Question

In an experiment, a group of students will determine the dielectric constant of paper. They have the following materials available, as well as other materials traditionally available in a high school physics lab.

• _____ Aluminum foil
• _____ Sheets of paper
• _____ Sheets of plastic
• _____ Multimeters with the ability to measure capacitance

(a) Outline an effective experimental procedure to gather the necessary data that can be used to determine the dielectric constant of paper. Place a check mark next to each item above that the students should use. Draw a labeled diagram to represent the setup used for this procedure.

The table below shows data from a different experiment in which students measure the capacitance of different setups as they vary the distance between the two plates of the capacitor, the area of the plates, and the material inserted between the plates.

Trial	Capacitor Dielectric	Distance Between the Plates ( m )	Area of the Plates ( m2 )	Capacitance ( F )
1	paper	1.00×10−4	0.04	8.1×10−9
2	paper	1.00×10−4	0.09	18.3×10−9
3	paper	1.00×10−4	0.16	32.6×10−9
4	paper	1.00×10−4	0.25	49.8×10−9
5	paper	2.00×10−4	0.25	23.1×10−9
6	paper	3.00×10−4	0.25	18.9×10−9
7	paper	4.00×10−4	0.25	14.9×10−9
8	paper	5.00×10−4	0.25	9.2×10−9
9	plastic	1.10×10−4	0.04	11.3×10−9
10	plastic	1.10×10−4	0.09	25.3×10−9
11	plastic	1.10×10−4	0.16	45.1×10−9
12	plastic	1.10×10−4	0.25	70.4×10−9
13	plastic	2.20×10−4	0.25	35.2×10−9
14	plastic	3.30×10−4	0.25	23.5×10−9
15	plastic	4.40×10−4	0.25	17.6×10−9
16	plastic	5.50×10−4	0.25	14.1×10−9

(b)

i. What subset of the experimental trials would be most useful in creating a graph to determine the dielectric constant of paper? Explain why the selected trials are most useful.

ii. Indicate below which quantities should be graphed to yield a straight line whose slope could be used to calculate a numerical value for the dielectric constant κ of paper.

Vertical axis: Horizontal axis:

(c) Plot the data points for the quantities indicated in part (b)(ii) on the graph below. Clearly scale and label all axes including units, if appropriate. Draw a straight line that best represents the data.

(d) Use the data to determine a value for κ of paper.

(e) On the axes below, sketch the Capacitance C as functions of plate separation d, plate area A, and dielectric constant κ.

Answer 1

The given data is very useful because we can draw a graph between C and A with constant separation between the plates.

We have

Here k is dielectric constant, A area and d separation,

Here C is directly preportional to A. So the graph between them is a straight line with slope,

So we can find slope from the graph. Substitute known values of d and .

We can fink k for paper and similarly for plastic.

Take C on x axis and A on y axis.