electricity - Can I describe resistance without using an Ohm?

Can resistance be described with units $\rm cm^2/sec$? If so, how would this (resistance) relate to permeability?

Answer

In SI units, electric charge is a fundamental quantity of nature. All the SI electrical units contain at least one factor of the "base" electrical unit. (This base unit is currently the ampere, but will soon become the coulomb.) The SI unit of resistance is

$$\Omega = \rm \frac{V}{A} = \frac{J/C}{C/s} = \frac{J\,s}{C^2}$$

In CGS units, charge is not a fundamental quantity of nature. The force between two electrical charges is defined to be

$$F = \frac{q_1q_2}{r^2}$$ which means that electric charge must have units of $\rm dyne^{1/2}\, cm = erg^{1/2}\,cm^{1/2}$. That gives the relations $$\begin{align} \text{current} &= \frac{\text{charge}}{\text{time}} &&= \rm erg^{1/2}\,cm^{1/2}\,s^{-1} \\ \text{potential} &= \frac{\text{potential energy}}{\text{charge}} &&= \rm erg^{1/2}\,cm^{-1/2} \\ \text{resistance} &= \frac{\text{potential}}{\text{current}} &&= \rm cm^{-1}\,s \end{align}$$ This is close to your suggestion but not quite the same.

The relationship to permeability is really boring, because in CGS units the permeability of the vacuum is defined to be unity, with no dimension.