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[MUSIC]

Â Welcome back to Linear Circuits.

Â This is Dr. Ferri.

Â This lesson is on equivalent resistance.

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

Â with an equivalent resistor.

Â For example, look at this case right here.

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

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

Â 0:28

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

Â that is, resistors in series where I can replace

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

Â Or resistors in parallel where the formula for

Â the equivalent resistance is right here.

Â Let's look at this example.

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

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

Â Now, people looking at something like this.

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

Â series with one another, they're not.

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

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

Â part of it this way.

Â So it's not the same current.

Â So they are not in series with one another.

Â However, these two are in series with one another

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

Â So I can take these two.

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

Â And that's what I usually do on here.

Â I draw a sequence of circuits.

Â Each time I simplify, I redraw the circuit.

Â So that's 20.

Â And this is a sum of the 2 is 20.

Â And this is 30.

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

Â parallel with one another.

Â So then if I redraw that one I

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

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

Â And then that's 30.

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

Â 2:24

Let's do another example.

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

Â I know because they share a node here and here.

Â And so this is R1 in parallel with R2.

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

Â 2:55

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

Â So that is R3 in parallel with R4.

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

Â so that is 0 ohms.

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

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

Â And the order of precedence is this right here.

Â I do the parallel first, and then the series.

Â 3:35

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

Â But actually it's not,

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

Â I've just redrawn the physical layout of it.

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

Â resistors in parallel, you see this right here?

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

Â But electrically,

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

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

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

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

Â So I can redraw it this way.

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

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

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

Â 4:38

Now, I've got a quiz for you.

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

Â this node c.

Â Before we were doing between a and b.

Â Now, I want you go between a and c.

Â 5:03

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

Â to get to R6, or R1 to get to R6.

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

Â want to go this way.

Â Current follows the path of least resistance.

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

Â 5:39

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

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

Â And we replace each one with their equivalent resistance.

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

Â then I reduce it again.

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

Â Other combinations of parallel or series resistance.

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

Â