Question

Changing the thickness of the myelin sheath surrounding an axon changes its capacitance and thus the conduction speed. A myelinated nerve fiber has a conduction speed of 55 m/s .

If the spacing between nodes is 1.1 mm and the resistance of segments between nodes is 26 MΩ , what is the capacitance of each segment?

A. C = 1.5×10^-13 F

B. C = 7.7x10^-13 F

C. C = 5.4x10^-12 F

D. C = 1.5x10^-11F

Answer 1

The time constant for a RC circuit is given by

\(t=R C=\frac{V}{d}\)

Hence the capacitance of each segment is given by \(\begin{aligned} C &=\frac{V}{R d} \\ &=\frac{1.1 \times 10^{-3} \mathrm{~m}}{\left(26 \times 10^{6} \Omega\right) \times(55 \mathrm{~m} / \mathrm{s})} \\ &=7.7 \times 10^{-13} \mathrm{~F} \end{aligned}\)

The capacitance of each segment is

B. \(C=7.7 \times 10^{-13} \mathrm{~F}\)