Question

Nerve impulses are carried along axons, the elongated fibers that transmit neural signals. We can model an axon as a tube with an inner diameter of 10 μm. The tube wall is insulated, but the fluid inside it has a resistivity of 0.50 Ω⋅m.What is the resistance of a 2.0-mm-long axon?

Answer 1

Answer:

The resistance of the axon is $1.27\times 10^7\ \Omega$.

Explanation:

Given that,

Inner diameter of the model of an axon, $d=10\ \mu m$

Radius of the model, $r=5\ \mu m=5\times 10^{-6}\ m$

Resistivity of the fluid inside the tube wall, $\rho=0.5\ \Omega -m$

Length of the axon, l = 2 mm = 0.002 m

We know that the resistance in terms of resistivity of an object is given by :

$R=\rho\dfrac{l}{A}\\\\R=0.5\times \dfrac{0.002}{\pi (5\times 10^{-6})^2}\\\\R=1.27\times 10^7\ \Omega$

So, the resistance of the axon is $1.27\times 10^7\ \Omega$. Hence, this is the required solution.