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A simplified model for an erythrocyte is a spherical capacitor with a positively charged liquid interior...

A simplified model for an erythrocyte is a spherical capacitor with a positively charged liquid interior of surface area A. The interior fluid is separated by a membrane of thickness b from the surrounding, negatively charged, plasma fluid. The potential difference across the membrane is 128 mV, and the thickness of the membrane is about 100 nm with a dielectric constant of κ = 5.1. Use 1.06 g/cm3 as the density of blood.

(a) Calculate the volume of the blood cell assuming that an average erythrocyte has a mass 1 ✕ 10−12 kg. From the volume determine the surface area of the erythrocyte (in m3).

volume________ m3

surface area________m3

(b) Calculate the capacitance of the blood cell. For this calculation, model the membrane as a parallel plate capacitor with the area found in part (a).

(c) Calculate the charge on the surface of the membrane (in m2). How many elementary charges does this represent?

volume_______ m3

surface area______ m2

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