The quantities Rm, Ra, Cm, Vm, etc. that appear in the diagram and equation are given in ohms, farads, or volts, and will depend on the size of the compartment. In order to specify parameters that are independent of the compartment dimensions, specific units are used. For a cylindrical compartment, the membrane resistance is inversely proportional to the area of the cylinder, so we define a specific membrane resistance RM, which has units of ohms·m².
The membrane capacitance is proportional to the area, so it is expressed in terms of a specific membrane capacitance CM, with units of farads/m². Compartments are connected to each other through their axial resistances Ra. The axial resistance of a cylindrical compartment is proportional to its length and inversely proportional to its cross-sectional area. Therefore, we define the specific axial resistance RA to have units of ohms·m.
For a piece of dendrite or a compartment of length l and diameter d
we then have
WARNING: Many treatments of the passive properties of neural tissue use the symbols Rm, Ra, and Cm for the specific resistances and capacitance, instead of this notation with RM, RA, and CM. Also, many textbooks and journal papers define the resistance and capacitance in terms of that for a unit length of cable having a specified diameter.