AP Physics Lab – Capacitors and RC Circuits

Purpose

Charging and discharging behavior of capacitors will be explored using various values for voltage, resistance, and capacitance.  The theoretical voltage and current functions of time will be verified, as will the defining relation between capacitance, charge, and voltage. 

Procedure

Voltage and current for the capacitor will be measured with Logger Pro 3.  The Vernier circuit board will be used as a power supply and switching device.  The Pasco circuit board will supply the various resistors and capacitors needed for R and C.  Construct the following circuit using appropriate connectors.  Note: the small numbers in the schematic correlate with those found on the Vernier Board.  Connect the current and voltage probes so that both will read positive values when the capacitor is charging.  (The probes are shown as an ammeter and a voltmeter in the schematic.)  Switch SW1 selects which battery is in use and switch SW2 selects for charging or discharging the capacitor.

Connect the voltage probe to channel 1 and the current probe to channel 2 of the Lab Pro interface and connect the interface to the computer using the USB cable.  Open the file “RC Circuit” in Logger Pro 3.

You should see live readouts of the sensors.  You can try flipping the switches in the circuit to check for proper operation.  Before proceeding you should zero both sensors by connecting a wire across the inputs of each sensor to ensure that the current and voltage are each truly zero and then click on the Zero button in Logger Pro.  This is similar to the Tare button on an electronic balance.

Capacitor Charging

Use switch SW1 to select the external 6-volt battery.  Use the 330 μF capacitor and the 100 W resistor.  The file is set up to record the charging of a capacitor.  Initially the trigger is a voltage increasing across 0.05 V, which means that the computer will collect data when the voltage is greater than 0.05 V after being less than 0.05 V.  Simply click on the Collect button and then flip the switch SW2 to charge the capacitor.  If all goes well you should be able to produce smooth curves showing the increasing voltage and the decreasing current for the capacitor.  (Tip:  select a graph and click Autoscale to get a good view of all the data).  If you do not have a sufficient amount of data to show the complete charging process you may need to adjust the number of pre-Trigger points or duration of the experiment (under Experiment, Data Collection…).

If you cannot produce graphs:  check all connections, make sure the sensor is connected to register a positive voltage, make sure the capacitor is initially completely discharged.  Also check the triggering settings and modify if necessary.

Data and Curve Fits

Use the analysis tools of Logger Pro to complete the appropriate parts of your data table.  Note:  Pages 2 and 3 of the Logger Pro file have larger versions of the same graphs so you can see better details.  Charged voltage can be found by using the Statistics button to find the mean value of the “final” charged voltage attained by the capacitor (select the “plateau”).  Stored charge can be found by Integration of the current vs. time graph to determine the amount of charge put into the capacitor.  Capacitance can be found by dividing the two values.  Resistance can be found by a linear regression of voltage vs. current graph on Page 4 of the Logger Pro file.  The time constant can be found using an exponential Curve Fit of the voltage vs. time graph and using the value of the coefficient of the variable t (note this coefficient is not the time constant but can be used to calculate the time constant). 

Repeat the above steps using a different voltage on the same RC combination.  Then repeat the process varying voltage, capacitance, and resistance as needed to complete your data table.

Capacitor Discharging

To record the discharge of the capacitor all you need to do is change the trigger.  Refer to the previously recorded charging data to find the charged voltage for the external 6 V battery.  Then, under Experiment and Data Collection set the trigger to a voltage decreasing across a value of:  0.05V less than the charged voltage.  For example, if the charged voltage is 5.70 V then set the trigger to be voltage decreasing across 5.65 V.  Once the trigger is set, then simply charge the capacitor, click on the Collect button, and flip the switch SW2 to discharge the capacitor.  To save time use the same voltage for each combination.

Use basically the same process as outlined above to complete the table with one exception.  This time there is no “final” charged voltage.  You can simply find the appropriate “initial” charged voltage in the data table.  (Or, depending on your settings for pre-Trigger data you may be able to use the Statistics tool again.)

Printing Graphs

Once you have completed the data table then print off one “representative” graph of each type used in the experiment.  Include on each of the three graphs two sets of data: show both the charging and the discharging on each graph.  You can use the Store Latest Run option under the Experiment menu to accomplish this.  You need only one combination of voltage, resistance, and capacitance for these graphs.  Include curve fits for the printouts.  Only print one voltage vs. time graph, one current vs. time graph, and one voltage vs. current graph for each person in your group.  Note:  if you are unable for technical reasons to print the graphs, then make a careful sketch of each graph, including the results of the curve fits, and turn these in with your report.

Questions

1. Discuss whether or not your experiment supports the theoretical relations for capacitors and explain how so by referring specifically to tables, graphs, etc.

2. The voltage measured in this experiment was that across the capacitor.  Explain why the slope of this voltage can be used to determine the resistance of the resistor for both charging and discharging.  Is there any systematic error in this technique?

3. (a) Determine the mean capacitance for each capacitor using the six values found in the table.  (b) Determine six values of capacitance for each capacitor by using the resistance and the time constant and then compute the mean of the set.  Show work for both parts.

4. Discuss the three types of values of capacitance for each capacitor:  the value indicated by the manufacturer, the value found by the ratio of charge to voltage, and the value found by using the time constant and resistance.  Which do you think is most accurate and why?  Are the differences among the values reasonable?

5. Do you think the internal resistance of the battery or the probes had a significant effect on the experiment?  Support your answer with specific references to tables, graphs, etc.

A complete report (50 pts):  (5 or 6 pages in this order)

q Completed data/results tables.  (10)

q Voltage vs. Time graph w/ curve fits for charging and discharging.  (10)

q Current vs. Time graph w/ integration result for charging and discharging.  (10)

q Voltage vs. Current graph w/ linear regressions for charging and discharging.  (10)

q On separate paper, answers to the questions using complete sentences.  (10)

	Capacitor Charging
	Charged Voltage (V)	Stored Charge (mC)	Capacitance, Q/V (μF)	Resistance, |slope| of V-I  (W)	Time Constant, t (s)
R = 100 W C = 330 μF
R = 10 W C = 330 μF
R = 100 W C = 100 μF
R = 33 W C = 100 μF

	Capacitor Discharging
	Charged Voltage (V)	Stored Charge (mC)	Capacitance, Q/V (μF)	Resistance, |slope| of V-I  (W)	Time Constant, t (s)
R = 100 W C = 330 μF
R = 10 W C = 330 μF
R = 100 W C = 100 μF
R = 33 W C = 100 μF