In class, we learned that the resting membrane potential results from charge sto

Question

In class, we learned that the resting membrane potential results from charge stored on the inner and outer surfaces of the cell membrane. Because the membrane is so thin, we can model the cell as a parallel-plate capacitor with a capacitance given by C = A elementof/d, where elementof = K elementof_0 (dielectric constant times the vacuum permittivity) and A is the area of one plate. (a) Calculate the capacitance per unit area (in mu F/cm^2) for the cell membrane given a membrane thickness of 5 nm and a dielectric constant of 5. (b) Find the capacitance for a spherical neuron 10 mu m in diameter.

Explanation / Answer

C =Ae/d = Aeo*k/d

(a) k = 5 , d = 5 nm

C/A = eo*k/d

C/A = 8.85*10^-12*5/(5*10^-9)

C/A = 0.00885 F/m^2

C/A = 0.885 uF/cm^2

(b) d = 10 um ,r = 5 um

C =A*0.885 uF/cm^2

C = (3.14*5*5*10^-12)*0.00885

C = 0.695 pF

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