Physics 360 Lab 3B - Neumann Virtual

Lab 3B – Physics 360 Neumann Virtual Lab 3B: Capacitance PHET

PURPOSE To understand how charge is stored on the capacitor, what role a dielectric plays in storing charge, and how capacitors are connected in series and in parallel.

Preliminary Go to https://phet.colorado.edu/en/simulations/capacitor-lab , and play the Capacitor Lab simulation. Choose the “Run CheerpJ Browser-Compatible Version” in the pop-up window.

Part I: Capacitance and permittivity of free space 1. In the Introduction tab, set the Separation of the plates to be 10.0 mm, the Plate area to be 100.0 mm2. Enable the voltmeter, and “attach” its leads to the top and bottom plates (can be a little above/below the plates). You simulation should look as follows:

2. Keep the separation value constant at 10.0 mm, and change the plate area. Record the capacitance associated with different plate areas in the table below (or you can do this directly in Excel, if desired). You need five different data points; pay attention to units.

Area [m2] Capacitance [F]

3. Transfer your table to Excel, and plot Capacitance on the y-axis vs. Area on the x-axis. Don’t forget to label the graph and the axes (with units). Fit a best-fit line to your graph, and display the equation of this line on your graph together with the R2 value.

https://phet.colorado.edu/en/simulations/capacitor-lab

4. How can you use the slope of your best-fit line to determine the value of the permittivity of vacuum? Derive the relationship between the slope and the permittivity.

5. From your best-fit line, determine the value of ε0. Show all work, and don’t forget units.

6. Calculate % error between the value you determined in the previous question and the actual value.

Part II: Relationship between capacitance, charge, and volume

7. Reset the simulation.

8. Set the value of the capacitor to 0.89?10-13 F (0.089 pF).

9. Move the slider on the battery up and down (don’t use the negative values just yet), and enable the Plate Charge meter. Record the charge associated with different voltage readings in the table below (or you can do this directly in Excel, if desired). You need five different data points; pay attention to units.

Voltage [V] Charge [C]

10. Transfer your table to Excel, and plot Charge on the y-axis vs. Voltage on the x-axis. Don’t forget to label the graph and the axes (with units). Fit a best-fit line to your graph, and display the equation of this line on your graph together with the R2 value.

11. How can you use the slope of your best-fit line to determine the value of the capacitance? Derive the relationship between the slope and the capacitance, and determine the value of the capacitance. Don’t forget units!

 12. Calculate % error between the value you determined in the previous question and the actual value.

Part III: Relationship between voltage and electric field

13. Reset the simulation.

14. Pick a value of voltage and the plate separation, and record it here (don’t forget units!): V = _____________________ d = __________________

15. From the two values recorded in the previous question, calculate the value of the electric field between the plates. We are going to ignore fringe effects here.

16. Enable electric field lines.

 17. Change the voltage of the battery (use both positive and negative values now), and observe what happens to the electric field lines, as well as to the charge accumulated on the plates, and the direction of electron flow. Describe your observations in detail (you should have about 5-10 sentences). Your explanation should include a description of charge polarity, magnitude of electric field, direction of electric field lines, and the direction of electron flow.

Part IV: Exploring dielectrics

18. Reset the simulation and click on the Dielectric tab.

 19. Set the area to be 200 mm2, the separation to be 8 mm, battery voltage to be 1.5V. Choose a “custom” dielectric on the right, and set the dielectric constant to 1.00. Set the offset to be 0.0 mm. Enable the Capacitance meter.

20. Using the values of A and d, calculate the value of C0, and compare it to the value from the Capacitance meter.

21. Change the value of the dielectric (for example, K = 1.0, 2.0, 3.0, …), and record it in the table below (first two columns), together with the value of capacitance (or you can do this directly in Excel, if desired). You need five different data points; pay attention to units.

Dielectric constant Capacitance [F] Stored Energy (J)

22. Transfer your table to Excel, and plot Capacitance on the y-axis vs. Dielectric Constant on the x-axis. Don’t forget to label the graph and the axes (with units). Fit a best-fit line to your graph, and display the equation of this line on your graph together with the R2 value.

23. What does the slope of this graph tell you? Explain! 24. Calculate % error in C0.

25. Enable Stored Energy meter. Rerun the simulation. Fill in the third column of the table.

26. Describe qualitatively (one or two sentences), what happens to the stored energy as the value of dielectric constant increases. Why is this trend observed?

 Part V: Capacitors in Series

27. Reset the simulation, and click on the Multiple Capacitors tab.

28. Click on three capacitors in series. Set the voltage of the battery to maximum (1.5 V), and set the capacitance of the three capacitors to 1.00?10-13 F, 2.00?10-13 F, and 3.00?10-13 F, respectively.

29. Enable the Total Capacitance meter. Calculate the total capacitance, and compare it to the measured value.

30. Measure the voltage across each capacitor. Do these values make sense? Describe the trends!

31. How was the stored charge calculated? Describe the trends for charges stored in the capacitors connected in series, and show the calculation.

Part VI: Capacitors in Parallel

32. Reset the simulation.

33. Click on three capacitors in parallel. Set the voltage of the battery to maximum (1.5 V), and set the capacitance of the three capacitors to 1.00?10-13 F, 2.00?10-13 F, and 3.00?10-13 F, respectively.

34. Enable the Total Capacitance meter. Calculate the total capacitance, and compare it to the measured value.

35. Measure the voltage across each capacitor. Do these values make sense? Describe the trends!

36. How was the stored charge calculated? Describe the trends for charges stored in the capacitors connected in parallel, and show the calculation. Additional practice This is not collected, but it would be a great practice to investigate what happens to charges and to stored energy when you have a combination of capacitors connected 2 in series + 1 in Parallel or 2 in Parallel + 1 in Series.