Lab 2 Report (2)

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Northeastern Illinois University *

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108

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Electrical Engineering

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Apr 3, 2024

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docx

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Erin Weisser: Skeptic Sophie Arostegui: Principal Investigator Shreyas Rajagopalan: Analyst Tara Pavithran: Analyst Lab 2: RC CIRCUIT INTRODUCTION For this week’s experiment, we will be measuring the capacitance of 22 µF capacitors and calculating the uncertainty measurements. To complete these objectives, we will utilize an RC circuit and calculate the capacitance values by determining the change in voltage across the resistor while turning the DAC output on and off. Since the charge and current of our circuit change with time, we found our values using the equation V(τ) = V0(1-e^-t/RC). This part of the process allows us to calculate the charging capacity of our capacitor, which should equal the nominal capacitance value of 22 µF. METHODS The RC circuit is created with four wires, a breadboard, a 10 kΩ resistor, and a 22µF capacitor. We connected the DAC output to the resistor and the GND output to the capacitor. The resistor was in series with the capacitor. We then used the A7 and A8 connections to monitor voltage points at V1 and V2. The DAC voltage was set to 2.0 V. Our uncertainty values will be calculating using the standard error equation below: The values in place of A,B,C etc. are the measured quantities of capacitance that our group calculated form the collected data.

We found τ by using the V(τ) = V0(1-e^-t/RC) equation, where τ was the time when V = V0e^-1. We first calculated V0e^-1, then looked on the charging graph to see at what point on the graph hit that voltage.

RESULTS In the figure below, the DAC was turned off until about 7s before it was then switched on between 7s and 18s on our graph below. The second graph shows the exponential decline of voltage after the DAC is turned off while the current continues through the circuit due to the charge of the capacitor. We ran 3 trials like this for the first part of data collection.

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The rest of the data tables are included in the Average Joe’s folder on Teams. Results Trial 1 (discharging) Uncertainty Trial 2 (discharging) Uncertainty Trial 3 (discharging) Uncertainty Time Constant (s) measured 0.25 0.01 0.25 0.01 0.23 0.01 Cap measured ( µF ) 25 25 25 τ = 0.25 ± 0.01 . (τ=RC) Final average capacitance: 24.333 ± 0.56 µF Average Capacitance error equation: DISCUSSION We found our capacitor to have a capacitance of 24.333 ± 0.56 µF. This is close to the nominal 22 µF. This value is similar to what other groups observed, as most groups got between 24-25 µF. Differences are likely due to standard error and material tolerances. Because our experiment yielded results that were in concordance with those of the rest of the class, it is likely that the difference in the expected value and the calculated value for capacitance is due to the device and how it measures capacitance. It could be that the sensor is inaccurate, or that the DAC output is not exactly what we had set it to.

UNCERTAINTY Since the circuit we created is real, our calculated values of uncertainty could have evolved from a number of factors. Some of the potential considerations our group considered is the fact that the capacitor may not have been fully charged by the time we collected our voltage values for some of the trials. It is also possible that the time constants that we extracted from the iOLab data were not completely accurate, as there was some level of estimation involved. It is worthy to note our uncertainty is very low, indicating that our results were consistent with each trial. CONCLUSION Using a circuit with a resistor and capacitor in series, we measured our capacitor’s capacitance to be 24 c. This is relatively close to the nominal 22 µF and consistent with the class average of 24.3 µF, which is also close to the expected value. We achieved this by observing change in voltage when the switch was turned on or off. The fact that our value was so similar to other groups’ observed values shows that manufacturing tolerance was consistent, but slightly above the nominal value.