Introductory Physics Volume Two

3.3 Ohm’s Law 59
Some materials, such a copper, allow charge to pass through it
with very little resistance, and therefore it takes very little electric field
to sustain a large current. Other materials, such a carbon, resist the
flow of charge, and it requires more electric field to sustain the same
current. Carbon is more resistive. This property is quantified in the
following law.
Fact: Ohm’s Law: Resistivity
For many materials the current density and the electric field are
proportional.
⃗J = σ ⃗ E
The constant σ is called the conductivity and depends on the material.
The inverse of the conductivity is called the resistivity:
ρ = 1/σ.
Not all materials follow this relationship: those that do are called
ohmic materials, those that do not are called non-ohmic.
Here is a table with the resistivity of a few materials.
Material Resistivity(×10 −8 Ω · m)
Silver 1.6
Copper 1.7
Aluminum 2.8
Tungsten 5.5
Iron 10
Nichrome 100
Carbon 3500
Silcon 64000000000
Wood 1000000000000000
Amber 50000000000000000000000
Imagine a piece of conductive material, with two terminals connected
to it, and with a current I passing into the material through
terminal a and draining out through terminal b. Such a circuit element
is called a Resistor.
In order to sustain this current there will need to be an electric field
in the conductor going from terminal a to terminal b. Thus there will