Lakeside High School

Aluminum Foil Text Book Capacitor

AP Physics

Tasnim Khan1/25/2011

INTRODUCTION

A capacitor is a device that stores charge. The amount of charge a capacitor can hold for a given potential difference across it is called the capacitance, which is measured in unit called the Farad. The formula for capacitance is expressed as:

C=QV

where C stands for capacitance(F), Q stands for charge(C), and V stands for potential difference(V). However, for the purposes of this lab, we used a variation on the formula:

C=ε0 AD

where ε0 stands for the permittivity of free space(8.85*1012), A stands for the area of the metal plates of the capacitor, and D stands for the distance between the plates of the capacitor. Also, to find the dielectric constant of the pages of the text book, we used this formula:

C=K ε0 AD

the only new variable being K, which stands for the dielectric constant.

PURPOSE

The purpose of this lab is to:

Investigate the quantitative nature of the dependence of capacitance on plate separation and on the area of the two plates

Determine the dielectric constant for text book paper

PROCEDURE

Make two sheets of Aluminum Foil of equal size and place them in your text book separated by a reasonable amount of pages. The sheets shouldn’t extend past the edges of the book except for small tabs for making a connection with the multimeter. The capacitance can directly be measured by the multimeter. Repeat this step with varying number of pages between the sheets of Aluminum Foil. Next, cut the sheets of aluminum foil into pairs of varying areas. Place these pairs in the text book separated by a constant number of pages. Take readings with the multimeter.

DATA

Number of Pages vs. Capacitance

Area of Aluminum Foil: 0.066m2

Number of Pages Capacitance35 3.5*10-9 F40 3.0*10-9 F45 2.5*10-9 F

Varying Areas of Aluminum Foil vs. Capacitance

Number of Pages: 40

Area of Foil Capacitance0.0484m2 2.2*10-9 F0.0660m2 3.0*10-9 F

ANALYSIS

To find the distance between the sheets of foil, we used the formula:

C= (8.85*10-12) AD

and plugged in values for C and A to find the D.

EX: 3.0*10-9 = (8.85*10-12) 0.0660D

Distance between Sheets of Foil vs. Capacitance

Distance between Foil Capacitance0.00017m 3.5*10-9 F0.00019m 3.0*10-9 F0.00023m 2.5*10-9 F

To find the dielectric constant of text book paper, we used the formula:

C=K (8.85*10-12) AD

and plugged in values for C, A, and D to find the K.

3.0*10-9=K (8.85*10-12) 0.06600.00019

K=0.979

GRAPHS

0.00016 0.00017 0.00018 0.00019 0.0002 0.00021 0.00022 0.00023 0.000240.00E+00

5.00E-10

1.00E-09

1.50E-09

2.00E-09

2.50E-09

3.00E-09

3.50E-09

4.00E-09

Distance between Foil vs. Capacitance

Distance between Foil (m)

Capa

citan

ce (F

)

0 0.01 0.02 0.03 0.04 0.05 0.060

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Varying Areas of Foil vs. Capacitance

Areas of Foil (m2)

Capa

citan

ce (F

)

Conclusion

According to the data collected during the experiment, there is a positive correlation between the area of the sheet of aluminum foil and the capacitance; there is a negative correlation between the distance between the sheets of foil and the capacitance. Those were the results to be expected, and they can be proved by looking at the formula. The dielectric constant for text book paper was found to be 0.979, whereas according to Table 17-3 in the textbook, the dielectric constant of paper is stated to be 3.7. The percent error for the dielectric constant comes out to be 73.5%.