Lab Aluminum Foil Parallel Plate Capacitors
This lab is adapted from the University of Virginia Physics Department Lab 4:Capacitors & RC Circuits (PHYS 2042, Spring 2014). It is designed to develop an understanding of the geometry of a parallel plate capacitor composed of two sheets of heavy-duty aluminum foil and the effect of inserting a dielectric between its plates.

Equipment

• Multimeter with capacitance (our values will be in nF)
• Two leads with alligator clips
• 125 sheets of 21.6 cm × 27.9 cm printer paper separated into 4 “30-sheet” piles + 5 extra sheets
• Ruler with a centimeter scale
• Two sheets of heavy gauge aluminum foil (each should be 20 cm × 23 cm with one 3 cm × 3 cm offset tab)
• Several heavy books to firmly press the foil sheets together
• a piece of unfinished wood on which to place the capacitor as it is measured
• EXCEL to analyze graphs

Background

Although a capacitor can be formed using any type or shape of conductor, our analysis will focus on a parallel-plate capacitor created from two sheets of aluminum foil. The unit of capacitance is the farad F named after Michael Faraday. One farad is equal to one coulomb/volt. In our lab you will be working in nanofarads (nF).

In this lab we will measure the dependence of capacitance on the area of the plates and their separation distance. You will construct a parallel plate capacitor out of two rectangular sheets of aluminum foil separated by sheets of paper. You will slip two sheets of foil in-between sheets of paper and uniformly weigh the entire assembly down with numerous heavy books (perhaps as many as 10) to squeeze the plates together. A digital multimeter will be used to measure the capacitance of your capacitor.

You will use the capacitance-measuring function to directly measure capacitance. Since our capacitor is uncharged and not connected to a battery, you can connect either lead (red = positive, black = negative or ground) to either sheet of foil. However, it is recommended that you keep the same orientation throughout all of your trials. The meter operates by charging and discharging the capacitor being tested with a small known current and measuring the rate at which the resulting voltage changes - the slower the rate of increase, the larger the capacitance.

It is common for the multimeter to take a few seconds for the capacitance value to stabilize. When you measure the capacitance of your “parallel plates,” be sure that the aluminum foil pieces are pressed firmly and uniformly together and that they are electrically insulated from each other. Your sheets of aluminum foil should not stick out past the pages except where you make the connections. To help with reducing any accidental electrical contact, offset the locations of the two connection tabs. For 8.5 × 11 inch paper, a recommended set of dimensions is 20 cm by 23 cm, with connection tabs of 3 cm x 3 cm. The precise measurements are not critical - just get as close as you can.

Procedure

In Part I of the experiment you will measure how the capacitance depends on the separation between foils. In this phase you are keeping the area constant. A good initial separation is 5 sheets of paper and then increase the thickness by ≈ 30 sheets at each step. Important: When you measure C with the multimeter, be sure to subtract the capacitance of the leads (the reading just before you clip the leads onto the aluminum sheets). Remember to uniformly flatten (squeeze) the plates together with numerous heavy books! You must use the same number of books in each trial. You will take a minimum of five data points and record your values in the data table provided.

 What is the width of the smaller of the two sheets of aluminum foil (in meters)?

 What is the length of the smaller of the two sheet of aluminum foil (in meters)?

 What is the effective area of the plates of your capacitor?

In the table below, the best method to determine the thickness of the paper used is to measure the height of 500 pages and divide that total height by 500 to get the "thickness" of one page. A good value for the thickness is that, on average, a piece of 20 pound mimeo paper has a thickness of 0.092 mm.

 trial plate separation Cleads Cfoil Cfinal thickness # pages (m) (nF) (nF) (nF)
 1
 2
 3
 4
 5

After you have collected all of your data, open EXCEL and enter your data from the columns for the separation distance (x-axis) in meters and the final capacitance (y-axis). Create a scatter plot. This graph should NOT be linear. Fit a trend line. Before printing, title the graph and label your axes. Then print at least one graph for your group. Save your EXCEL file as Capacitor_LastnameLastname.xlsx

 What is the power of your trend line?

 What was the correlation coefficient of your trend line?

In Part II of the experiment you will measure how the capacitance depends on the area of the plates. A good separation to use in this phase of the experiment is 5 sheets of paper. The area can be varied by simply folding one of the foils in half and so on. Recall that the effective area of the plates is the overlap, or common, area that they share (that is, the area of the smaller sheet). Again, you will take five data points and record your values in the data table provided.

 How many pages separated your plates?

 What was the separation distance in meters?

 trial foil width foil height foil area Cleads Cfoil Cfinal (m) (m) (m2) (nF) (nF) (nF)
 1
 2
 3
 4
 5

After you have collected all of your data, open EXCEL and enter your data from the columns for the area in square meters (x-axis) and the final capacitance (y-axis). Create a scatter plot and fit a trend line. Before printing, title this second graph and label your axes. Then print at least one graph for your group. Resave your file.

 What is the slope of your trend line?

 What is the y-intercept of your trend line?

 What was the correlation coefficient of your trend line?

Conclusions

Based on your EXCEL graph in Part I, which of the following best describes the relationship between separation and capacitance?
Based on your EXCEL graph in Part II, which of the following best describes the relationship between area and capacitance?
 What difficulties did you encounter in making accurate measurements?

The actual mathematical expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d is derived using Gauss’ Law and is derived in most physics textbooks. The result is

Where εo is the permittivity of free space – air or a vacuum – which represents the willingness of a region to set up an electric field. εo has a value of 8.85 x 10-12 F/m. κ is called the dielectric constant and it measures how the electric field between the plates can be modified to allow the capacitor to have a greater capacitance (more charge per plate per volt) without any “sparking” occurring between the plates.

 Discuss how well your data on the variation of capacitance with separation and plate area agreed qualitatively with this result.

 You will now use your data to determine the dielectric constant κ for paper. Using this equation and the results of your trend line from phase two of the experiment, calculate a value of κ. Show your numerical calculations on your graph from Part II of the experiment. What value for the dielectric constant of paper did you determine? (The actual dielectric constant varies considerably depending on what is in the paper and how it was processed.) Typical values range from 1.5 to 6.