A nerve cell in its resting state has a membrane potential of -70 mV, meaning th

Question

A nerve cell in its resting state has a membrane potential of -70 mV, meaning that the potential inside the cell is 70 mV less than the potential outside due to a layer of negative charge on the inner surface of the cell wall and a layer of positive charge on the outer surface. This effectively makes the cell wall a charged capacitor. When the nerve cell fires, sodium ions, Na+, flood through the cell wall to briefly switch the membrane potential to +40 mV. Model the central body of a nerve cell-the soma-as a 50-m-diameter sphere with a 7.0-nm-thick cell wall whose dielectric constant is 9.0. Because a cell's diameter is much larger than the wall thickness, it is reasonable to ignore the curvature of the cell and think of it as a parallel-plate capacitor.

Explanation / Answer

here by using the formula

C = e0 * A * k / d

e0 = 8.854 * 10^-12

A = 4 * pie * r^2

C = 8.854 * 10^-12 * 4 * pie * (5 * 10^-5 / 2) * 9 / 7 * 10^-9

then by soving this equation we get

C = 8.93 * 10^-11 F

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