AP Physics 2 Lab – Battery Properties and Capacitance
The goals are to verify the emf and internal resistance model of a battery and to explore the properties of capacitors. This lab exercise also provides practice analyzing data and employing graphical analysis.
Part A: Battery model – emf and internal resistance
A simple circuit will be created in which a battery is powering a resistor or a combination of resistors. A voltage probe will be used to measure the terminal voltage of the battery as it produces various currents through differing amounts of external resistance.
1. Connect the voltage probe to Graphical Analysis running on a laptop. The connection can be either Bluetooth or USB cable.
2. In the View Options menu turn on Meters, so that you can see a live readout of the voltage probe. Also, click on the three dots on the meter and under Column Options choose to show 3 decimal places of voltage.
3. Connect the two alligator clips of the voltage probe to one another (and not to anything else). This forms a closed circuit in which the voltage must be zero. Then under the Sensor Actions menu choose to Zero the voltage measurement.
4. Now connect the two leads from the voltage probe to the positive and negative terminals of the battery (posts 1 and 35 on the Vernier Circuit Board 2). Make sure that switch SW1 is set to Battery. You can choose different voltages by using switch SW4, which connects either 1, 2, 3, or 4 cells in series.
5. Set the voltage of the battery to one particular value and record the reading of the voltmeter in the table. Because the resistance of the voltage probe itself is very large, there is very, very little current pulled from the battery in this case. Therefore, the reading of the voltmeter is essentially equivalent to the emf of the battery.
6. Now use jumper cables to connect a certain amount of external resistance to the battery. Each value shown in the table can be created by using one or more resistors that are included on the board. NOTE: make all connections to the numbered metal posts – do not try to connect directly to the wires on the resistors or other components on the board. If need be you can connect jumper cables to one another “outside of the board”.
7. Once a particular value of resistance is connected to the battery you should notice the terminal voltage being measured will change. Allow the measured value to “settle” on a relatively constant result (but don’t “wait forever” – if you wait long enough you will drain the battery!!)
8. Disconnect the battery and set up the next value of external resistance and then repeat the process with a new resistor or combination of resistors. In this way you should be able to complete the table.
Part B: Capacitor Discharge – C = q/V and τ = RC
A circuit with a momentary SPST switch will be used to charge and discharge three different capacitors while using a voltage probe to measure and graph the voltage as a function of time across each capacitor as it discharges.
1. Create a simple single loop circuit with the battery, the 1.0 µF capacitor, and SPST switch SW3 (the red button). When the switch button is pressed down it completes the circuit and the capacitor will be charged by the battery.
2. Connect the voltage probe to measure the voltage across the capacitor. Set the voltage of the battery to its maximum value. Test the circuit by pressing and holding the switch down – you should see the voltage change from zero to that of the battery (around 6 V). When the switch is released you should see the voltage decrease as the capacitor discharges.
3. Adjust Data Collection Settings – set the rate to 20 samples per second and duration 30 s. AND, change Start Collection to a triggering event voltage decreasing across 6.00 V.
4. Now you are ready! Press down switch SW3 to charge the capacitor to a value above 6.0 V. Click on the Collect button to start data collection and then release switch SW3. If you have the set up correct, the result will be a graph that shows the voltage decreasing smoothly, starting at a value very close to 6.0 volts.
5. Repeat this process but this time use the 10.0 µF capacitor and change the parameters to a duration of 200 s and a rate of 3 samples per second.
6. For the final data set, create a “homemade capacitor” with two pieces of aluminum foil separated by a single sheet of paper. Place a book on top to hold the foil and paper together tightly. Record the width and length of the amount of aluminum foil that actually overlaps. It is fine if the two pieces are not exactly the same size or if some parts don’t actually overlap. Disconnect the capacitor on the circuit board and instead connect to your foil capacitor! NOTE: it is critical that the pieces of foil do not make contact with one another – the two pieces must be separated by an insulator in order to be a working capacitor!
7. Repeat the graphing process that was used for the commercially made capacitors, but change the parameters to a duration of 0.4 s and a rate of 1000 samples per second.
Analyses of Data
1. Complete the data table for part A: Use the measured emf of the battery and the external resistance to calculate the internal resistance for each trial. Calculate decimal values for reciprocal of the external resistance and reciprocal of the terminal voltage.
2. Produce a large, high quality, scientific graph of reciprocal voltage versus reciprocal resistance. Determine the line of best fit, including equation and correlation coefficient shown on the graph.
3. For part B: Under Graph Options menu activate the Interpolate feature on the voltage graph. For each of the three trials determine the precise time at which the voltage drops to 36.8% of its initial value (at time t = 0). This amount of time should be the time constant τ = RC. Use this fact and the labeled capacitance to calculate the apparent resistance of the voltage probe for each of the first two trials. Determine the mean value of the probe based on these two trials. Print only the voltage graph for the 1.0 µF capacitor with the tracing tool located at the time t = τ. This is a record showing how the time constant was determined.
4. Use the resistance of the voltage probe (now determined) to calculate an experimental value for the capacitance of the foil capacitor (based on its observed time constant).
5. Use the mean value of the voltage probe’s resistance to create a new column in Graphical Analysis that gives the current of the capacitor as it discharges. Hint: use Ohm’s Law!
6. Graph current vs. time for the trial using the foil capacitor. Use the integral tool to determine the area under the curve for an interval of time equal to 5τ. Print this graph showing the curve and the area under the curve.
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Part A |
Battery emf: |
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External Resistance (Ω) |
Terminal Voltage (V) |
Calculated Internal
Resistance |
Reciprocal External
Resistance |
Reciprocal Terminal
Voltage |
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187 |
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119 |
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68 |
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51 |
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35.5 |
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20 |
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Part B |
V0 (V) |
0.368V0 (V) |
τ (s) |
Rprobe (MΩ) |
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1.0 µF |
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10 µF |
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mean Rprobe: |
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V0 (V) |
0.368V0 (V) |
τ (s) |
C (nF) |
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foil capacitor |
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foil dimensions: |
W = |
L = |
paper thickness: |
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Questions
1. Show how the internal resistance values in the table were calculated by deriving an expression for the internal resistance, r, in terms of the emf, ℇ, the terminal voltage Vt, and the external resistance R. Show your work!
2. Determine the mean value and the mean or standard deviation in the set of values of internal resistance for each trial shown in the table.
3. Consider the graph of reciprocal voltage vs. reciprocal resistance. Using the coefficients from the equation of the line of best fit, determine the emf and the internal resistance of the battery. Show your work and/or explain!
4. (a)
Calculate the expected capacitance of the foil capacitor using the dimensions
of the foil and the properties of the paper. Show your work.
(b) Determine the capacitance of the foil capacitor by using the area under the
curve of its current vs. time graph. Show your work.
(c) Determine the percent difference in these two values.
(d) Determine the percent difference in the capacitance of the foil resistor
shown in the table and the expected capacitance found in part (a) above.
5. Discuss error. This should be a concise paragraph or two that specifies the signs of error apparent in the results and the most likely sources of experimental error.
Completed report (assembled in this order please):
o Schematic diagrams of lab setup for both Part A and Part B (include the voltmeter!)
o Completed tables with data and calculated values
o Reciprocal voltage vs. reciprocal resistance graph with best fit
o Graph of voltage vs. time for the 1 µF capacitor, showing the time at which V = 0.368V0
o Graph of current vs. time for the foil capacitor including the area under the curve
o Answers to questions 1 thru 5