17.3. Resistivity http://www.ck12.org
17.3 Resistivity
Objectives
The student will:
- Understand how to solve problems involving resistivity.
- Understand how to read the resistor code.
Vocabulary
- resistivity: A constant of proportionality which depends upon the material used to make the wire, expressed
in unitsΩ∗m. - resistor:Electric components whose only purpose is to add resistance to a circuit.
- semiconductors: Materials that fall between the two extremes of conductors and insulators. Semiconductors
permit a limited amount of electron flow and are very useful in constructing electronic devices. - superconductors: Materials that lose resistance when cooled to near absolute zero.
Introduction
If you have ever been in an electrical supply store, you may have noticed that some wires are very thin and some are
very thick. The thickness (the diameter) of a wire is called the gauge of the wire. Wires with small gauge numbers
have larger diameters than wires with large gauge numbers
Resistivity
The resistance of a given wire depends upon its cross-sectional area and its length. One wire that has twice the
diameter of another wire has four times the cross-sectional area of the smaller wire. It is four times easier for the
electrons to travel through a wire that has twice the diameter of another wire. Conversely, the longer the wire is, the
more resistance the electrons encounter. It is easier to move through a short tunnel filled with people than a long
tunnel filled with people!
We can sum up these statements mathematically as follows:
The resistanceRis directly proportional to the lengthLof a wire and inversely proportional to the cross-sectional
areaAof the wire→R=ρLA, whereρ, a constant of proportionality, is called theresistivitywhich depends upon
the material used to make the wire.
The units of resistivityρareΩ∗m.