# Building a capacitor to find the dielectric constant

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1. Oct 2, 2015

### xSpartanCx

1. The problem statement, all variables and given/known data
I have a lab where I have to use two methods to find the capacitance of printer paper.

2. Relevant equations
C = kAeo / d

3. The attempt at a solution

From these slopes, I got k = .897 for the first type (using changing distance between the plates of the capacitor)
for the second method, altering the size of the capacitors, I got k = 1.8. Is there something I'm doing wrong or did we just get inconsistent data?

2. Oct 3, 2015

### rude man

Capacitance should rise with area, not area1/2.
Did you expect the two k's to be the same? Not sure why they should be ...
The computed capacitances are all within reason.
What is the area for the 1st plot? How many sheets for the second plot?

3. Oct 3, 2015

### xSpartanCx

I expect the two k's to be the same since it's still got paper in between. the first plot has an area of .252m by .2m, the second plot has 4 sheets. If I do A vs C, then I get k to be 3.7. Why are they so different?

EDIT: Oh, I see! is the 3.7 the dielectric constant for 4 sheets, and therefore I should divide it by 4 to get the constant for one?

4. Oct 4, 2015

### Staff: Mentor

The slopes should not be the same, as you compare different things (fixed area and variable 1/d versus fixed 1/d and variable area). Converted to the parameter in the general formula for the capacitance, you should get the same result.

The first plot should show a linear relationship, so the trend line should go through the origin. It does not, so something went wrong there.
For the second one it's hard to tell because you plotted the square root, but I think there is an offset issue as well.

The dielectric constant does not depend on the number of sheets. It is a material constant.

5. Oct 4, 2015

### xSpartanCx

So then why do I get .89 for one calculation and 3.7 for the other? The slope I get for C vs A is 8x10^-8

6. Oct 4, 2015

### Staff: Mentor

Something is wrong with the measurements if the trend lines don't go through the origin.
I don't know what, and I guess it would be necessary to analyze the measurement procedure in detail.

7. Oct 4, 2015

### xSpartanCx

On page 53 of this paper (http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/e&m/dielectr_const_2k4.pdf), they show a graph of inverse thickness vs the capacitance. In that paper, they show that based on the amount of pressure, the y intercept varies, and none of their lines ever go through the origin, so is that really an issue?

8. Oct 4, 2015

### Staff: Mentor

The variation with area data is wrong/erroneous. After looking at your table, I conclude your measurements were probably of the side of a square vs. capacitance, and you need to convert that to area vs. capacitance before plotting.

You deserve praise for the neat presentation of your data and graphs here.

9. Oct 4, 2015

### xSpartanCx

Unfortunately those are the dimensions of the area; we kept the x dimension stable at .252m, whereas the y would decrease -- {.2, .19, .183, .173, .16)m

10. Oct 5, 2015

### Staff: Mentor

Have you compared your results with what might be expected? With the relative permittivity of paper being in the range 2-4.5, what capacitance might you expect with a 0.0002m thickness sandwiched between metal plates 0.25m x 0.2m?

How to account for any discrepancy?

11. Oct 5, 2015

### Staff: Mentor

How did you measure capacitance?
Could something else in the circuit increase capacitance?