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Hello again. This is Roger Coke Barr for the
Bioelectricity course, Week two, and this is our ninth segment.
In this segment, we talk about membrane capacitance.
And the capacitance per unit area is designated C sub m.
0:22
First, it's just worth asking why does membrane have capacitance?
Somehow or other, it seems very reasonable that membrane has resistance, but
capacitance, well, we're not quite so sure about that.
However, think about the general definition of capacitance.
There is capacitance between one point and another when you have two conductors
separated by an insulating region. So, membranes are certainly an insulating
region. So, the question is, if capacitance comes
from two conductors separated by an insulating region, what are the
conductors? Well, let's make ourselves a sketch and
talk about that. So, let's suppose, this is a cell and
cross section. We said that the membrane [unknown] which
is diagrammed there in red, is a very good insulator.
And, this region in the interior, that's a conductor.
That's not a metal plate. We think of capacitors as having metal
plates because human-made capacitors are built that way.
But there's nothing about the phenomenon that requires that the conductors be
plates. And, in fact, this solution is quite a
good conductor because it's got a lot of ions floating around in it.
So, that's one of the plates. And then, the other plate is this reaching
outside. So, this exterior volume, which is also a
conductor, is the other side of the capacitor.
So, if we say to ourselves, capacitors have two conductors separated by an
insulating region, that's exactly what we have here.
A conductor inside, a conductor outside, insulating region in between.
So, of course, it has capacitance. Let's talk about capacitors and
capacitance and membrane current that flows through the capacitants as people
describe it. The definition of capacitance, C = Q/V.
2:47
Get that equation and turn it around, we'll have Q is equal to the membrane
capacitance times V. Q, of course, is the charge on the
capacitor. So, here's the charge right here.
It's on the capacitor. I better make a note of that.
Just write it in. Here is the charge.
If we now mathematically differentiate the second equation, we get the third.
And equation three says, that if things change as a function of time, the dQ/dt
here is equal to the amount of capacitance times the derivative of the voltage.
And if we rearranged that equation to get equation four, you could say dQ/dt is the
same thing as the membrane current, that's the change in charge that's present
membrane so that's like a current, a change in charge per time.
So, I am then as the, as the current through the membrane that's coming by
because of a, a current through the capacitor.
Now, I have made a mistake here. So, I should say that's a C, the current
through the capacitor. A C is equal to Cm times dVm / dt.
We use that equation all the time in later mathematical work, so it's very helpful.
Dr. Roger BarrAnderson-Rupp Professor of Biomedical Engineering and Associate Professor of Pediatrics
