Rsp and vi dividers 2 of 2

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.