Question

The thickness of a single membrane is about 7 nm. A myelin sheath consists of multiple membranes produced by coils of Schwann cell or oligodendroglia cells. Suppose a myelin sheath results from 100 membranes stacked on top of each other.

A) What is the specific capacitance of the myelin?

B) If the myelin sheath is a right circular cylinder 1 mm long, what is its total capacitance?

C) How much charge does it take to produce a voltage of -70 mV across this capacitor?

D) If the myelin were just 1 membrane--i.e, not myelin--what would be its capacitance? How much charge would it take to produce a voltage of -70mV across the single membrane?

Answer 1

Please note that there is some information like specific capacitance of single membrane and radius is missing. I will tell you the concepts and steps.

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(a) There are 100 membranes stacked on top of each other, means specific capacitance will be

specific capacitance = (1/100) * specific capacitance of single membrane

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(b) we need to find cross section of surface area

Area = 2rL

where r is radius of cylinder and L is length of cylinder

then

total capacitance =  specific capacitance (solved above) * Area

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(c) charge is given as

Q = CV

where C is total capacitance and V is potential given as 70 mV or 70e-3 V

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(d) if it were just a single membrane

then

C = specific capacitance of single membrane * Area

and

charge will be

Q = CV

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Please let me know if get stuck , I am here to help,.....

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