00:01
We'd like to find i0 in this network.
00:05
The i0 is over here.
00:08
So let's see.
00:09
We don't have a ground anywhere by default, so i'm just going to stick ground here arbitrarily and see what we can figure out.
00:19
I see we've got vx over 4 amps coming down here.
00:24
Vx over 4, which means we also have vx over 4 amps coming through this resistor because they're in series.
00:32
Which means up here, v is equal to, of course, the current.
00:37
Vx over 4 times the resistance 8 is 2vx.
00:41
So this is 2vx relative to our vx there.
00:46
And that tells us that this whole top node actually has a voltage of 3 times vx right there.
00:55
So that's good.
00:56
That's nice.
00:59
And what else can we figure out from that? so you have 3 times vx.
01:07
We have vx over 4 amps coming through that.
01:13
And then i'm going to say at this point, let's just start using some junction laws.
01:18
So right here, this green junction, we have 5 amps coming in.
01:24
We have 3 times vx amps coming out.
01:30
And we also have this current here.
01:32
I'm going to arbitrarily decide that currents are coming out of this node.
01:36
Let's say this is i1.
01:37
This is i2.
01:40
So on the green node, we have 5 amps coming in.
01:42
We have i1 coming in.
01:44
That is equal to the 3 times vx coming out.
01:48
And then at this node, which i'm going to actually color in red, we have only things that are coming out.
01:54
So we get vx over 4 plus i1 plus i2 all need to be 0.
02:08
So that's nifty.
02:09
That's nifty...