Capacitance
Pre-Lab questions
1. What is stray capacitance? Why do we care about it? How do we know when it is
important?
2. Will stray capacitance add in series or in parallel to our measurements in this lab?
3. What is the expected dependence of capacitance on plate separation?
4. What is the smallest that a dielectric constant can be?
5. Show how/why the equivalent capacitance equations work (derive the equations
for adding capacitors in series and in parallel).
Introduction
Capacitors are common electronic components used to store and deliver electrical energy, much
like rechargeable batteries, but on time scales that are significantly faster. A capacitor consists of two
conductors held near each other but separated by an insulator. When an electrical potential difference,
V, is applied to the conductors, opposite charges of equal magnitude, Q, reside on each conductor,
creating an electric field between the conductors. The amount of charge that can be stored by the
capacitor for a given voltage can be expressed as a ratio, which is the definition of capacitance:
Q
C
V
While we cannot directly measure the amount of charge on a capacitor, we can measure its capacitance
(in units of farads, F) using a capacitance meter.
In this lab, you will examine several capacitors commonly used in electronic devices and investigate the
parameters that affect the capacitance of a parallel-plate capacitor. This parallel-plate capacitor is the
simplest capacitor design and the basis for many commercial capacitors. One type of capacitors
purchased from manufacturers are essentially rolled-up sheets of foil separated by a layer of paper or
other thin insulating material. The capacitance of a parallel-plate capacitor depends on the area A of
each conductive plate, the separation between the plates, d, and the dielectric constant  for the
insulating material between the plates ( = 1 for vacuum):
A
C   0
(1)
d
The constant  0 is known as the permittivity of free space = 8.85x10-12 C2/N*m.
While we can investigate many different behaviors of capacitors directly in the lab, we will also utilize
an online simulation to show even more situations and nearly endless parameter adjustments. Look at
each section of the lab for both hands-on measurements as well as online simulations to follow.
Procedure: Part 1
Setup: Turn on your BK-815 capacitance meter and set it to the 200-pF setting. Without connecting
any wires to the meter, adjust the “zero adj.” dial until the meter reads as close to zero as possible (note
the change of sign for values on either side of zero). Now attach two short banana plug wires to the
capacitance meter and note the capacitance value that appears as a result of these conductors (which
constitute a capacitor). Move the wires close together and far apart to determine the range of
capacitance that can occur simply from the wires. You can change the length of the wires you use for
measurements – try different configurations and decide within your group the best way to setup all
future measurements to minimize the effects of this stray capacitance. Be sure to consider this “stray
capacitance” in your experimental procedure and data analysis, especially if the measurements that you
make are of similar magnitude (i.e. low signal-to-noise ratio).
Note: The BK-815 capacitance meter has an official accuracy rating of ± 0.5% for readings up to 100
nF, and 1% accuracy for higher readings. However, experience has shown that accurate readings of
capacitance are often difficult to obtain, so it is advisable to be skeptical and check the validity of the
meter readings by confirming with another meter or the advertised capacitance value (depending on the
capacitor being used – finding the advertised capacitance may not be trivial).
Part A: Measuring capacitance (please spend no more than 5 minutes on this – the point here is to
familiarize yourself with the use of the meter)
1. Find at least two different kinds of capacitors and use your meter to measure the capacitance of
each.
2. Compare the measured capacitance with the nominal (rated) capacitance value. Do the values
agree within the accuracy rating of the meter?
Part B: Capacitance as a function of plate separation (this is the bulk of the part 1 experiment)
1. The two aluminum plates that you will use as the conductors for the capacitor are approximately
20 cm in diameter. Use a ruler or Vernier caliper to measure the precise diameter, and use this to
calculate the area, A.
2. Set the two plates on the magnetic track facing each other and placed as close together as
possible without touching. Connect them to the capacitance meter and record the reading, along
with the separation distance, d.
3. Change the distance between the plates several times, and record each new capacitance reading,
along with the corresponding plate separation. You should take enough measurements over a
range that is sufficiently wide enough to adequately examine the functional dependence of plate
separation on capacitance. Consider making a rough sketch as you take data to convince
yourselves that you have appropriate data.
4. Unplug the wires from the parallel plates, but keep them in the meter. Note the capacitance
reading and consider this stray capacitance when you analyze your data.
Part C: Online Simulation (separate document) – open and complete part 1.
Analysis/Discussion
Part 1: Measuring capacitance
1. Did your measured capacitance values agree with the nominal values? If not, what is the most
likely source of error? Did you find larger relative errors for small or large capacitance values?
Part 2: Capacitance as a function of plate separation
1. Estimate the uncertainties of your capacitance measurements, uc, and your distance
measurements, ud. Identify the primary source of these uncertainties.
2. Plot a graph of C versus 1/d, but first predict what you think it will look like. What is the slope of
your graph? Identify any discrepancies from what you expected.
3. Create a linear fit trend line for the graph and record the y-intercept. What does this value
represent? Do you need to account for it in your analysis?
4. Calculate  0 from your graph and compare with the known value.
Discuss your findings and explain any discrepancies between what you expected and what you actually
measured. How did the stray capacitance from the wires affect your results? What lessons or insights
did you learn from this experiment?
Part 2 – Capacitors and the effects of Dielectrics
Dielectrics are electrical insulators. They can be polarized when placed in an electric field. The
polarization caused by the electric field (in this case, from the parallel plates of the capacitor), cause an
electric field within the dielectric material that reduces the overall field of the system.
Dielectrics are commonly used in capacitors in part to prevent the conducting plates of the capacitor
from coming into direct electrical contact. More importantly, however, using a material with high
permittivity allows more charges stored in the capacitor at a given voltage, thereby increasing the
capacitance of the system.
Procedure - The effect of dielectric materials on capacitance
1. Two types of dielectrics should be available: clear Plexiglas and gray PVC. Take one slab of
PVC and place it between the parallel plates so that both plates are touching it.
2. Record the capacitance and the distance between the plates.
3. Remove the slab without changing the distance between the plates and record the capacitance
reading with air as the dielectric.
4. Repeat this for two and three slabs of PVC.
5. Obtain similar measurements using one, two, and three slabs of Plexiglas.
6. Obtain similar measurements with at least one other dielectric in the room (be creative!)
7. Open the virtual capacitor lab and complete part two on dielectrics (short!)
Analysis - The effect of dielectric materials on capacitance
1. Use your data to calculate the dielectric constant  for the Plexiglas, the PVC and your selected
material. Which one is greatest?
2. According to the Handbook of Chemistry and Physics, the dielectric constants for PVC and
Plexiglas are 3.39 and 3.12, respectively. How do your results compare to these numbers?
3. Use the internet to look up the dielectric constants of PVC and Plexiglas (find a few different
websites and remember to cite your sources). How do these numbers compare to your results?
How do they compare to those of the Handbook of Chemistry and Physics?
Discussion –
Discuss your findings and explain any discrepancies between what you expected and what you actually
measured. What lessons or insights did you learn from this experiment? What are some commonly
used dielectrics as well as the situations where dielectrics would be used frequently?
Part 3 – Capacitors in circuits
Capacitors in isolation are interesting, but they are used in a nearly every single circuit that you can find.
Seeing how they behave in different types of orientations is important. Capacitors can be connected in
either series or parallel with other capacitors – this will affect the overall capacitance of the circuit.
The equivalent capacitance can be calculated according to the following equations:
1
1
1
1



Capacitors in series:
(2)
C C1 C 2 C3
Capacitors in parallel:
C  C1  C2  C3
(3)
Note that capacitors in parallel add because the same voltage is applied to each capacitor, so the effect is
equivalent to one large capacitor with the total plate area of all the individual capacitors (assuming
identical components). For identical capacitors in series, the effect is the same as a single capacitor with
a wider separation equivalent to the total separation of the individual gaps. A capacitor with two or
more materials between the conductive plates can be treated simply as a series combination of individual
capacitors.
Procedure: Capacitors in series and parallel
1. Find two or three capacitors that have similar values. Connect these in parallel and measure the
combined capacitance. Does this value agree with the expected equivalent capacitance for this
parallel combination?
2. Repeat using the same two capacitors connected in series. Is the combined capacitance what you
expect it to be?
Analysis: Capacitors in series and parallel
1. Using the values of the two individual capacitors, calculate the expected equivalent capacitance
for the series and parallel combinations and compare with the measured values. Do they agree
within the experimental uncertainties? If not, why?
Discussion
Compare your results to predictions – do they match? Why or why not? Discuss how resistors
act differently in circuits in both series and parallel configurations and why.