Now we´re going to discuss conductivity
which is slightly different than resistivity
which is something that we had already talked about.
We talked about the resistivity as being a rho, this Greek letter rho,
which is describing the resistance of just the material itself,
independent of the geometric properties or saying it another way,
the resistance of a wire like this one will depend not only on the material,
which has a particular resistivity rho, but it will also depend on the geometry of that object.
It depends on the length and the resistance depends on the cross sectional area.
So this is the resistance or the resistivity rather, rho.
We can also define a conductance which tells us not how resistive is your material
but how conductive is your material and is defined simply as 1 divided by the resistivity.
In other words, if you have a great resistivity, a high letter rho,
then your conductivity will be a small number and vice versa.
If you have a small resistivity, you?ll have a high conductivity.
The question is for either of these values, the resistivity or the conductivity,
how can we experimentally determine what the resistivity or conductivity is
of a particular material like copper. For a simple wire, if we had some metal
and we wanted to find out its resistivity, it would´t be so hard.
All we´d have to do is make sure we knew the length of the cross sectional area
of the wire that we put into the circuit and if we knew those geometric factors
then we can put it in a circuit like this one where we knew the voltage we were applying
and also knew the amount of current by putting an ammeter in the circuit,
and by knowing both the voltage and the current,
we could find the resistance just by using Ohm?s law.
If we knew the resistance, we could use the equation for the resistance
that we just had relating it to the resistivity
and we would just need to rearrange this equation for the resistance.
So using Ohm´s law, we know that the resistance through this wire
has to be the voltage divided by the current
but we also have this other equation for the resistance
from geometric terms and from the material itself
which is rho times the length over the area. So just rearranging this equation,
we can figure out what the resistivity is just with the parameters given.
So we have the voltage that we?re applying to our circuit
times the cross sectional area, careful that´s not A for amps there, that´s A,
the cross sectional area of that metallic piece that we´ve put into our circuit,
divided by the current that is in our circuit which we measure using our ammeter, A,
also times, the current is times the length of our resistor
and then it´s very simple to find the conductivity
because we know the conductivity is simply related to the resistivity as 1 over the resistivity.
And so for a metallic it´s not so difficult.
We just need to find the geometry of our metallic, put it into a simple circuit,
measure the properties of that circuit, and we can quickly find the resistivity of our material.
On the other hand, if we wanted to try to find the resistivity
or the conductivity of an electrolyte, some sort of a liquid solution,
this becomes more tricky because we can´t geometrically define our liquid.
We can´t make a liquid capsule without any other objects on it and just put it into our circuit.
So we have to do something a little different here.
For a liquid like we have here, what we could instead do is something very similar
where we have a battery with applying a voltage, V again,
we have A, an ammeter put into our circuit to measure the current
that´s flowing in our circuit and then what we put into the liquid
would maybe be two plates whose cross sectional area we knew
and the distance between those plates which we also knew.
If we know these geometric parameters of the object that we put into the liquid,
we could sort of imagine in this diagram here
the current flowing from one plate to another through this area, A.
In that case, you could sort of think of your resistor as having a cylindrical property
with the liquid inside of it. In this case, we could do the exact same thing
as we did for the metallic using the same parameters A and L,
and in fact having the exact same equation for both the resistivity and the conductivity
except this time we have found it for the electrolyte in the solution.