Question

1. An average nerve axon is about 5x10^-6m in radius, and the axoplasm that composes the interior of the axon has a resistivity of about 2 $LaTeX: \Omega\cdot$ Ω ⋅m.  What is the resistance of just 2-cm length of this axon? Provide your answer in mega-ohms (1 mega-ohm = 10⁶ ohms or "millions of ohms"). (Note, this value is so large -- it corresponds to the resistance of tens of thousands of miles of the thinnest copper wire normally manufactured(!) -- that it explains why a nerve pulse traveling down an axon CANNOT simply be a current traveling along the axon. The voltage required to achieve a perceptible current in the axon would have to be gigantic! We will investigate how voltage pulses -- not current -- travel down axons in a future lab.)

2. The current required to stimulate the heart during ventricular fibrillation is about 110mA (1000mA = 1A). Assuming that a conducting gel is used in conjunction with a defibrillator to overcome skin resistance, so that the main resistance of the body to an applied voltage is solely due to the internal resistance of the body, which is roughly around 400 ohms, what voltage is required for defibrillation? (Note, the actual value used is 10-100 times this since the skin's large resistance cannot necessarily be neglected.)

Answer 1

1.

Area of nerve axon

A=pi*r²=pi*(5*10^-6)²= 7.854*10^-11 m²

Resistance of axon is given by

R=pL/A =(2)(0.02)/(7.854*10^-11)

R=509.3*10⁶ ohms =509.3 Mohms

2.

Voltage required for defibrillation

V=IR =(110/1000)*400

V=44 Volts