and C the uncertainty was determined to be 5.099, with a total uncertainty of 7.14%.

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