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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 :

lublana

Answer:

[tex]1.27\times 10^{12}\Omega/m[/tex]

Explanation:

We are given that

Diameter=d=[tex]\mu m[/tex]

Thickness=[tex]1\mu m[/tex]

Radius=[tex]r=\frac{d}{2}=\frac{1}{2}\mu m=0.5\times 10^{-6} m[/tex]

Using [tex]1\mu m=10^{-6} m[/tex]

Dielectric constant=8

Resistance =[tex]R=2\times 10^5\Omega cm^2[/tex]

Internal specific resistance=r=100 ohm cm=[tex]100\times \frac{1}{100}\Omega-m=1\Omega m[/tex]

Using 1 m=100 cm

Internal resistance per unit length=[tex]\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[/tex]

Using [tex]\pi=3.14[/tex]

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

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