Silicon, Circuits, and the Digital Revolution
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Resistivity and
Play-Doh |
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The principles of science, the definition, almost, is the following:
the test of all knowledge is experiment.
Experiment is the sole judge of scientific truth.
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Richard Feynman, 1963
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Objective:
Measure dependence of resistance on diameter of resistor and determine the general
relationship between the two quantitites.
Hypothesis:
Formulate a hypothesis about how you think the resistance will vary with diameter.
Procedure:
- Roll as many of the following cylinder diameters as material and time permits.
- You may also wish to fabricate and measure samples having different cross-sectional shapes.
- In addition, each group member should fabricate a cylinder having the same nominal
diameter, say 1.0 cm; the measurements of the four or five "identical"
cylinders will allow you to estimate the uncertainty and reproducibility associated
with your measurements.
| Sample |
Diameter |
Circumference |
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cm |
cm |
| 1 |
0.8 |
2.5 |
| 2 |
0.9 |
2.8 |
| 3 |
1.0 |
3.1 |
| 4 |
1.1 |
3.5 |
| 5 |
1.3 |
4.1 |
| 6 |
1.6 |
5.0 |
| 7 |
2.0 |
6.3 |
- Cover the full range; that is, make cylinders numbers 7, 5, 3, and then 1.
- Fill in the intermediate values next.
- Make each cylinder at least 12 cm long; it will be necessary to measure the larger cylinders before fabricating the smaller ones.
- The quality of the experimental results will depend strongly on the uniformity of the cylinders.
- Maintain the same diameter over the entire length.
- Avoid cracks or voids, knead thoroughly before rolling.
See photos of experimental set-up.
- As the cylinders are completed, bring them to the multimeter workstation
for measurement in the circuit shown:
- Record voltage across 10 cm of material.
- Record current through cylinder.
- The two measurements above should be made simultaneously!
- For each cylinder:
- Calculate its resistance using Ohm's Law; that is, find the ratio of voltage
and current.
- Calculate its cross-sectional area.
- Your final report should include:
- Color of Play-Doh sample
- A table of Diameter (in cm), Area (in sq. cm), Voltage (V), Current (mA)
and Resistance (in ohm) of each cylinder.
- A graph of Resistance vs. Diameter, as well as vs. other functions
of the Diameter as they occur to you -- in the quest to determine a simple
relationship between Resistance and Diameter you should be looking for a graph
with a straight line... This is the "holy grail" of this exercise.
- When you find the straight line, please determine its slope.
- Please include any other observations made during the course of this exercise,
including the discussion of reproducibility and possible sources of error.
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Comments, suggestions, or requests to ghw@udel.edu.
"http://www.physics.udel.edu/~watson/scen103/colloq2000/problems/playdoh.html"
Last updated March 7, 2000.
© George Watson, Univ. of Delaware, 2000.
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