Chapter 18, Problem 1RQ

To determine

Comparing between telephone cable and an axon.

Answer to Problem 1RQ

Compared to a telephone cable, an axon has much more resistance, is much more poorly insulated, and needs much more frequent amplification.

Explanation of Solution

Write the expression or the resistance of the axoplasm

$R=\frac{{\rho }_{0}l}{\pi r^2}$        (I)

Here, $R$ is the resistance, ${\rho }_0$ is the resistivity, $l$ is the length, $r$ is the radius.

Conclusion:

Substitute, $2\text{Ω-m}$ for ${\rho }_0$, $1\text{cm}$ for $l$, $2\text{μm}$ for $r$ in equation (I) to find $R$.

$\begin{array}{c}R=\frac{\left(2\text{Ω-m}\right)\left[\left(1\text{cm}\right)\left(\frac{1\times {10}^{-2}\text{m}}{1\text{cm}}\right)\right]}{\pi {\left[\left(2\text{μm}\right)\left(\frac{1\times {10}^{-6}\text{m}}{1\mu \text{m}}\right)\right]}^2}\\ =1.59\times {10}^9\Omega \end{array}$

Here. The resistance of axon is equal to the resistance of telephone cable which contains 70 km of number 40 copper wire.

Thus, Compared to a telephone cable, an axon has much more resistance, is much more poorly insulated, and needs much more frequent amplification.