Investigating Electricity

This activity was written especially for the Vernier hands-on workshop. It includes two of the more popular electricity-based experiments from the lab manual Physics with Vernier. The introduction below is the introduction for the Series and Parallel Circuits experiment. This introduction typifies the detailed introductions that are available for all of the experiments in Physics with Vernier, including the Capacitors experiment found in the second half of this activity.

Experiment 1—SERIES AND PARALLEL CIRCUITS

Components in an electrical circuit are in series when they are connected one after the other, so that the same current flows through both of them. Components are in parallel when they are in alternate branches of a circuit. Series and parallel circuits function differently. You may have noticed the differences in electrical circuits you use. When using some decorative holiday light circuits, if one lamp burns out, the whole string of lamps goes off. These lamps are in series. When a light bulb burns out in your house, the other lights stay on. Household wiring is normally in parallel.

You can monitor these circuits using a Current Probe and a Voltage Probe and see how they operate. One goal of this experiment is to study circuits made up of two resistors in series or parallel. You can then use Ohm’s law to determine the equivalent resistance of the two resistors.

objectives

• To study current flow in series and parallel circuits.

• To study voltages in series and parallel circuits.

• Use Ohm’s law to calculate equivalent resistance of series and parallel circuits.

MATERIALS

PRELIMINARY QUESTIONS

1. Using what you know about electricity, hypothesize about how series resistors would affect current flow. What would you expect the effective resistance of two identical resistors in series to be, compared to the resistance of a single resistor?

2. Using what you know about electricity, hypothesize about how parallel resistors would affect current flow. What would you expect the effective resistance of two identical resistors in parallel to be, compared to the resistance of one alone?

3. For each of the three resistor values you are using, note the tolerance rating. Tolerance is a percent rating, showing how much the actual resistance could vary from the labeled value. This value is labeled on the resistor or indicated with a color code. Calculate the range of resistance values that fall in this tolerance range.

PROCEDURE

Part I Series Circuits

1. Connect the Current Probe and the Differential Voltage Probe to LabQuest and choose New from the File menu.

2. You need to zero both probes with no current flowing and with no voltage applied. Connect the black and red clips together for this step only.

a. Choose Zero from the Sensors menu and select All Sensors from the list of sensors.

b. With no current flowing and with no voltage applied, wait for the readings on the screen to stabilize, and then select Zero. The readings for both sensors should be close to zero.

c. Select OK.

3. If you have an adjustable power supply, set it at 3.0 V.

4. Connect the series circuit shown in Figure 2 using the 10 Ω resistors for resistor 1 and resistor 2. Notice the Voltage Probe is used to measure the voltage applied to both resistors. The red terminal of the Current Probe should be toward the + terminal of the power supply.

5. You can take readings from the screen at any time. To test your circuit, press on the switch to complete the circuit; hold for several seconds. Both current and voltage readings should increase. If they do not, recheck your circuit.

6. Press on the switch to complete the circuit again and read the current (I) and total voltage (V_TOT). Record the values in the data table.

7. Connect the leads of the Voltage Probe across resistor 1. Press on the switch to complete the circuit and read this voltage (V₁). Record this value in the data table.

8. Connect the leads of the Voltage Probe across resistor 2. Press on the switch to complete the circuit and read this voltage (V₂). Record this value in the data table.

9. Repeat Steps 5–8 with a 51 Ω resistor substituted for resistor 2.

10. Repeat Steps 5–8 with a 51 Ω resistor used for both resistor 1 and resistor 2.

Part II Parallel circuits

11. Connect the parallel circuit shown in Figure 3 using 51 Ω resistors for both resistor 1 and resistor 2. As in the previous circuit, the Voltage Probe is used to measure the voltage applied to both resistors. The red terminal of the Current Probe should be toward the + terminal of the power supply. The Current Probe is used to measure the total current in the circuit.

12. As in Part I, you can take readings from the screen at any time. To test your circuit, press on the switch to complete the circuit; hold for several seconds. Both current and voltage readings should increase. If they do not, recheck your circuit.

13. Press the switch to complete the circuit again and read the total current (I) and total voltage (V_TOT). Record the values in the data table.

14. Connect the leads of the Voltage Probe across resistor 1. Press on the switch to complete the circuit and read the voltage (V₁) across resistor 1. Record this value in the data table.

15. Connect the leads of the Voltage Probe across resistor 2. Press on the switch to complete the circuit and read the voltage (V₂) across resistor 2. Record this value in the data table.

16. Repeat Steps 12–15 with a 68 Ω resistor substituted for resistor 2.

17. Repeat Steps 12–15 with a 68 Ω resistor used for both resistor 1 and resistor 2.

Part III Currents in Series and Parallel circuits

18. For Part III of the experiment, you will use two Current Probes. Disconnect the Voltage Probe and, into the same channel, connect a second Current Probe. Select OK.

19. You need to zero both probes with no current flowing.

a. Choose Zero from the Sensors menu and select All Sensors from the list of sensors.

b. When the readings on the screen stabilize, select Zero. The readings for both sensors should be close to zero.

c. Select OK.

20. Connect the series circuit shown in Figure 4 using the 10 Ω resistor and the 51 Ω resistor. The Current Probes will measure the current flowing through the two resistors. The red terminal of each Current Probe should be toward the + terminal of the power supply.

21. For this part of the experiment you will monitor the current through each of two resistors. Note that the two resistors are not the same. What do you expect for the two currents? Will they be the same or different?

22. Press on the switch to complete the circuit, holding for several seconds. The power supply should still be set for 3.0 V. Record the currents in the data table.

23. Connect the parallel circuit as shown in Figure 5 using the 51 Ω resistor and the 68 Ω resistor. The two Current Probes will measure the current through each resistor individually. The red terminal of each Current Probe should be toward the + terminal of the power supply.

24. Before you make any measurements, predict the currents through the two resistors. Will they be the same or different? Note that the two resistors are not identical in this parallel circuit.

25. Press on the switch to complete the circuit, holding for several seconds. Record the currents in the data table.

DATA TABLE

Part I Series Circuits

ANALYSIS

1. Examine the results of Part I. What is the relationship between the three voltage readings: V₁, V₂, and V_TOT?

2. Using the measurements you have made above and your knowledge of Ohm’s law, calculate the equivalent resistance (R_eq) of the circuit for each of the three series circuits you tested.

3. Study the equivalent resistance readings for the series circuits. Can you come up with a rule for the equivalent resistance (R_eq) of a series circuit with two resistors?

4. For each of the three series circuits, compare the experimental results with the resistance calculated using your rule. In evaluating your results, consider the tolerance of each resistor by using the minimum and maximum values in your calculations.

5. Using the measurements you have made above and your knowledge of Ohm’s law, calculate the equivalent resistance (R_eq) of the circuit for each of the three parallel circuits you tested.

6. Study the equivalent resistance readings for the parallel circuits. Devise a rule for the equivalent resistance of a parallel circuit of two resistors.

7. Examine the results of Part II. What do you notice about the relationship between the three voltage readings V₁, V₂, and V_TOT in parallel circuits.

8. What did you discover about the current flow in a series circuit in Part III?

9. What did you discover about the current flow in a parallel circuit in Part III?

10. If the two measured currents in your parallel circuit were not the same, which resistor had the larger current going through it? Why?

EXTENSION

Try this experiment using three resistors in series and in parallel.

Experiment 2—CAPACITORS

Figure 1

objectives

• Measure an experimental time constant of a resistor-capacitor circuit.

• Compare the time constant to the value predicted from the component values of the resistance and capacitance.

• Measure the potential across a capacitor as a function of time as it discharges.

• Fit an exponential function to the data. One of the fit parameters corresponds to an experimental time constant.

Materials

Preliminary questions

1. Consider a candy jar, initially with 1000 candies. You walk past it once each hour. Since you don’t want anyone to notice that you’re taking candy, each time you take just 10% of the candies remaining in the jar. Sketch a graph of the number of candies remaining as a function of time.

2. How would the graph change if instead of removing 10% of the candies, you removed 20%? Sketch your new graph.

Procedure

1. Connect the circuit as shown in Figure 1 above with the 10 μF capacitor and the 47 kΩ resistor. Record the values of your resistor and capacitor in your data table, as well as any tolerance values marked on them.

2. Connect the Voltage Probe to LabQuest and choose New from the File menu.

3. Connect the clip leads on the Voltage Probe across the capacitor, with the red (positive lead) to the side of the capacitor connected to the resistor. Connect the black lead to the other side of the capacitor.

4. Set up the interface for data collection.

a. Change the rate of data collection to 50 samples/second and the length to 5 seconds.

b. Select OK.

5. Verify that the switch has been in the “32” position illustrated in Figure 1 for ten seconds, ensuring that the capacitor is charged.

6. Start data collection. Wait a moment, and throw the switch to its other position to discharge the capacitor. After data collection is complete, a graph of voltage vs. time will be displayed.

7. Next you will fit the exponential function y = A e^–Cx+B to your data.

a. Use the stylus to select the region of decaying potential.

b. Choose Curve Fit from the Analyze menu.

c. Select Exponential as the Fit Equation.

d. Record the value of the fit parameters in your data table. Note that the “C” in the fit equation is not the “C” of the capacitor.

e. Select OK.

8. Print or sketch the graph of voltage vs. time.

Data Table

Analysis

1. In the data table, calculate the time constant of the circuit used; that is, the product of resistance in ohms and capacitance in farads. (Note that 1 Ω^∙F = 1 s).

2. Compare the fit equation to the mathematical model for a capacitor discharge proposed in the introduction,

Interpret the fit parameters A and C. What aspects of your experiment do they measure? What are their units?

3. From the fit parameter C, calculate and enter in the data table 1/C for each trial. Compare each of these values to the time constant of your circuit.

Note that resistor and capacitor are not marked with their exact values, but only approximate values with a tolerance. Ask your instructor the tolerance of the resistors and capacitors you are using. If there is a discrepancy between the two quantities compared in question 2, can the tolerance values explain the difference?