Capacitors

October 2, 2014

Kortney Melancon and Austin Morris

Abstract

The purpose of the experiment was to observe the properties of a parallel

plate capacitor as well as determine the equivalent capacitance of several capacitors

connected in series and parallel. The capacitance of each individual capacitor was

measured using the LCR multimeter. The capacitors were then connected in a

parallel and series connection and their capacitance values were recorded. It is clear

that it is ineffective to calculate the dielectric constant from only a single

measurement.

Introduction

The purpose of the experiment was to observe the properties of a parallel

plate capacitor as well as determine the equivalent capacitance of several capacitors

connected in series and parallel. Capacitance is characterized by a parallel plate

arrangement and is defined in terms of the charge stored by

C=QV

Where Q is the magnitude of the charge stored and V is the potential

difference between them. The capacitance is expressed in units of Farad, equal to 1

Coulomb/volt. A capacitor is a charged storage device that is typified by two parallel

plates separated by a layer of insulating material and is dependent on dielectrics. If

the size of these two plates is greater than the spacing that exists between them, the

equation for this arrangement is

C=K ε0 Ad

Where K is the relative permittivity of the dielectric material between the

plates, ε 0 is the permittivity of vacuum, A represents the area of a plate and d is the

separation distance that exists between the plates. K is equal to 1 in free space,

greater than 1 for other materials.

If two or more capacitors are connected, the equivalent capacitance can be

determined by using the following equations

1) If the capacitors are connected together in series:

1C

= 1C1

+ 1C2

+ 1C3

+…

2) If the capacitors are connected in parallel:

C=C 1+C2+C3+…

The dielectric constant will be determined by rearranging to solve for K in

the second formula given above. The capacitance of this capacitor will be measured

for several separation distances, d, to observe the affect the distance has on the

capacitor. Individual capacitors will be connected in series and parallel and their

equivalent capacitance will be measured and compared to those given by the third

and fourth equations stated above.

Experimental Procedure

Using a micrometer, the thickness of a single insulating sheet was measured

at four different places to determine the consistency of thickness. Average thickness

was recorded. A single sheet of the transparency blanks was placed between the two

flat disk shaped conductors. The short cables of the LCR multimeter were then

connected to the upper and lower connecting terminals on the capacitor setup. The

LCR multimeter was switched to the capacitance position. The ends of the leads

were connected to the two connectors on the capacitor setup into the slots on the

LCR multimeter. The capacitance was then measured and the value for the dielectric

constant was determined.

The capacitance was then measured as a function of the number of

transparency blanks placed between the two parallel plates. One additional

transparency sheet was added in between the plates and the capacitance was again

measured using the LCR multimeter. This process was repeated until ten

measurements were obtained.

The capacitance of each individual capacitor was measured using the LCR

multimeter. The capacitors were then connected in a parallel and series connection

and their capacitance values were recorded.

Measurement Results

Table 1. The measured capacitance values as a function of the number of sheets of

transparency.

0 0.0002 0.0004 0.0006 0.0008 0.001 0.00120

500000000

1000000000

1500000000

2000000000

2500000000

3000000000

f(x) = 2346854722178.89 x + 433273868.889184R² = 0.971034204913911

Graph 1. Graphical analysis of capacitance values as a function of the number of

transparency sheets separating the parallel plates.

Data Analysis

C=K ε0 Ad

To calculate the dielectric constant, K, the above equation can be rearranged

as follows

K= Cdε0 A

=(0.0001m )(5.85×10−12)(8.85×10−12)(0.0165)

=0.004006

K= 1ε0× A ×a

= 1(8.85×10−12) (0.2347 ) (0.0165 )

=2.917

Discussion

The dielectric constant of the transparencies (cellulose acetate) is 2.917. This

is well within the expected range of 2.5-5.0. In the first part of the experiment, the

dielectric constant was calculated to be 0.004006, which is nonphysical because it is

below 1. The dielectric constant is a ratio between the permittivity of the material

and the permittivity of free space. Thus, it cannot hold a value below 1. It is clear

that it is ineffective to calculate the dielectric constant from only a single

measurement.