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Hello again. This is Roger Coke Barr the instructor for
bio electricity and we're in week two and this is the ten lecture.
The question for this lecture is why is CM the membrane capacitance so big?
Way, way bigger than your would normally expect.
And the answer very briefly is because the membrane is so thin.
In biological membrane, the membrane capacitance is about one micro [inaudible]
for each square centimeter. Now, there is a lot of centimeters^2 of
membrane surface in just one person. So if you were to say that, in a person,
there's a million centimeters^2, that would say the total capacitance within a
person would be one farad. When I was in school, I remember a teacher
telling me that one farad is so much capacitance that you could not imagine it
existing in the whole entire world. Well, he meant that, as a good
illustration. But he was not thinking in terms of
bio-electricity. If you think in terms of body electricity,
each of us may carry around a whole farad of capacitance which is an enormous amount
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material is, but it, it has a value that is more or less known.
The point of looking at the equation is to see that the capacitance gets bigger when
the area gets bigger. And it also gets bigger when D gets
smaller. So bigger capacitance occurs with a bigger
A or a smaller D. So, you might, if you draw this out, you
might say, okay, here's our capacitance. Here's the outside.
Here's the inside. D is this thickness.
A is the area, surface area. Now, lets do a little comparison with an
ordinary object. Think about a stack of 1000 sheets of
office paper. You can do this experiment yourself.
Get two reams of ordinary office paper, like copier paper.
Stack one ream on the other. You know, ream is a package that has 500
sheets. So get two packages of office paper, like
copier paper. Put them on top of each other.
And then marry, measure how high the stack is.
I did that. I mean I actually did it in preparation
for this lecture and my stack was about four centimeters high.
That means that the thickness of one sheet of office paper can be found by going
through this calculation, four centimeters for a 1000 sheets.
And I think that results in about 400,000 Angstroms for one sheet.
400,000 angstroms for one sheet. So if now we compare the thickness of
paper to the thickness of membrane we'd say well these things are quite different
in thickness, because with paper it is 400,000 angstroms.
That's just a numeric conversion from 4cm into angstroms.
One angstrom is ten to the minus tenth meters.
About 40 angstroms that miss four membrane.
That is to say, the thickness of the non conducting region is about 40 angstroms.
So the ratio there is 10,000. Wow!
Take a piece of office paper, hold it up in front of you, look at it on the edge.
Now when I do that, my vision is not perfect, so I barely see anything when I
hold it and look right at along the edge to see the thickness of a single sheet of
paper. Nonetheless, it is 10,000 times the
thickness of membrane. Well whether or not we've done the
calculation exactly right, you get the point.
It's thousands of times thicker, to have a sheet of office paper, than it is to have
a sheet of membrane. So the, since the, capacitance, goes
inversely as to thickness. The thinner the membrane, the greater the
comparison, the capacitance, and the conclusion is, membranes have a lot of
capacitance. I don't bring that up just as a random
thought, the fact they have a lot of capacitance means that they can store a
lot of charge, and that's very important to their electrical function.
Another fascinating, item. Is that all electrically active membranes
from whatever organ or system within you or people, or animals, or other elective,
electrically active structure, they all seem to be built out of the same kind of
lipid baler, more or less. And the coral area of that is.
All electrically active. Membranes from whatever ore in our system,
have about the same amount of capacitance. So you read different problems, or
different situations, and they, in those you have to specify a lot of different
parameters. Often times the membrane capacitance is
one of them, you can almost think of it as a constant of nature, not quite like pi,
or some other mathematical constant, but you can just be sure it's gonna come out
to be a round-about one microferret per centimeter square.
Not too far from then. So thank you very much for your attention.
And in the next segment we'll move onto a problem session.
Dr. Roger BarrAnderson-Rupp Professor of Biomedical Engineering and Associate Professor of Pediatrics
