Lab 4 Build a Capacitor

Energy storage is very important in a technology driven society. In this lab, you are building a device that can store energy called a capacitor. From Coulomb’s law and the superposition principle in book’s section “Two Uniformly Charged Disks: A Capacitor”, you determined that the electric field between two capacitor plates can be almost constant and equal to \(|E| = Q / (\epsilon_0 A)\) given large disks and small separations. Here, \(Q\) is the charge on each plate, and \(A\) is the area of each of the plates. The plates are separated by vacuum. If the space between the plates is filled with an insulating material, then the electric field is reduced by a factor \(K\) due to polarization, see “Potential Difference in an Insulator” section in the M&I book. Therefore, \(|E| = Q / (\epsilon_0 A K)\), where K is called the dielectric constant for the filling material. Measuring electric potentials is easier, and the definition in one dimension is \(\Delta V = - \int E_x \; dx\). The definition of the capacitance \(C\) (measured in units of Farad after Michael Faraday) is provided through the measurement of the electric potential across a capacitor, \(\Delta V = Q / C\); therefore, in a parallel plate capacitor, the capacitance solely depends on its geometry and the dielectric constant K of the material and is independent of the applied voltage or stored charge. Before the lab, familiarize yourself with the capacitance meter using its manual, so that you can take accurate measurements.

By the end of this activity, you should be able to do:

  1. Learn how to use a capacitance meter
  2. Design an electric component

4.1 Goals

  1. Build a capacitor with Aluminum foil and paper. Measure its capacitance. Note: there will always be some air between the two plates (possibly even water), therefore your capacitor should be modeled as Al-air-paper-Al caoacitor.
  2. Either vary the separation distance or the capacitor area and verify experimentally, whether the uniformity of the electric field holds for your capacitor.

4.2 Prediction

  1. Derive an equation for the capacitance \(C\) from a parallel-plate capacitor given \(K\) as the dielectric constant for a filler medium (air + paper).
  2. Make a graph of the capacitance \(C\) versus plate area \(A\).
  3. Make a graph of the capacitance \(C\) versus plate separation distance \(d\).
  4. Find the dielectric constant for paper in the literature, cite your source using a reference.

4.3 Equipment

  1. Capacitance Meter, ELIKE DT6013 (see manual posted on BeachBoard)
  2. Wires with alligator clips
  3. Paper, Aluminum foil
  4. Scissors

4.4 Caution

  • Make sure the distance between the Al foils is even (use something heavy to press the capacitor flat), very close, and completely separated (no “shorts”). Test the repeatability of your experimental setup.

4.5 Procedure

  1. Design and build a capacitor by using Aluminum foil and paper as a separation.
  2. Use two alligator clips and connect each Aluminum plate and determine the capacitance using the capacitance meter.
  3. Ensure to make precise measurements.
  4. Choose to either vary the surface area or the separation distance of the capacitor plates, make the decision as a group; vary one parameter.
  5. Calculate the capacitance using the geometrical parameters of the designed capacitor and the dielectric constant of paper from the predictions.

4.6 Measurement

Create a table corresponding to your measurements. Make sure to include columns for uncertainty in the measured capacitance. Compute the value for the dielectric constant K and compare with the value from the literature.

4.7 Graph

Make a graph of the measured capacitance versus the varied parameter (either surface area or thickness). The experimentally measured data points are added as points with their relative uncertainties.

Add the calculated capacitance values to the data as a continuous line curve.

4.8 Discussion

Share the graphs of the capacitance versus area or thickness. Also share quantitative values of the highest measured capacitance value with uncertainty and what geometry resulted in this. How do the results agree / disagree with the predictions qualitatively. What about quantitatively? How did you measure the area of the capacitor? How did you make electrical contact to the bottom plate?

Does the parallel-plate capacitor approximation work in this case?

4.9 Summary

Summarize your results with regards to the goals. Moreover, discuss how you built your capacitor and how your results relate to the prediction. What did you learn?