00:02
So in a tuning circuit, you often have what's called a variable capacitor.
00:10
And what that capacitor is, is it is a set of stationary plates that are all connected electrically, as you can see with the conductors down at the bottom.
00:23
And then there is another set of plates electrically connected that can rotate.
00:29
And as you rotate that second set of plates, they over.
00:34
Overlap the area of the stationary plates and therefore create a variable capacitance, as we will see.
00:44
So the first thing to use is the capacitance of an air gap capacitor.
00:51
It is proportional to the area times epsilon dot, the permittivity of free space, divided by the spacing, we'll call that t, between the place.
01:05
Okay, so plates of area a, spacing t, etc.
01:15
And that area must overlap.
01:18
So the first thing to realize is that the area will affect the capacitance.
01:23
The second thing to realize is if all the stationary plates are connected together and all the movable plates are connected together, what you have is a parallel configuration, and capacitancees add in parallel c total equals c1 plus c2 plus c3, etc.
01:55
And assuming that these plates are all identical, et cetera, if there are n of them that overlap, we will get a total equal to n times the, c of a single plate.
02:18
Okay.
02:19
The next thing to worry a little bit about is what is t.
02:23
So we are told that the stationary plates are separated by distance d.
02:33
And so when the movable plates start to overlap, they will cut that d in two.
02:44
So the last thing to worry about is the, so c so far, we have c is equal to n times the area of overlap, o, ov, times epsilon, times epsilon, over 2, and the d flips up into the numerator.
03:20
So the last thing to worry about is the area of overlap.
03:26
Now, unlike the plates that i'm showing in this little photograph, is the plates we are going to assume are both semi -circular.
03:38
So we're going to work on the area of overlap...