We have been told that in myelinated fibres, conduction velocity is proportional to the diameter of the axon. In unmyelinated fibres, velocity is proportional to the square root of the diameter.
Can this be derived from use of the length constant? The length constant being the distance over which the voltage drops to 37% (1/e) of its original value.
length constant = sq.root(transmembrane resistance/longitudinal resistance)
I understand that longitudinal resistance would (if analogous to electrical resistance in a wire) be inversely proportional to the cross-sectional area, which would lead to being inversely proportional to the square of the diameter (from area = pi.r^2).