Question

Variations in the resistivity of blood can give valuable clues to changes in the blood's viscosity and other properties. The resistivity is measured by applying a small potential difference and measuring the current. Suppose a medical device attaches electrodes into a 1.5-mm-diameter vein at two points 5.0cm apart.What is the blood resistivity if a 8.9V potential difference causes a 240uA current through the blood in the vein?

Answer 1

The blood resistivity = 13. 13 Ωm.

Explanation:

Resistivity: The resistivity of a material is defined as the product of the resistance and the cross sectional area, per unit length of the material.

The S.I unit of resistivity is Ωm

It can be expressed mathematically as

ρ = RA/L................... Equation 1

Where ρ = resistivity of the material,. R = resistance of the material, l = length of the material, A = cross sectional area of the material

From Ohm's Law,

V = IR ................... Equation 2

Making R the subject of the equation,

R = V/I .................. Equation 3

In the equation above, R = Resistance, V = potential difference, I = current through the blood in the vain

Given: V = 8.9 V, I = 240 uA = 240 × 10⁻6 A

Substituting these values into equation 3,

R = 8.9/(240 × 10⁻⁶)

R = (8.9× 10⁶)/240

R = 3708.33 Ω.

Also Given: L = 5.0 cm = 0.05 m.

A = πd²/4 Where d= 15 mm = 0.015 m

∴ A = 3.143(0.015)²/4

A = 0.000177 m²

Substituting these values into equation 1

ρ = RA/L

ρ = 3708.33(0.000177)/0.05

ρ = 13. 13 Ωm.

The blood resistivity = 13. 13 Ωm.