II.  CONSTRUCTING A CAPACITOR

Equipment List: Aluminum foil and scissors (50 yds at 12" length)
             Wax paper
             One Simpson VOM and banana leads
             one 2 meter stick per lab table
             Thin, stranded, insulated wire and cutters
             scotch or masking tape
             a "dowel" to roll up the cap (a few for the whole class)
             a capacitance meter (one for the whole class)    

Purpose: To construct a capacitor from common items, estimate it's capacitance using a standard formula, and confirm its value with a capacitance meter.  

Introduction: One way to understand how something behaves is to build a working model of it. In this lab you will gain insight into the behavior of a capacitor by making one.

A capacitor is composed of two conductors separated by an insulator or a dielectric. Typically, the two conductors have an equal area. When charged, each conducting sheet of the capacitor holds the same magnitude of charge but of different sign, one sheet positive, the other sheet negative.

The formula for the capacitance, C, of a parallel plate capacitor is:

{bold{C}~=~{epsilon~A} over{d}}~~~~~~
In this lab you will construct a capacitor and predict its capacitance based on the above formula. To predict its value, you must take measurements of the relevant materials you use to construct the capacitor. The dielectric constant for wax paper is: κ = 2.0. You will need micrometers to measure the thickness of the wax paper, d. After your capacitor is constructed and you have a numerical prediction for its value, you may then measure the capacitor's value with a "cap" meter provided by your instructor and compare the results.

Procedure:
1. Choose two equal lengths of wax paper (your dielectric). Make them each about four feet long. The exact size is not important.

2. Now cut two equal lengths of aluminum foil (but shorter in length than your waxed paper by about 3 inches at each end). Make the widths of the aluminum foil also shorter than the wax paper by one inch on each side. The two sheets of aluminum foil should have the same physical dimensions (length and width) so that their areas are equal. Measure these lengths and widths for each of the two aluminum foil sheets precisely with the meter stick and calculate the area of each sheet. Use units of square meters.

3. Work on a clean lab table as dirt particles can cut the foil. Lay down one sheet of wax paper. Then lay one sheet of foil on the paper such that the foil lies evenly within the boundaries of the paper. Now lay down the second wax paper sheet on the foil sheet and finally the second piece of foil on top of the wax paper. Make sure that the two pieces of foil do not touch one another as this will "short" out your capacitor. See the accompanying figure.

4. Before you start rolling up the capacitor, gently attach your two leads to the two foil sheets, one lead to one sheet.
Be careful to not let the wires pierce the paper or foil. Spread out the strands of the braided wire evenly on the sheet of foil and tape the strands down firmly with the tape provided. Have each lead pointing out and away from the other lead. Make sure each lead has a good electrical connection to the sheet.

5. Now carefully roll all four sheets around the dowel but not so tightly that you can't take the dowel out! Remove the dowel, tape the capacitor closed and tape your name on it.

Now that your capacitor is complete, test it to make sure its working. Use the Simpson VOM on the resistance scale to measure the "resistance" of the capacitor. You will measure either a very high resistance or a zero resistance. Which of those two values indicates the capacitor is operational and why? Explain why the other value would indicate the capacitor is not working.

Other things to do: If charged, a capacitor will retain its charge for some time before it "bleeds" away. Try connecting your capacitor to the DC power source (one lead in each output jack). Have the DC power source on its full voltage setting for a maxium charge. Disconnect the capacitor from the power supply and then connect the capacitor to your VOM ON DC VOLTS SCALE - 50 VOLTS MAXIMUM. Observe the capacitor discharge through the VOM by seeing the needle start out at a large value (a voltage value equal to its original charged voltage) and gradually fall to zero. Repeat the process until you are bored. Comment on the "way" the needle goes to zero, it is a special process you will learn about later called "exponential decay".

Analysis: Estimate the capacitor's value from the standard formula given above and compare it to the measured value from the capacitance meter. Tape the most reliable value on the capacitor and save it for future labs. If the dielectric strength of the wax paper is 40 X 106 V/m, to what maximum voltage could your capacitor be charged?

Conclusion: Comment on the agreement between the estimated and measured values. State any reasons how the agreement could be improved in future attempts. Are there any systematic errors in the procedure? Could they be eliminated or minimized? What would be worse during the construction phase, puncturing the aluminum foil or the dielectric? Does the diameter of the rolled capacitor have an effect on its capacitance?