## Aluminum Foil Capacitors

Finding the dependence of capacitance on geometric properties.

You will be constructing capacitors using aluminum foil as the conducting metal plates and pages of your text as a uniformly thick insulator that separates the metal plates.  We want a fairly large rectangular sheet of aluminum foil with a small tab sticking out to attach the meter that will be used to attach the clips from the meter used to measure the capacitance.  Once you have cut two identical sheets, carefully measure the dimensions of the rectangle (less the tabs) and record the values.  When you start making capacitors, turn one of the aluminum sheets over so that the tabs are separated from each other.  Carefully smooth out any wrinkles in each piece of aluminum foil without tearing it. Please read and follow the notes before continuing.

Notes:

Frequently check for the low battery indicator on the Capacitance Meter as indicated in the figure.
Your foil plates should be rectangular and about 60 to 80 % of the size of a page in your text. The tabs should be about 1 cm by 1 cm or smaller.
Drawing the plates with tabs on a sheet of paper and then cutting the plates out of a folded piece of aluminum foil works well.
Best results are obtained when the plates are in the central portion of the book - front to back.  The weight of the pages helps to reduce the air gaps.
Before you use the capacitance meter, be sure to zero it with the meter in place and the leads hanging loose near where the tabs will be.  Please make sure the capacitance meter hovers around zero.
Ensure that the foil 'plates' are aligned with each other - areas that don't overlap don't contribute much to the capacitance.
When taking data always use the most sensitive range of the capacitance meter.  Don't forget to check your zero if you change ranges.
Make sure your plots include the origin.  Also extend the axes a bit to show the last data point.  Turn off 'Connect Points' for your data.
If any graph is linear add the best fit line.

a.) Use two equal sized sheets of aluminum foil and a large textbook to make your own capacitor. Use the capacitance meter to find the capacitance of your home-made capacitor. Make different capacitors by inserting between the sheets at least 5 different separations in your textbook (i.e. 30 pages, 60, 90, 120, 150 works well.) Be careful to make sure the pages are flat and not wrinkled before your measure the capacitance.  Plot capacitance first as a function of number of pages and then as a function of inverse number of pages. (hint: use a calculated column)  How does capacitance depend on plate separation?

b.) Now re-measure C for your homemade capacitor, but this time, leave the page separation at about 50 pages and step down the size of the sheets by carefully folding them in half, then quarters, then eighths, etc.  Record the number of pages used to separate the plates and make a table of area and capacitance.   Plot C as a function of plate area, A. If the plot is linear, add the best-fit line.  Does the line pass through the origin?  If not, what is the meaning of the y-intercept?

c.) Now that you have separated out all dependence on the geometry of the capacitor, what is left is a specific property of the material between the plates - in this case the  paper of your textbook. This property is called the permittivity, e, of your textbook's paper. Measure the thickness of a large number of pages and calculate the thickness of one page. Use this value to convert your separations in pages into standard units.  The relative dielectric constant is the ratio of your measured capacitance to the calculated capacitance of a capacitor with the same area and spacing but with air (or vacuum) between the plates.  If necessary, convert your values into SI units and compute the relative dielectric constant of the paper by comparing your measured capacitance to that expected with air between the plates.  Check your text for a list of dielectric constants.  If paper is not listed in your text go online and search Wikipedia for the appropriate table.  Compare your experimental value to the accepted value for paper.  How well does it agree? Speculate on possible causes if your value is not in reasonable agreement.

(There may be an additional component that will be discussed during lab.)