Lab 7_ RC Circuit

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City College of San Francisco *

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Electrical Engineering

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Dec 6, 2023

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Lab 7: RC Circuit Willem Brotha Deborah Harris 10/5/2023 Abstract: In this lab we studied the time behavior in charging and discharging a capacitor. The instruments used were similar to those of previous labs such as a power supply, oscilloscope, capacitor, RC circuit board, function generator, and Logger Pro software. Procedure: In part 1 of the lab we were tasked with measuring the long time constant on the oscilloscope. After plugging in our RC Circuit board to the power supply and oscilloscope, we turned our voltage up to 8.0V. We then charged and discharged the capacitor and observed that the line on the graph curved upward indefinitely. Beginning our experiment we charged our RC circuit board and observed that the graph created an upward line indicating charge. Noticing that our graph did not line up exactly on 0 seconds we started logging our data from -2 seconds and adjusted the remaining values accordingly. We simultaneously logged our voltage by increasing our horizontal knob on the oscilloscope 1.2 seconds and recorded the values. Furthermore, we discharged the capacitor and noticed that the line on the graph curved downward indefinitely indicating that the capacitor was now discharged. We then repeated the steps for charging by logging our results. After recording the values in the graphs below we utilized the Python program to perform a linear fit. Using the function np.log() we took the natural log of our y-axis data for discharge and used the equation ln VC = ln V0 - t/RC to find the value and error of time constant RC. This resulted in a slope of -0.36854078873715923, which is equal to the negative inverse of our time constant. We proceeded to create another plot with our values for charge and discharge on the same graph where they cross at time T ½. We found that the two graphs intersect at a time of 1.74s and Voltage of 4.42 giving us T ½ =1.74s. Using equation 2 from the lab manual we found the time constant of RC as 2.51 ± 0.0069s. Finally we compared our values of RC constant with the values of RC using the individual values of R & C. The actual values of R&C and R=220Ω and C=0.01F, giving us a theoretical value of 2.2 ± 0.0102s. Experimental Data: Our recorded voltages and their corresponding times are shown in the following two data tables. Table one shows the voltages over time when we charged the circuit, and table two shows the voltages over time when we discharged the circuit. Charge:

Time ± 0.001 (seconds) Voltage at Time T ± 0.001 (V) 0 0.160 1.200 3.360 2.400 5.600 3.600 6.560 4.800 7.200 6.000 7.600 7.200 7.760 8.400 7.840 9.600 7.920 10.800 8.000 Discharge: Time ± 0.001 (seconds) Voltage at Time T ± 0.001 (V) 0 8.080 1.200 5.600 2.400 3.040 3.600 1.840 4.800 1.120 6.000 0.800 7.200 0.480 8.400 0.320 9.600 0.240 10.800 0.160 Data Analysis: We can find the time constant value of a circuit using the equation Tau = RC where R is resistance and C is the capacitance of a capacitor. This Tau value, otherwise known as the RC value, can be found through three different methods. The first method involves calculating the

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