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[MUSIC]

Welcome back to Linear Circuits.

This is Dr. Ferri.

This lesson is on equivalent resistance.

The objective is to simplify a combination of resistors by replacing them

with an equivalent resistor.

For example, look at this case right here.

It's kind of a messy circuit and I'd like to be able to simplify it and

it'd be so much easier to work with a single resistor here.

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This lesson builds upon the concepts we've covered before,

that is, resistors in series where I can replace

a series set of resistors with one resistor with this formula.

Or resistors in parallel where the formula for

the equivalent resistance is right here.

Let's look at this example.

The way to approach something like this is to first recognize resistors in series or

resistors in parallel and to replace them with their equivalent resistance.

Now, people looking at something like this.

A common mistake that they make is to think that these two resistors are in

series with one another, they're not.

In order to be in series, you have to have the same current flow through them.

But the problem is the current flowing this way, part of it could go this way and

part of it this way.

So it's not the same current.

So they are not in series with one another.

However, these two are in series with one another

because the same current has to flow through both of them.

So I can take these two.

And I'm going to redraw the circuit with that simplification.

And that's what I usually do on here.

I draw a sequence of circuits.

Each time I simplify, I redraw the circuit.

So that's 20.

And this is a sum of the 2 is 20.

And this is 30.

So now it's much clearer because I've redrawn it that these two are in

parallel with one another.

So then if I redraw that one I

used two resistors that are in parallel in fact, these are the same and

whenever they are the same, the equivalent is going to be half of that.

And then that's 30.

And now I've got two resistors that are in series with one another.

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Let's do another example.

In this particular case, I've got these resistors are in parallel,

I know because they share a node here and here.

And so this is R1 in parallel with R2.

And here I'm using the notation R1 in parallel with R2 to mean that

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So, over here, these are also in parallel because they share the nodes at both ends.

So that is R3 in parallel with R4.

And in this case, I've got a resistor in parallel with a short circuit,

so that is 0 ohms.

So then, this combination is in series with this combination,

I have R1 in parallel with R2 plus R3 in parallel with R4.

And the order of precedence is this right here.

I do the parallel first, and then the series.

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Now looks a little bit more complicated than the last one.

But actually it's not,

it's actually the same circuit as the example that we just did.

I've just redrawn the physical layout of it.

And that something that for people to realize when we talk about

resistors in parallel, you see this right here?

It is actually in parallel with this although physically it doesn't look it.

But electrically,

this is in parallel because they are connected by nodes at both ends.

So I could redraw this as R4 in parallel with R5 like this.

And similarly, these two in parallel, and then that combination, this combination of

resistors is connected to this combination through only this particular node.

So I can redraw it this way.

So, the one thing that we might be able to do if you get used to this, is to redraw

the circuit into something that looks a little bit more familiar to you and also

to recognize that electrically parallel is different than saying physically parallel.

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Now, I've got a quiz for you.

I'd like for you to find the equivalent resistance between this node a and

this node c.

Before we were doing between a and b.

Now, I want you go between a and c.

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And then across here, and all the current is either going to flow through R2

to get to R6, or R1 to get to R6.

None of it is going to go in this direction because all of it's going to

want to go this way.

Current follows the path of least resistance.

So this right here essentially short circuits, all of this part of the circuit.

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So to summarize, when we want to reduce a circuit that

is fairly complicated, we look for parallel or series combinations.

And we replace each one with their equivalent resistance.

And what I tend to do is to redraw the circuit every time I reduce something and

then I reduce it again.

Every time I redraw it then it becomes a little bit more clear.

Other combinations of parallel or series resistance.

And I keep following that path until I get down to one resistor.