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

`1.27* 10^(12)\Omega/m`

Step-by-step explanation:

We are given that

Diameter=d=
`\mu m`

Thickness=
`1\mu m`

Radius=
`r=(d)/(2)=(1)/(2)\mu m=0.5* 10^(-6) m`

Using
`1\mu m=10^(-6) m`

Dielectric constant=8

Resistance =
`R=2* 10^5\Omega cm^2`

Internal specific resistance=r=100 ohm cm=
`100* (1)/(100)\Omega-m=1\Omega m`

Using 1 m=100 cm

Internal resistance per unit length=
`(r)/(A)=(1)/(\pi r^2)=(1)/(3.14* (0.5* 10^(-6))^2)=1.27* 10^(12)\Omega/m`

Using
`\pi=3.14`

Internal resistance per unit length=
`1.27* 10^(12)\Omega/m`