00:01
Okay, we want to find the equivalent resistance of this circuit.
00:05
This is a little tricky because it's not series or parallel.
00:11
So i'm going to use a transformation called the delta y transformation and i'm going to do it on the right hand square loop up above.
00:27
So what the delta y says, if i take essentially a triangle, because that's what we got here, i can convert it into a y so the resulting circuit looks like this.
00:52
Okay, and i'll come back to how we got those numbers in a moment and then we can kind of do a series and parallel, some combinations here, some series combinations.
01:12
So we get this one that's in series and then these two down here in series and then these two over here are in series and so we get this and then the 34 and the 65 are in parallel and we get that circuit and then those three resistors are in series.
01:53
We just add them together we get 142 .3 ohm.
01:58
So back to the delta y transform.
02:00
So the delta y transform tells us how to calculate the, so we had these three, the 10, the 40, and the 50.
02:13
This is our delta.
02:15
The y, you can see there's a y here, the 4, the 5, and the 20 and the way we get those numbers to get, so 50 times 10 over 100.
02:27
So you add all these together you get 100.
02:30
40 plus 10 plus 50, that's 100.
02:34
So that goes in the denominator.
02:36
So that's 5.
02:41
The next one is 40 times 10 over 100 and that's 4.
02:45
And the last one is 40 times 50 over 100 and that's 20.
02:55
Okay and so the 5 goes down there, the 4 goes over there, and the 20 goes there.
03:06
So that's where all those numbers came from.
03:13
So the delta y transform is kind of unusual but it is correct.
03:24
So here's our final resistance.
03:31
So for the second one, i'll tell you i tried to do it with a delta y transform and i kept making mistakes.
03:39
So i'm not going to do it that way.
03:41
So we have a network here.
03:48
All the resistors are 30 ohm resistors and we want to figure out what the net resistance is.
03:55
So the other, the other way to do this, or the way i'm going to do it, is i imagine i'm attaching a battery across the terminals with some voltage e, which i'll specify later.
04:12
And then once i've done that, i basically find all the currents and then i can get the total resistance by taking the battery voltage divided by the current in the battery.
04:29
And then the battery voltage doesn't matter and it would actually work in any thing.
04:36
That way i can do it numerically, which is what i'm really going to do...