Okay, here's a problem that we were working in class today, and
I would like to just go over this example again for you.
We want to be able to find Vx.
We can see we have a lot of resistors here we can combine in series and parallel.
Let's first color code all of our nodes.
Here is a red node, that's a extraordinary node.
Here is an orange node, that's another extraordinary node.
Here is a blue node, also extraordinary.
And we can see that at the bottom, we have a black node that is also
an extraordinary node that includes all of these elements.
Well let's begin by combining our resistors in parallel.
We can see that, these two 16 are in parallel,
because they are red on the top and black on the bottom.
When we have resistors in parallel, we combine them in this way and
if they happen to be equal as the two 16 are.
Then we end up with half of the original resistance.
So, when you combine these two in parallel 16 and parallel with 16,
it's going to give us 8.
We can now see the 4 and the 8 are in series,
because they have a single ordinary node between them.
So, when we combine those in series we just add them up, and the 8 and
4 together, right here, is going to give me a resistance of 12.
Now, we have a 12 from yellow to black and yellow to black,
those two are in parallel.
So 12 and 12 in parallel, because of the same going to give me 6.
Now, something cool happens here.
I end up with a 6 on a resistance right here, which I can bring to the other side
of my current source and that's because, they have the same node
across the topic and rearrange anything that's connected in the same nodes.
So, my 6 is going to come over there and then the 6 and 6 in parallel,
is going to get me something that is 3.
So my final circuit, is going to look like a 10 amp current
source in parallel with 3 ohms, and then I have a 4 and
let's combine these in series 8, and I want to find this voltage.
There's not a minus there.
I want to find Vx.
Now, I also can see that 8 and 4 go together in series.
But, because I want to find Vx, I need to leave the element that it's across and
not combine it with other stuff or else it will get all mixed up in my circuit.
Now, here's the circuit that we have, and
I'm going to show you two different ways of being able to solve it.