Question

Measurements are made of the longitudinal axoplasmic resistance of two unmyelinated axons. Along a 1 cm length of one axon, which has a diameter of 1 mm, the resistance is 10 MOhms. For the same length of another axon that has a diameter of 4 mm but is otherwise identical, what resistance (in MOhms) would you expect to measure

Answer 1

0.625‬ MOhms

Step-by-step explanation:

Since the resistance of the unmyelinated axon ,R is inversely proportional to the square of its diameter, d

R ∝ 1/d²

R₁/R₂ = d₂²/d₁² where R₁ = resistance of first axon = 10 MOhm, d₁ = diameter of first axon = 1 mm, R₂ = resistance of second axon and d₂ = diameter of second axon = 4mm

So, R₂/R₁ = d₁²/d₂²

R₂ = (d₁²/d₂²)R₁

R₂ = (d₁/d₂)²R₁

substituting the values of the variables into the equation, we have

R₂ = (d₁/d₂)²R₁

R₂ = (1 mm/4 mm)²10 MOhms

R₂ = (1/4)²10 MOhms

R₂ = (1/16)10 MOhms

R₂ = ‭0.0625‬ × 10 MOhms

R₂ = ‭0.625‬ MOhms