**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 tomeasure 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.

*Note: before you use the capacitance meter, be sure to zero it. Let
the leads hang loose and make sure
the capacitance meter hovers around zero.*

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. 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 find 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. 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.)*

*Last Modified onWednesday, September 25, 2013*