Now, we want to solve this circuit for vx.
Let's do it this particular way where we're going to use a current divider and
let's find the current right here, let's call that I1 and
let's find this current right here, let's call that Ix.
We can say that we can find the voltage because we know the resistance.
So if we do this to the current, we'd be able to find the voltage using Ohm's law.
This is the current divider.
When we have a current divider, the easiest way to handle that is to take
our source and divide it through, let's say, R1 and R2.
The current I1 and I2 is going to be found this way.
Let's take our R and convert it to G, which is 1 over R1, and
let's convert this one to G2, which is 1 over R2.
Then we know that I1 is equal to G1 over G1 + G2,
times our original source current.
And I2 is equal to G2 over G1 + G2, also times our source.
So let's do that over here.
I can see that if I combine these two in series, that would be 12 Ohms,
that's what I'll be using in that arm.
So if I wanted to have G1, that would be one-third and
then converting this to G2, that would be 1 divided by one-twelfth.
So I1 is going to be 10 Amps times G1 over G1 + G2.
I2 is going to be 10 Amps times G2 over G1 + G2.
Do the math to work out what the current will be.
Then because I now know I2, oops, I guess I called it x2, but
there's I2, we can say that vx is going to be = I2 times the resistance which is 4.
Mm-hm, let's work out the polarity on this.
We can see that vx is defined from plus to minus.
Let's make sure that's right.
My current is defined in this direction from plus to minus, and so
because these two are matching, I have the correct polarity.
If I had defined my current the other direction,
then I would have had a minus instead of a plus here.
Okay, great, that's one way of doing this problem.
Let's go do it another way.
Let's say that I have the current, So here's 3, 4, and 8.
And this is the voltage that I want to find.
This is 10 amps.
One thing that we can do is convert this thing into a voltage source and
then be able to do a voltage divider.
So to convert this to a voltage source, I simply say, what is the voltage across it?
It's going to be 10 amps times 3.
So I'm going to have a voltage source plus to minus vs of 10 times
3 which is 30 volts.
And then my original current this 3, that's right here,
is going to end up being in series instead of in parallel.
So just 3 in parallel, sorry, 3 in parallel became 3 in series.
So these two things are equal, then I have my 4 Ohm and
my 8 Ohm resistance, 4 and 8.
And what I want to find is vx here.
Remember when I have a voltage divider like so and
I have a series of three resistances, R1, R2, and R3.
Vs =, sorry V1 like this = vs times
R1 divided by R1 + R2 + R3,
similar for V2, V3, and V4.
So finding xx now, I can just say that is equal to vs times 4, divided by 3 + 4 + 8.
And by vs is 30 volts.
So again, 30 times 4 times 3 + 4 + 8.
So that's the second way of being able to solve the circuit.