College Physics Lab
PH 144
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Resistivity
Purpose:

To study the relationship between the length, cross-sectional area, and total resistance of a resistor. To determine the resistivity of a particular material.

Discussion:
The resistance of a rectangular resistor is given by R = rL/A where L is the length in the direction of current flow, A is the cross-sectional area perpendicular to the current flow, and r is the resistivity. The resistivity is a property of the material and does not depend on how much material there is or what geometrical shape it is in. The cross-sectional area is given by A = WT where W is the width and T is the thickness. You will verify the formula for R in two steps. First you will show that if A is kept constant, R is proportional to L. Then you will show that if L is kept constant, R is inversely proportional to A.

The resistive material you will be using in this experiment is the carbon impregnated paper which you used in the equipotential drawing experiment. You will be using relatively narrow strips of this paper in order to insure that the current follows a relatively straight path.
You will be using a VOM (Volt-Ohm-Milliammeter) to measure resistances. Notice that the resistance scale decreases from 'infinity' on the left to 0 on the right. When the VOM is set to measure resistance it is actually responding to the current which passes through the resistor as a result of the potential difference provided by a battery inside the VOM. The resistance scale has been marked in such a way that resistance is read directly instead of being computed from the known battery voltage and measured current.

Materials:
Multimeter (analog or digital)
strips of carbon impregnated paper from equipotential lab
micrometer
paper clips

Procedure:

1. Measure the thickness T using a micrometer.
2. First you are going to determine how R depends on L, keeping A constant. Start with a strip 28 cm long and 1 cm wide. By successively reducing L measure the resistance for L = 27.5, 25.0, 22.5, 20.0, 17.5, 15.0, 12.5, and 10.0 cm. As you cut the strip leave an extra 2 mm at each end for your electrical connections.
3. Make a graph of R vs. L. Draw the best line through your points. Calculate the slope of this line. Make sure everything is in ohms and meters, otherwise your units will not work out correctly in the end! In symbolic terms, to what does the slope of this line correspond? Use your results to determine a value for the resistivity of the carbon impregnated paper.
4. Next, you are going to determine how R depends on A, keeping L constant. The only way to vary A is to vary W. For L = 25 cm, measure R for various values of W from 0.5 to 2.0 cm. Make sure that your strips are fairly rectangular, i. e. that W does not change along the length of the strip. Leave an extra 2 mm of length at each end for your electrical connections.
5. Make a graph of R vs. 1/A. Draw the best line through your points. Calculate the slope of this line. As before, make sure everything is in ohms and m2. In symbolic terms, to what does the slope of this line correspond? Use your results to determine a value for the resistivity of the carbon impregnated paper.
6. Is the carbon paper a conductor, an insulator, or somewhere in between? Explain your reasoning.

As a rough check on the experiment, compare the resistivities calculated in steps 3 and 5.
Remember % difference = X 100