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

The resistance of the axon is
`1.27* 10^7\ \Omega`.

Step-by-step explanation:

Given that,

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

Radius of the model,
`r=5\ \mu m=5* 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(l)/(A)\\\\R=0.5* (0.002)/(\pi (5* 10^(-6))^2)\\\\R=1.27* 10^7\ \Omega`

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