Silicon, Circuits, and the Digital Revolution

 
Resistivity and Play-Doh

  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 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 
  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.


SCEN103 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.