M. Conner Name: AP Physics C: RC Circuits Lab

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1 M. Conner Name: Date: Period: Equipment: breadboard jumper wires one 1 k, one 4.7 k, and one 5.6 k resistors one 1000 F, one 2200 F, and one 470 F capacitor one small alligator clip wire variable power supply Vernier differential voltage probe LabPro Mini interface for voltage probe Computer with LoggerPro software Purpose: Verify solutions for 1 st order circuits and equations for equivalent capacitance through realworld data. Methodology: Use the small alligator clip wire to make sure that all capacitors are discharged before starting. Plug the voltage probe into Channel 1 of the LabPro Mini interface. Make sure that the LabPro Mini is plugged in and connected to the computer. Log into the computer and start the LoggerPro software. If everything is connected correctly, then the digital display in the lower lefthand corner of the LoggerPro window should be showing the voltage being measured by the voltage probe. Go to the Experiment menu and click on Data Collection. Change the sampling rate to 20 samples/second and the duration to 20 seconds. Experiment #1 1. Build a simple series RC circuit (shown in Figure 1) on the breadboard, wiring the variable power supply to allow for a varying input voltage. Make sure that one side of the capacitor is connected to the low potential side of the voltage input. 2. Connect the black connector from the voltage probe to the low potential side of the capacitor, and connect the red connector to the high potential side of the capacitor, as shown in Figure 1. (Be sure to pay attention to the polarity of the capacitor indicated by the arrows on the side of the cylinder.) 3. Set the source voltage on the variable power supply but do not start it yet. 4. Click on the green Collect button in the middle of the main toolbar in LoggerPro. Allow the program to collect a few voltage values and then start the power supply. 5. Once the collection has ended, highlight the region of the graph where the capacitor was charging. Then, go to the Analyze menu and click on Curve Fit. a. Do an exponential curve fit (A*exp(Ct) B). Click Try Fit and then OK. b. Use the values associated with the curve fit to determine the time constant for the circuit. R C Figure 1: Basic RC Circuit

2 6. With the charging region of the graph still highlighted, go to the Analyze menu and do another Curve Fit. a. This time, do an exponential curve fit (A*exp(Ct) B), but click on time shift toward the bottom of the window giving the function A*exp(C*(t t 0 )) B. b. Be prepared to compare this curve fit to the previous fit. 7. Reset the maximum and minimum values on the vertical axis so that the graph takes up the majority of the window. Use the Print Screen function to capture a screenshot. Paste this image into a Word file (saving the Word file as you go). 8. Use the multimeter to measure the total voltage across the circuit and record this value. 9. Disconnect the power supply and use the small alligator clip wire to fully discharge the capacitor. (You can watch the voltage display in LoggerPro to see when the capacitor is discharged.) 10. Repeat steps 4 10 two more times using different voltage settings for the source. Experiment #2 1. Modify your RC circuit to include a resistor that is in parallel with the capacitor, as shown in Figure Repeat the steps 4 10 from Experiment #1. C Figure 2: RC circuit with a parallel resistance Experiment #3 This experiment is essentially Experiment #2 in reverse. In this experiment, the goal is to start with the capacitor fully charged and then collect the data while it is discharging. 1. Choose a voltage setting for the variable power supply and connect the circuit, allowing the capacitor to charge fully. Use the multimeter to measure the value of the source voltage for the circuit. 2. Click on the green Collect button in the middle of the main toolbar in LoggerPro. Allow the program to collect a few voltage values and then disconnect the power to the circuit. (Note that the capacitor will then discharge through, in Figure 2. Breaking the connection with the source takes out of the circuit.) 3. Once the collection has ended, highlight the region of the graph where the capacitor was discharging. Then, go to the Analyze menu and click on Curve Fit. a. Do an exponential curve fit (A*exp(Ct) B). Click Try Fit and then OK. b. Use the values associated with the curve fit to determine the time constant for the circuit. 4. Look at the columns of data to the left of the graph and determine the time when the voltage first began to decrease.

3 M. Conner 3 5. With the discharging region of the graph still highlighted, go to the Analyze menu and do another Curve Fit. a. This time, do an exponential curve fit (A*exp(Ct) B), but click on time shift toward the bottom of the window giving the function A*exp(C*(t t 0 )) B. b. Be prepared to compare this curve fit to the previous fit. 6. Reset the maximum and minimum values on the vertical axis so that the graph takes up the majority of the window. Use the Print Screen function to capture a screenshot. Paste this image into a Word file (saving the Word file as you go). 7. Disconnect the small alligator clip wire from the resistor. 8. Repeat steps 3 8 two more times using different source voltage settings. Experiment #4 1. Modify your RC circuit to include a second capacitor that is in parallel with the capacitor, as shown in Figure 3. (Be sure to pay attention to the polarity of the capacitor indicated by the arrows on the side of the cylinder.) 2. Repeat the steps 4 10 from Experiment #1. Figure 3: RC circuit with parallel capacitors Experiment #5 1. Modify your RC circuit so that the two capacitors are in series with each other and then in parallel with the second resistor, as shown in Figure Connect the black connector from the voltage probe to the low potential side of the branch containing the capacitors, and connect the red connector to the high potential side of the same branch, as shown in Figure Repeat the steps 4 10 from Experiment #1. Figure 4: RC circuit with series capacitors Experiment #6 4. Modify your RC circuit so that the two capacitors in series with each other are then in parallel with a third capacitor (and then in parallel with the second resistor), as shown in Figure Connect the black connector from the voltage probe to the low potential side of either capacitive branch, and connect the red connector to the high potential side of the same branch, as shown in Figure Repeat the steps 4 10 from Experiment #1. C3 Figure 5: RC circuit with series & parallel capacitance

4 PreLab: Select the resistance and capacitance values that you will use in each of the six experiments from the list of values provided in the Equipment section. 1. Experiment #1 Draw the circuit for Experiment #1, labeling the known values and charging. 2. Experiment #2 Draw the circuit for Experiment #2, labeling the known values and charging. 3. Experiment #3 Draw the circuit for Experiment #3, labeling the known values and discharging. a. Determine the initial voltage (just after the source is unplugged & the alligator wire is connected), final voltage, and the time constant. (For Experiments #4 #6, note that. C eq is the equivalent capacitance, and R eq is the equivalent resistance from the perspective of the equivalent capacitance.) 4. Experiment #4 Draw the circuit for Experiment #4, labeling the known values and 5. Experiment #5 Draw the circuit for Experiment #5, labeling the known values and 6. Experiment #6 Draw the circuit for Experiment #6, labeling the known values and

5 M. Conner 5 Analysis: Answer each question completely! Provide examples to justify statements that you make. 1. Provide a general comparison of the curve fits of the form ( ) to those of the form ( ) ( ). What is different? Why? What is the same? Why? 2. Compare the ( ) ( ) curve fit from each experiment to the equation you obtained for each experiment using the modeling method. Do the experimental results correspond to the theoretical results? 3. Discuss the differences that you found between the experimental values and the theoretical values for the time constants. Provide some reasons that you would expect to find differences (based on the last lab).

Lab 3: RC Circuits. Construct circuit 2 in EveryCircuit. Set values for the capacitor and resistor to match those in figure 2 and set the frequency to

Lab 3: RC Circuits. Construct circuit 2 in EveryCircuit. Set values for the capacitor and resistor to match those in figure 2 and set the frequency to Lab 3: RC Circuits Prelab Deriving equations for the output voltage of the voltage dividers you constructed in lab 2 was fairly simple. Now we want to derive an equation for the output voltage of a circuit