This screencast will introduce the topic of
electrical conductivity through a short example where we examine the electrical
properties of
two different materials. Let's say you have a specific application that
requires
a one millimeter diameter by one meter length
wire that has a high conductivity. You have the option of aluminum alloy
and the other option's a copper alloy. So the testing process here
use an electric circuit with the current of 5 amps and the following table
shows the measured
voltage drop for the wires. So given this information we want to know which wire
has a higher conductivity
Now with any problem best place to start is with a picture
Now below here his a easy schematic
of the testing procedure in which we have our battery
our variable resistor. We have our ammeter
that's going to measure the amps along circuit and then we have our voltmeter down
here
and we're gonna measure the voltage drop across our material at two specific
points
and these two specific points have a distance between them
designated L. Now conductivity
is a characteristic of a material that is indicative of the ease at which the
material is capable of conducting
an electric current. This also helps classify materials into three groups
We have conductors which by the name of it is something that
conducts electricity well. We have semiconductors
and we have insulators. We know insulators are the opposite of conductors whereas semiconductors
kind of bridge the gap between the two materials
Conductivity we will designate
as lower case sigma. And this is the reciprocal
of the resistivity of the sample which we will use lower case rho.
Thus the lower resistivity of a material
the higher the conductivity. So we need to calculate the resistivity to get an
idea of what the conductivity these materials are
and resistivity is independent of geometry
because we're measuring just from two points at distance L
it's related to resistance to the following expression. Resistance times
the
area, cross-sectional area the material over
the length between the two points we're measuring. So if we look at the information
we have for these materials, we're given voltage drop
we have the current in the system and that's about it
We know the length and we calculate the area
So we have these two properties but we don't have the resistance
So we are going to go back to using a very familiar
equation, Ohm's Law which states that the voltage
is going to be proportional to the current times
the resistance. Now we know the voltage drop for our two materials
we're given the current the system. We can calculate the resistance
So let's go ahead and do that. I have written out the reconfigured equations
of Ohm's Law so that we can calculate the resistance
for each material. So you can see I converted this to volts from the
millivolt
presented in the table and divided by the 5 amps in the circuit
So for aluminum this is gonna give us a resistance of
4.3*10^-2
and the units on that is ohms. For copper
this should come out to about 1.7*10^-2
ohms. So the resistivity going back to the equation
is equal to the resistance of the material times
the cross-sectional area divided by the length. So
in the comparison case here the cross-sectional area and the length for
both materials
is the same so we will go ahead and calculate that out. Now a cross-sectional area for
a wire or
a cylinder is gonna be pi times r^2
and I've converted to meters here, divided by the one meter length
of our sample. This results in approximately
7.9*10^-7 meters. We could use this value
and multiply by both resistances to calculate the resistivity
of each sample. As you can see from the calculations the resulting units
for resistivity are ohm meters
If you recall since the conductivity is the reciprocal
of the resistivity we could get a quick idea from
just this comparison that the conductivity of copper
is going to be higher since the resistivity is lower. Let's go ahead and do
that calculation
to finish the problem. The conductivity of the aluminum alloy
is just going to be 1 over 3.4*10^-8
ohm meters and this gives us a value
of roughly 2.9*10^7
ohm meter inverse. I am doing the same for copper
results in a material that has a conductivity
7.6*10^7 ohm meter inverse
So when we compare these two materials we can see that the conductivity of copper is
higher than aluminum alloy
and so we want to choose this material. Now of course making this decision we
don't assume anything else about the materials such as the weights or the
cost
that we may need to take into consideration when using these.
So hopefully that gives you a good idea of how we calculate the conductivity
for a material.