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Rio Salado Community College *

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112

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Electrical Engineering

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Feb 20, 2024

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PHY112 Lab 4 Name: Dami Esan Capacitors Section PHY 112 MEID: olu2158910 38/40 Access the PhET Capacitor Lab Simulation . Click the Play button and select the option to “Run CheerpJ Browser- Compatible Version”. Use the simulation to answer all the following questions. Part 1 – Capacitance 1. Check the boxes marked plate charge and voltmeter. Move the red voltmeter lead so that it touches the top plate, and move the black voltmeter lead so that it touches the bottom plate. Your simulation should look something like this:

2. Move the slider on the battery up to change the voltage between the capacitor plates. The voltage between the plates will match the voltage of the battery. Record the voltage and the resulting stored charge. Measure six different values and complete the data table below: Voltage ( V ) Stored Charge ( C ) 0 0 0.34 0.30 * 10 -13 0.38 0.34 * 10 -13 0.68 0.60 * 10 -13 0.82 0.73 * 10 -13 1.5 1.3 * 10 -13 3. Use Excel, another spreadsheet, or a graphing program to create a scatter plot graph of voltage versus charge data. Graph the voltage on the horizontal axis and the stored charge on the vertical axis. Make sure that your graph has an appropriate title and that you properly label both axis. Apply a linear fit to your graph and include the equation. Copy and paste your graph below:

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0 0 f(x) = 0 x + 0 R² = 0.96 Voltage (V) vs Stored Charge (C) Voltage (V) Stored Charge (C) It looks like your last point is the one that is throwing off your results. That last graphed point doesn’t match you’re the charge value in your data table of 1.3E-13 C. (-1)

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4. Check the capacitance box on your simulation. How does the capacitance compare to the slope of your graph? What is the physical meaning or the significance of the graph slope? 5. If the voltage applied by the battery doubles, what happens to the amount of charge stored on the plates and the capacitance of the capacitor? 6. If you double the plate area, by what factor does the capacitance change? Explain the reason for this change. Don’t explain the math but explain the theory behind the math. The capacitance is greater than the slope of my graph. Capacitance is demonstrated by the equation Q=CV, where capacitance is proportional to the stored charge, meaning my graph’s slope is the capacitance. My graph shows a positive and slightly linear relationship between voltage and stored charge, mirroring the equation. Okay. Typically, this comes out much better than what you came up with. But you got the main point. If you had plotted that last point correctly, then the slope would have matched the simulation capacitance If the voltage doubles, the charge of the plates will double, but the capacitance will remain constant as the plate area is also constant. Correct Doubling the plate area of a capacitor reduces the charge repulsion and increases the energy storage. The capacitance is directly proportional to the plate area, so it also doubles. Good

7. Reduce the plate separation distance by half (move the plates closer together). By what factor does the capacitance change? Explain the reason for this change. Don’t explain the math but explain the theory behind the math. Part 2 – General Observations and Analysis 8. Reset the simulation. Check all the boxes. Move the voltmeter leads so that the red lead touches the top plate and the black lead touches the bottom. Place the field meter in the space between the plates. Increase the battery voltage to 1.5. Your screen should now look something like the picture below. The capacitance of a parallel-plate capacitor is directly proportional to the plate area and inversely proportional to the distance between the plates. Halving the distance doubles the capacitance, and the charge can be stored more efficiently. What do you mean by ‘more efficiently’? The closer the plates are together, the stronger the force of attraction between charges on opposite plates. The stronger the force, the less the influence of repulsion between like charges on a single plate. Thus, more charges will be attracted onto the plate (-1)

Decrease the plate separation distance. Note the effects of this change on the - stored charge, - stored energy, and - voltage (note that you will need to adjust the voltmeter leads as you move the plates, and the leads need to be in contact with the plates to get a proper reading). Record your observations on the data table below. Explain why each of the changes occurs. Remember that math describes WHAT happens but does not explain WHY – you may use math to aid your discussion, but your explanations should focus on what is happening in the system. You may need to review the lesson to help you in this section. Observed value Observed change as capacitor plates move closer Explanation for the change (battery connected) Stored charge ( C ) Increases Stored charge will increase because capacitance is inversely proportional to plate distance. Stored energy ( J ) Increases Stored energy increases because of the attractive forces in the plates. Voltage ( V ) Constant Voltage does not change because the potential plate difference remains constant since the voltage does as well, and in this part of the experiment, the voltage did not change. For three different separation values, measure the voltage across the plates using the voltmeter. Then calculate the Electric field strength ( E = Voltage separation = V d ). Record the data and calculations. Voltage (v) Separation (m) Electric field strength (V/m) 1.5 0.01 1.5 V/0.01 m = 150 V/m 1.5 0.0075 1.5 V/0.0075 m = 200 V/m 1.5 0.005 1.5 V/0.005 m = 300 V/m Following your calculations, what do you observe about the Electric field strength as the capacitor plates move closer (with the battery connected). Observed value Calculated change as capacitor plates move closer Explanation for the change (battery connected)

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Electric field strength (V/m) Electric field strength increases When the plates move closer together, electric field strength increases because capacitance is directly proportional to the field strength, so plates moving closer together both capacitance and electric field strength increases. Good 9. Reset the simulation back to its default settings. As before, check all the boxes and move the voltmeter and field meter into position. Slide the battery to the 1.5 V position, and then click on the disconnect battery button . Decrease the plate separation distance. Note the effects of this change on the - stored charge, - stored energy, and - voltage (note that you will need to adjust the voltmeter leads as you move the plates, and the leads need to be in contact with the plates to get a proper reading). Record your observations on the data table below. Explain why each of the changes occurs; however, you may need to revisit the textbook or lesson discussion to help with the explanation section of the table. Observed value Observed change as capacitor plates move closer Explanation for the change (battery NOT connected) Stored charge ( C ) Constant When the plates are moved closer, the stored charge does not change, as neither plate received a new charge (from the battery), so the stored charge does not change. Stored energy ( J ) Decrease The stored energy of a capacitor depends on the charge and the distance between the plates. When the distance decreases, the energy decreases, unless more charge is added. Voltage ( V ) Decrease Reducing the distance between capacitor plates increases the capacitance and decreases the voltage, while keeping the charge constant. The stored energy also decreases, as it is proportional to the voltage and the capacitance. For three different separation values, measure the voltage across the plates using the voltmeter. Then calculate the Electric field strength ( E = Voltage separation = V d ). Record the data and calculations. Voltage (v) Separation (m) Electric field strength (V/m) 1.5 0.01 1.5 V/ 0.01m = 150 V/m

1.132 0.0075 1.132 V/0.0075m = 150.9 V/m 0.75 0.005 0.75 V/0.005m = 150 V/m Following your calculations, what do you observe about the Electric field strength as the capacitor plates move closer (with the battery NOT connected). Observed value Calculated change as capacitor plates move closer Explanation for the change (battery NOT connected) Electric field strength (V/m) Constant / Near Constant Without a battery, the electric field strength will stay the same even if the plates get closer. Well done Part 3 – Series and Parallel 10. Click on the multiple capacitor tab at the top of the simulation. Check the box for the total capacitance meter. Increase the number of capacitors in series and note the effect on the total capacitance. Describe your observations and provide an explanation for this behavior. 11. Increase the number of capacitors in parallel and note the effect on the total capacitance. Describe your observations and provide an explanation for this behavior. Connecting more capacitors in series makes the total capacitance smaller. In this connection, the bottom plate of one capacitor meets the top plate of another. It acts like making the space between one capacitor’s plates larger. This weakens the attraction between the plates. So, less charge can go on the plate with the same voltage, and the capacitance goes down. This is because the forces that resist are larger. The formula to use for series capacitors is 1/Cs = 1/C1 + 1/C2. Good job When capacitors are connected in parallel, the top plate of one joins the top plate of another. This increases the total capacitance as more capacitors are added. This is because the parallel connection is like making the area of the plates bigger. More area means more space for extra charge to go on a plate. Good

Part 4 – Final Conclusions and Summary Give a concise summary of the findings for this lab. What do you understand now that you did not understand before? Be specific. Understanding capacitance, especially its relationship with distance and area, was challenging before the lab. The experiment made me conclude that increasing voltage led to proportional growth in stored charge, maintaining constant capacitance. The formula C = Q/V helped me to calculate capacitance, showing its inverse correlation with voltage and direct correlation with charge. Increased plate area strengthened attracting forces between plates, enhancing capacitance. The lab demonstrated that connecting a battery increased stored charge, energy, and electric field strength with constant voltage, while reducing distance boosted capacitance. Well done

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