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

Part(a)

If a dielectric material has dielectric constant and it is used as a dielectric material between parallel plate capacitors, then Capacitance of parallel plate capacitor increases times.

If it is required to determine the dielectric constant of paper, then we insert paper between parallel plates and measure the capacitance using a multimeter that has ability to measure capacitance. From the known values of area of plate , distance between plates when paper is inserted and from the measured value of capacitance, we can determine the dielectric constant of paper.

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Part(b)

The following subset of experimental data will be useful to determine the dielectric constant because the capacitance is measured when paper is used a s dielectric material in parallel plate capacitor

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Capacitance C = ( A ) / d

where is dielectric constant, is permittivity of free space, A is area of parallel plates and d is distance between plates

if measured capacitance C is plotted as a function of (A/d), we get a straight line with slope equals

vertical axis :- Capacitance , Horizontal axis :- ( A/d )

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Excel Table is given below . Tabulated values are sorted in increasing order of A/d

Plot of capacitance Vs (Area/distance) is given below . Best fit Straight line and slope of the line

are shown in the plot

Since capacitance units is nF, slope = 0.02 10-9 = 2 10-11 ( F/m )

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slope = = 2 10-11 ( F/m)

Dielectric constant of paper = ( 2 10-11 ) / ( 8.85 10-12 ) = 2.26

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