If the conductivity of the electrolyte is $\kappa$ which is the reciprocal of resistivity, then at a given voltage, could the current be calculated? What I'm thinking is:
$$R=\frac{\rho l}{A}$$
$$R=\frac{1}{\kappa}\times\frac{l}{A} $$
Then using Ohm's Law,
$$I=\frac{V}{\frac{l}{\kappa A}}$$
If this calculation is ok, does it also work at different temperatures? Not talking about extreme temperatures just from $293\,\rm K$ to $333\,\rm K$. I've heard somewhere that solutions don't necessarily follow Ohm's Laws but I'm not too sure.
Thank you in advance.
Best Answer
Yes, but you have to bear in mind that the conductivity of the electrolyte will vary depending upon temperature and the electric field strength.
Yes, if you bear in mind that the conductivity will be different at different temperatures.
Ohm's law is a funny thing. it says
$$E = IR$$
However, $R$ is not some immutable property. It generally varies based upon a whole host of factors, including the current passing through the resistance, or the strength of the electric field. Because of the non-linearities of materials, we often say that "Ohm's Law" does not apply to those materials, or does not apply under certain conditions. But, from another point of view, the resistance is something we calculate from $E$ and $I$. When we do that, Ohm's Law does apply to "non-linear" materials. Which view is correct? It really depends upon your needs, how you will want to view it.