Copy_of_PHYS140_RC_Circuits_Lab_-_STUDENT_VERSION_(Graphical_Analysis)

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Siena College *

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Apr 3, 2024

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Siena College - General Physics 140 RC Circuits Lab NAME: GROUP MEMBERS: Learning Goals 1. In Section I, you will identify the conditions necessary to allow for a continuous flow of electric charge by observing and explaining patterns that occur when two objects at different electric potentials (a Van de Graaff generator and its grounding rod) interact with a third object. 2. In Section II, you will construct an idea of what constitutes a complete circuit by observing and explaining patterns involving the arrangement of circuit elements that make a lightbulb glow. 3. In Section III, you will investigate the charging and discharging of a capacitor from an electric charge perspective. 4. In Section IV, you will investigate the charging and discharging of a capacitor from an energy perspective. Driving Question(s): What conditions are necessary to allow for the continuous flow of electric charge in an electric circuit? How can a charge separation be maintained so that electric potential energy can be stored for eventual uses? In a resistor-capacitor (RC) circuit, how can a capacitor prevent or allow a lightbulb to illuminate? Section I - In this part of the lab, you will identify the conditions necessary to allow for a continuous flow of electric charge by observing and explaining patterns that occur when two objects at different electric potentials (a Van de Graaff generator and its grounding rod) interact with a third object. Equipment: Van de Graaff generator with grounding rod, aluminum foil ball hung from an insulated thread, long fluorescent lamp. Scientific Ability Missing Inadequate Needs Improvement Adequate B7 Is able to identify a pattern in the data No attempt is made to search for a pattern. The pattern described is irrelevant or inconsistent with the data. The pattern has minor errors or omissions. The pattern represents the relevant trend in the data. B9 Is able to devise an explanation for an observed pattern No attempt is made to explain the observed pattern. An explanation is vague, not testable, or contradicts the pattern. An explanation contradicts previous knowledge or the reasoning is flawed. A reasonable explanation is made. It is testable and it explains the observed pattern. Your instructor charges a Van de Graaff generator while its grounding rod is close to, but not touching the Van de Graaff. While this is happening, an aluminum foil ball is hanging from a thin thread made of insulating material and is already 1

Siena College - General Physics 140 RC Circuits Lab positioned in between the Van de Graaff and the grounding rod. The aluminum foil ball is allowed to move freely. After several seconds, the generator is turned off and the aluminum foil ball is still allowed to move freely based on its interactions with the Van de Graaff and the grounding rod. Answer the following questions with your group. A. Record your observations. What happened to the aluminum foil ball? The aluminum foil moves initially because of the electrostatic forces and it eventually settles into static equilibrium due to the charge distribution generated by the Van de Graaff generator. B. Explain why you observed what you did by describing all the energy conversions that took place when the ball moved from one sphere to the other and back again. Explain your thinking as to why you expect or don’t expect this motion to continue indefinitely. As the generator becomes positively charged it induces an opposite charge on the aluminum foil ball hanging. The repulsive force between like charges causes the aluminum foil to experience a force away from the positively charged dome of the generator and moves towards the grounding rod. The kinetic energy of the ball is partially converted to potential energy as it moves closer to the grounding rod. C. Explain why you observed what you did by using a microscopic model of charging and using the concept of electric potential. The generator builds up a high electric potential on its dome due to the accumulation of positive charge. The grounding rod being grounded maintains a lower electric potential but with an opposite charge distribution. Your instructor charges a Van de Graaff generator and places its grounding rod close to, but not touching the Van de Graaff. Then, each end of a fluorescent lamp is allowed to touch either the generator or the grounding rod. Answer the following questions with your group. D. Record and explain your observations by using the ideas you developed in the previous experiment. How is this similar to and different from the case of the aluminum foil ball? Once the lamp loses contact with either the generator or the grounding rod it stops emitting light. The lamp only remains light while in contact with the generator and grounding rod. In both experiments there’s positive charge around the dome. E. Explain why the flash of light lasts for such a short time interval. The flash of light only lasts a short amount of time because it is a result of the 2

Siena College - General Physics 140 RC Circuits Lab rapid discharge of stored electrical energy in the lamp’s tube . Section II - In this part of the lab, you will construct an idea of what constitutes a complete circuit by observing and explaining patterns involving the arrangement of circuit elements that make a lightbulb glow. Equipment: Batteries, lightbulbs, wires. Scientific Ability Missing Inadequate Needs Improvement Adequate A7 Sketch No representation is constructed. The sketch is drawn, but it is incomplete with no physical quantities labeled, or important information is missing, or it contains wrong information, or coordinate axes are missing. The sketch has no incorrect information, but has either no or very few labels of given quantities. Subscripts are missing or inconsistent. The majority of key items are drawn. The sketch contains all key items with correct labeling of all physical quantities that have consistent subscripts; axes are drawn and labeled correctly. B5 Is able to describe what is observed without trying to explain, both in words and by means of a picture of the experimental setup No description is mentioned. The description is incomplete. No labeled sketch is present. Or, observations are adjusted to fit expectations. The description is complete, but mixed up with explanations or patterns. The sketch is present, but it is difficult to understand. Clearly describes what happens in the experiments both verbally and with a sketch. Provides other representations when necessary (tables and graphs). You have a battery, two wires, and a lightbulb. Work with your group to try different arrangements of these four elements to make the lightbulb glow. Then, remove one wire and try to light the bulb with just a battery and one wire. A. Draw pictures of the arrangements that allow the bulb to light and several where it does not do so. Explain how this experiment is similar to the experiments in Part I and how it is different. 3

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Siena College - General Physics 140 RC Circuits Lab Both experiments have a complete circuit and they both have a battery source. The first experiments electrons come from the ground but this one comes from the battery. B. Based on your successful arrangements when the bulb lit up, discuss the conditions that are necessary for a lightbulb to illuminate. There must be a potential difference and it has to be a closed circuit with conductive wires. There also needs to be a functional light source. C. Summarize the conditions that are necessary for the continuous flow of electric charge in an electric circuit. There needs to be a continuous flow of electric charge in the circuit and a battery charge. D. Construct an analogy to explain how an electric circuit works. Use the following table to help you create your analogy. Using your analogy, fill in the table below to identify the counterpart for each element of an electric circuit. Note: An analogy involves mapping between the target phenomenon (the one we are trying to understand) and some source phenomenon (that we understand and are using to compare to the target phenomenon). The source phenomenon should be some everyday experience that you are familiar with, and whose physical processes are similar to the workings of the electric circuit you’re trying to explain (this is your target phenomenon). Source Phenomenon Target Phenomenon (electric circuit) 4

Siena College - General Physics 140 RC Circuits Lab Water pump Battery Pipes Connecting wires Faucet Lightbulb Flow of water Electric charges E. Explain how your analogy works. How are the elements of your source phenomenon similar to the battery, connecting wires, lightbulb, and electric charges? The water pump is the battery because they both provide electrical potential difference. The pipes are the wires because they provide somewhere for the eclectic current to flow. The faucet is the bulb because when the water passes through water is able to come out the facet and cause a flow of water. Section III - In this part of the lab, you will investigate the charging and discharging of a capacitor from an electric charge perspective. Equipment: Demonstration capacitor of 25,000 μF, a circuit to charge and discharge the capacitor, light bulb to indicate the flow of charge, wires, batteries or a power supply, Graphical Analysis, Vernier Go-Direct voltage probe, a switch. Scientific Ability Missing Inadequate Needs Improvement Adequate B5 Is able to describe what is observed without trying to explain, both in words and by means of a picture of the experimental setup No description is mentioned. The description is incomplete. No labeled sketch is present. Or, observations are adjusted to fit expectations. The description is complete, but mixed up with explanations or patterns. The sketch is present, but it is difficult to understand. Clearly describes what happens in the experiments both verbally and with a sketch. Provides other representations when necessary (tables and graphs). A11 Graph No graph is present. A graph is present, but the axes are not labeled. There is no scale on the axes. The data points are incorrectly connected to each other instead of using an appropriate trendline. The graph is present and the axes are labeled, but the axes do not correspond to the independent and dependent variable OR the scale is not accurate. The data points are not connected to each other, but there is no trendline either. The graph has correctly labeled axes, the independent variable is along the horizontal axis and the scale is accurate. The trendline is correct. 5

Siena College - General Physics 140 RC Circuits Lab G5 Is able to analyze data appropriately No attempt is made to analyze the data. An attempt is made to analyze the data, but it is either seriously flawed or inappropriate. The analysis is appropriate, but it contains minor errors or omissions. The analysis is appropriate, complete, and correct. SAFETY NOTE: This activity uses a demonstration capacitor such as those provided in CASTLE kits. The capacitor has a relatively high capacitance, but is safe for use in labs. PLEASE DO NOT REPLACE THIS CAPACITOR WITH A COMMERCIAL DEVICE OF HIGH CAPACITANCE. Such devices may have different voltage limits and may store and release dangerous amounts of charge. A capacitor is a device designed to store and release electric energy. The design consists of two conducting plates separated by an insulator, similar in principle to the early Leyden jar design. The charge that can be stored in a capacitor is: Q = C ∆V where Q is the charge, C is the capacitance that depends on properties of the device, and ΔV is the voltage across the capacitor. While it is straightforward to measure the voltage, and to calculate the capacitance, it is not readily possible to measure the charge. It is possible to measure the discharge time of the capacitor, and that value is proportional to charge. Apparatus and Procedure The set-up for this lab includes a demonstration capacitor of 25,000 μF, a circuit to charge and discharge the capacitor, a light bulb to indicate the flow of charge, and batteries or a power supply as a source of a potential difference. We will use a voltmeter to measure the potential difference, and LoggerPro and a Vernier Voltage Probe to measure the time-dependent change in potential difference across the bulb. See the image on the next page. 6

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Siena College - General Physics 140 RC Circuits Lab First, try throwing the switch back and forth, and note what happens with the light bulb. Consider if you notice a difference in the bulb behavior when you charge or discharge the capacitor. Could you accurately measure the time to charge or discharge with a stopwatch? 1. Open Graphical Analysis. Click on “Sensor Data Collection”. Turn on the Go Direct Voltage Sensor by clicking the power button on the sensor. Under “Discovered Wireless Devices”, connect your Vernier Go-Direct Voltage Probe to Graphical Analysis. Make sure the code on Graphical Analysis matches the code on your sensor. The sensor will automatically be set to measure voltage (potential difference) once the sensor is connected to Graphical Analysis. Click “Done”. 2. In the bottom left-hand corner, click the “Data Collection Settings” button. Set the sensor to collect 1000 samples/second and to end collection “after 20 seconds”. Choose “Done” to return to the main screen. 3. Open the circuit. Near the bottom right corner, check if the potential difference is reading 0 V. If not, click on this button and choose “Zero”. 4. Be careful not to exceed a potential difference (voltage) of 6.5 Volts. Record your values. Note if you are able to visibly see the bulb flash. You may still be able to collect data even if the bulb does not appear to illuminate (which may occur if the potential difference is too low). 7

Siena College - General Physics 140 RC Circuits Lab 5. Press the “Collect” button near the top of the screen to begin collecting data. Flip the switch to charge and then discharge the capacitor. 6. Find the time associated with when the potential first spikes, and the time when the potential returns to zero. The first measurement should be fairly easy to identify on the graph, but the second may be more arbitrary. Record both the start and end time, for both charging and discharging the capacitor. 7. Change the potential difference (voltage), either by using different batteries, or replacing the battery pack with a power supply. Measure several trials of charge and discharge time each for a variety of voltages. Be careful not to exceed a potential difference (voltage) of 6.5 Volts. Record your values. Note if you are able to visibly see the bulb flash. 8. (OPTIONAL) Replace the capacitor with a different capacitor of known value. Repeat step 7 with the new capacitor. COLAB LINK: https://colab.research.google.com/drive/1400yG7fmbYBXwrh_r0BYqkLOX2cdqvAh? usp=sharing Analysis of Charge vs. Voltage A. Do you notice any difference in the bulb behavior for charging or discharging the circuit? Describe your thoughts in detail. We can see a difference in electrical potential on the graph. When you change the switch and move it to the other side, the electric potential changes from positive to positive. B. Do you think you can accurately measure the discharge time with a stopwatch? Describe your thoughts in detail. No, because the human eye wouldn’t give a good approximation because you can’t see when the exact moment the light comes on or off. C. Make a graph of charge or discharge time vs. potential difference (voltage) for both of your capacitors. Describe if your graph meets your expectations, specifically: 8

Siena College - General Physics 140 RC Circuits Lab i. Does time vs. potential difference (voltage) give a linear plot? It does give a linear plot because its proportional. ii. How do the slopes relate for different capacitors? There would be different slopes because when the capacitor is lower it's a steeper slope and when it's higher it’s a flatter slope. Section IV - In this part of the lab, you will investigate the charging and discharging of a capacitor from an energy perspective. Equipment: Demonstration capacitor of 25,000 μF, a circuit to charge and discharge the capacitor, wires, batteries or a power supply, Graphical Analysis, Vernier Go-Direct voltage probe, a switch, a motor and wheel or Genecon generator. Scientific Ability Missing Inadequate Needs Improvement Adequate B8 Is able to represent a pattern mathematically (if applicable) No attempt is made to represent a pattern mathematically. The mathematical expression does not represent the trend. The mathematical expression represents the trend. However, an analysis of how well the expression The mathematical expression represents the trend completely and an analysis of how well 9

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Siena College - General Physics 140 RC Circuits Lab agrees with the data is not included, or some features of the pattern are missing. it agrees with the data is included. A11 Graph No graph is present. A graph is present, but the axes are not labeled. There is no scale on the axes. The data points are incorrectly connected to each other instead of using an appropriate trendline. The graph is present and the axes are labeled, but the axes do not correspond to the independent and dependent variable OR the scale is not accurate. The data points are not connected to each other, but there is no trendline either. The graph has correctly labeled axes, the independent variable is along the horizontal axis and the scale is accurate. The trendline is correct. G5 Is able to analyze data appropriately No attempt is made to analyze the data. An attempt is made to analyze the data, but it is either seriously flawed or inappropriate. The analysis is appropriate, but it contains minor errors or omissions. The analysis is appropriate, complete, and correct. SAFETY NOTE: This activity uses a demonstration capacitor such as those provided in CASTLE kits. The capacitor has a relatively high capacitance, but is safe for use in labs. PLEASE DO NOT REPLACE THIS CAPACITOR WITH A COMMERCIAL DEVICE OF HIGH CAPACITANCE. Such devices may have different voltage limits and may store and release dangerous amounts of charge. Energy Storage in Capacitors In the Hooke’s Law experiment last semester, the force vs. displacement graph gave a positive, linear coefficient. The area under the curve has units of Newtons x meters (or Joules) and has a triangular shape with formula: Area = 1/2 base × height = 1/2 force × ∆x = 1/2 (k ∆x) (∆x) = 1/2 k (∆x^2) where k is the spring constant. The area under the curve is recognized as the energy stored in the spring as it is stretched. Considering the capacitor: A. Should a plot of charge Q vs. potential difference ΔV be expected to give a linear plot? Yes since Q= c delta v it should be a linear relationship between charge Q and potential difference. B. What are the units for the area under the curve? The units for area under the curve is Coulomb's ( C ) times Volts ( V ). C. What is the expression for the area under the curve for charge Q vs. potential difference ΔV , and what physical quantity does it represent? 10

Siena College - General Physics 140 RC Circuits Lab A = ½ base x height = ½ Q times delta V. This represents the quantity of the electric potential energy stored in the capacitor. Energy Storage Procedure It is not straightforward to directly measure stored energy. However, it is possible to release the energy and make a quantitative comparison that is proportional to this energy. Replace the lightbulb in the circuit with a motor and wheel or Genecon generator. 1. Charge the capacitor, and discharge it through the motor instead of the light bulb. You should notice that the wheel or handle turns by a noticeable amount. 2. Find a way to “zero” the wheel or handle. Set it at a repeatable reference point. 3. Discharge the capacitor over a variety of voltage values. Count the number of turns (including estimated fractions of a turn) when the capacitor is discharged. Record the potential difference (voltage) and number of turns. 4. (OPTIONAL) Repeat Step 3 for a different capacitor and record similar data. Energy Storage Analysis D. Plot number of turns vs. potential difference (voltage) for each capacitor. Determine if the plot is linear, or what test plot variable is needed to linearize. 11

Siena College - General Physics 140 RC Circuits Lab E. Describe if your graph meets your expectations, specifically: i. Does the form of the graph agree with the expression for the area under the curve? Yes, because it’s a direct relationship. ii. How do the graphs relate for different capacitors? The slope would be different because the capacitors would make the slope steeper or flatter. F. How do the charge (time) vs. potential difference and energy (turns) vs. potential difference compare with the expressions Q = CΔV and U = ½ C ΔV 2 ? Both have capacity and voltage, but one is the change in voltage and the other is voltage squared and then halved. G. How does a larger capacitor affect the stored charge and stored energy? The larger the capacity the more energy it has stored and less capacity means less energy it has. H. Compare the analogy between this exercise and Hooke’s Law. Which aspects are similar, and which are different? Both are linear, but hooke’s law is about a spring constant. 12

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