Question

18-5 An unmyelinated segment of axon has a radius of 2 um and a length of 1 cm. Find its (a) membrane capacitance; (b) membrane leakage resistance.

Answer 1

A)

surface area of unmyelinated segment of axon is

$S=2\pi aL=2\pi \times (2\times 10^{-6})\times 0.01=1.256637\times 10^{-7}m^{2}$

Memebrane Capacitance is given by

$C=C_{m}S$

Where

Cm = 1uF/cm

Therefore

$C=(1\times 10^{-6}\times 10^{4}F/m^{2})(1.256637\times 10^{-7}m^{2})$

$C=1.256637\times 10^{-9}F$ (if answer was asked in nF then 1.256637 nF)

b)

Membrane Leakage resistance

$R=\frac{R_{m}}{S}$

Where $R_{m}=2250\Omega -cm^{2}$

$R=\frac{2250\times 10^{-4}\Omega .m^{2}}{1.256637\times 10^{-7}m^{2}}$

$R=1.79\times 10^{6}\Omega$ (if answer was asked in Mohms then it is 1.79 Mohms)