Question

Assume an axon has an internal diameter of 1μm and a myelin sheath 1μm thick. The internal specific resistance is 100 Ω cm. For the myelin sheath use a dielectric constant of 8 and a transmembrane resistance of 2 x 10^5 Ω cm^2 .
A) Calculate the internal resistance per unit length.
Please show equation and each variable meaning.

Answer 1

Answer:

$1.27\times 10^{12}\Omega/m$

Explanation:

We are given that

Diameter=d=$\mu m$

Thickness=$1\mu m$

Radius=$r=\frac{d}{2}=\frac{1}{2}\mu m=0.5\times 10^{-6} m$

Using $1\mu m=10^{-6} m$

Dielectric constant=8

Resistance =$R=2\times 10^5\Omega cm^2$

Internal specific resistance=r=100 ohm cm=$100\times \frac{1}{100}\Omega-m=1\Omega m$

Using 1 m=100 cm

Internal resistance per unit length=$\frac{r}{A}=\frac{1}{\pi r^2}=\frac{1}{3.14\times (0.5\times 10^{-6})^2}=1.27\times 10^{12}\Omega/m$

Using $\pi=3.14$

Internal resistance per unit length=$1.27\times 10^{12}\Omega/m$