3 find node voltages

Okay, one last part of our problem.

Let's say that we have found
our currents and our power, and

we want to find our node voltages.

Particularly, if we make this node
voltage right here, the ground.

So we're going to ground
that part of the circuit.

Okay, if I wanted to find my other
node voltages, what would I do?

I use Kirchhoff's Law with my
sources to find my current.

What other tools do I have,
that I could use?

I'm gonna spread these out.

What other tools do I have that I could
use to be able to find node voltages?

Well, I don't need the power equations,
let's get rid of that.

My current divider gives me current,
I certainly don't want that.

Now, my voltage divider
gives me voltage difference,

but do I have a voltage divider problem?

No, not really, so
we're gonna get rid of that one.

Do I have resistors in series and
parallel?

No, not really, let's get rid of that one.

Here are my choices.

I've used Kirchhoff's Law to find current,
and what I now want is node voltage.

Now, Ohm's Law doesn't
give me node voltage,

Ohm's Law gives me voltage difference,
so here's my only choice.

If I have Kirchhoff's Law and I found
current, that means I know current.

Here, I know current, and
I know one of the nodes.

If I know one of the nodes,
and the currents, and

the resistances,
I can find the other nodes.

So let's see how to do that.

I'm going to use this equation,
VA- VB = IR.

So let's see.

Let's suppose that I have this node,

VA- VB = IR, this is I2 times R2.

I have to line my current.

This current,
let's make this point yellow.

I have to line this yellow current
up with that yellow current.

So make sure they're going the same
direction so I get my signs correct.

So VA- VB = I2R2,

let's do that over here too, for VC.

VC- VB, cuz this is equal to VB,

it's all pink, is equal to I3R3.

Okay, I know I2, R2, I3, R3, and

I know one of these nodes, VA = 0.

So I can say VB = -I2R2, and

VC = VB, which I just found,

+ I3R3.

So now, I have found the node voltages.

Let's review this problem.

When we started out,
we didn't know any of this.

We were given our sources and
our currents, sorry, our voltage and

current sources and our resistors.

We wanted to find the currents,
we did that with Kirchhoff's Law.

Then, I wanted to find
the power through one element.

In order to find the power, I needed
to know the current and resistance.

All right, I knew the current and
resistance, so I could find power.

Then, we wanted to find the node voltages.

And in order to find the node voltages,
we used the currents and one of the nodes.

We have to know one node at least, we know
one node, and the current and resistance.

And that allowed us to find
the rest of the nodes.

The way we did that, is we lined
up this picture with the current.

And we were able to write these equations,
VA- VB = IR.