The outer membranes of cells are quite irregular at the submicron level, so the

Question

The outer membranes of cells are quite irregular at the submicron level, so the surface area of an apparently spherical cell differs from the value one would calculate from geometry. To determine the actual surface area of a cell membrane, electrophysiologists use intracellular electrodes to measure the membrane's capacitive reactance. They take advantage of the fact that the capacitance per unit area of all biological membranes is about 1.0 ?F/cm2.

Part A

What is the surface area of a 20 ?m-diameter sphere? Give your answer in square centimeters.

Part B

The capacitive reactance of the outer membrane of a 20 ?m-diameter cell is measured to be 6.4

Explanation / Answer

The reactance of a capacitor is given by

Zc = 1/(2 pi f C)

where f is the frequency in Hz, C is the capacitance in farads, and pi is 3.14. Solving for C we get

C = 1/(2 pi f Zc) = 1 / ((2*pi()*1000*6.4E6) = 2.65258E-11 farads

Thus, the area of the cell, as measured by the reactance, is

Area = 2.65258E-11 / 1E-6 = 2.65258E-05 cm2

The calculated area of the sphere is

Area_calculated =4*pi()*(10E-4)^2 = 1.25664E-05 cm2

thus the ratio of areas is

A_react/A_calc = 2.11

thus, the reactance area is about 2.11 times larger than the geometrical area

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