Physics 116 - Capacitors
Lab Manual Home
OBJECTIVES
·
To define capacitance
·
To determine how the capacitance of conducting
parallel plates is related to the separation distance between the plates and the
surface area of the plates
·
To determine the permitivvity constant
INTRODUCTION
Capacitors are widely used in a variety of electric
circuits to provide extra energy or help keep energy levels at a constant value.
As an example, a home cooling (AC) unit will have a capacitor that stores
charge (energy). When the system is
started, the capacitor can release the stored energy to assist the unit in
starting the compressor necessary to cool the home.
Electronics with flashing lights use a capacitor in a timing or RC
circuit.
The classical design of a capacitor, which you will use in
this lab, is two parallel conducting plates, separated by an insulator as shown
below.
From
https://goo.gl/images/Cb7OxV
Charges of opposite sign are stored on the two plates,
establishing an electric field between the plates.
The capacitance can be defined as a ratio of charge to voltage, or
where C is the capacitance, in Farads, Q the charge on one
plate in Coulombs (each plate has equal magnitude charge), and V is the
separation Voltage.
However, it is a misnomer to think that the capacitance of
a capacitor is defined by the amount of charge and voltage.
Capacitance is defined by the geometry of the capacitor design, or
particularly on the cross sectional area of the plates and the separation
distance of the plates (and also the material, if any, placed between the
plates).
In this lab, you will use a pHet simulation to derive the
relationship for capacitance, as a function of both separation distance and the
area of the plates.
PROCEDURE
PART 1
In this part of the lab, you will determine the
relationship between capacitance and plate area.
Using the simulation, fix the voltage at 1.5 V (the default), the plate
Area at 100 mm2 (default), and the separation distance at 5.0 mm.
Select the Capacitance meter, and measure the capacitance.
Repeat for the five values of plate area shown below.
Plate Area (mm2) |
Capacitance (F) |
100 |
|
150 |
|
200 |
|
300 |
|
400 |
|
Graph your data in EXCEL, Google Sheets, or on a graphing
calculator.
1.
What is the mathematical function suggested by
the graph (linear, quadratic/parabola, inverse/rational)?
If you are unclear as to the shapes of these graphs, visit
http://www.mtsac.edu/marc/worksheet/general_topics/15common_graph_shapes.pdf
2.
Write a corresponding equation based on your
answer, using C as the symbol for Capacitance, A as the symbol for plate Area,
and k as some arbitrary constant.
For example, if you felt the relationship was linear, you would write
.
If you felt the relationship was quadratic, you would write
.
If you felt this is an inverse relationship, you would write
.
PART 2
Now the relationship between
Capacitance and plate separation will be investigated.
Keep the plate area at 400 mm2 and the battery voltage at 1.5
V. Complete the table below for the
indicated plate separations
Plate separation (mm) |
Capacitance (F) |
5 |
|
6 |
|
7 |
|
8 |
|
9 |
|
10 |
|
Graph your data in EXCEL, Google Sheets, or on a graphing
calculator.
1.
What is the mathematical function suggested by
the graph (linear, quadratic/parabola, inverse/rational)?
2.
Write a corresponding equation based on your
answer, using C as the symbol for Capacitance, d as the symbol for plate
separation, and k as some arbitrary constant.
For example, if you felt the relationship was linear, you would write
and
so forth.
CONCLUSIONS
1.
Write an equation for Capacitance (C) as a
function of Area (A), separation distance (d), and a constant (k) by combining
your two equations. For example, if
you felt that both relationships were linear (
,
then you would write an equation for capacitance that shows capacitance varying
linearly with both A and d, or
.
Write a brief statement justifying your decision.
2.
Find the equation for Capacitance as a function
of Area and distance from a reputable source (text, appropriate website), and
copy the equation and source below.
If your equation above does not match, explain why your equation in #1 was
incorrect.
3.
You now know that the constant
k we used throughout the lab is the
permittivity of free space,
.
Research what this constant represents and report your findings below.
4.
Choose any one set of data from either table (a
known value of C, A, and d) and calculate
.
Show your work below.
5.
If your value in 5 differs from the actual value
of
(8.85
x 1012), explain why you think this difference exists.