Silicon, Circuits, and the Digital Revolution

Resistivity and
PlayDoh 

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.



Richard Feynman, 1963


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 crosssectional 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 

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 setup.
 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 crosssectional area.
 Your final report should include:
 Color of PlayDoh 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.

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.
