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Resistivity Lab 21 February 2017 PH 344 B I certify that the contents of this report are my original work

Statement of Problem

What is the relationship between the length, cross sectional area, and total resistance of a resistor? What is the resistivity of a particular material? Description of Experiment For this experiment, make the thickness of a stack of carbon impregnated paper and determine the thickness of a single sheet of the paper. Then start with a known length of paper that is 2 cm wide. Measure R for the particular length chosen. Then successively make the length shorter and shorter, continually measuring R. Make a graph of R vs. L. Then, measure out strips of paper with varying widths. Measure R for a constant length on each strip of paper. Make a graph of 1/A. Then calculate percent difference for the resistivity found. Data Width of paper (m) 0.004 0.004 0.004 0.004 0.004

Thickness (m) 0.000009 0.000009 0.000009 0.000009 0.000009

Cross sectional area (m^2) 0.000000036 0.000000036 0.000000036 0.000000036 0.000000036

Length (m) 0.05 0.1 0.15 0.2 0.25

Resistance (ohms) 337000 596000 864000 1118000 1371000

0.004 0.01 0.015 0.02 0.025 0.03

0.000009 0.000009 0.000009 0.000009 0.000009 0.000009

0.000000036 0.00000009 0.000000135 0.00000018 0.000000225 0.00000027

0.15 0.15 0.15 0.15 0.15 0.15

864000 300000 212000 200000 166000 140000

Results Graphical analysis was conducted on the data collected. A graph of R (Ohms) vs. length (m) was created. This graph established a linear relationship, which allowed for the determination of the resistivity. The graph produced an equation of y=5x106 x +80200, with an R2 value of 0.999. The slope then represented the relationship p/A. A graph of R (Ohms) vs. 1/A (1/m2) was created. This graph established a linear relationship, which allowed for the determination of the resistivity. The graph produced an equation of y=0.0301x+13108, with an R2 value of 0.989. This slope then represented the relationship pL.. When these two values were compared a percent difference of 23% was found. Percent difference: ((Actual-Experimental)/Actual) x 100 Figures

resistance vs. length 1600000 1400000 f(x) = 5180000 x + 80200 R² = 1

1200000 1000000 800000 600000 400000 200000 0

0

0.05

0.1

0.15

0.2

0.25

0.3

Figure 1. A plot f R (ohms) as a function of length (m) yields a plot where a linear relationship can be established. This relationship allowed for a linear graph to be made.

resistance vs. 1/area 1000000 900000 800000 700000 600000 500000 400000 300000 200000 100000 0

f(x) = 0.03 x + 13108.39 R² = 0.99

0

5000000

10000000

15000000 Linear ()

20000000

25000000

30000000

Linear ()

Figure 2. A plot of R (ohms) as a function of 1/A (1/m2) yields a plot where a linear relationship between can be established. Conclusion As a result of the experiment, it can be seen that a relationship between length, area and total resistance can be established. Also, the resistivity of an object can be determined. The resistivity difference between the two areas was found to be 23%. A potential source of error could have been in determining the area of the paper. When measuring the thickness of the paper, it was very hard to get an exact number because the paper is so thin. If the paper thickness was not exact, the collected data would produce a resistivity that is not accurate....