0:12

We use Thevenin Equivalent Circuits when we want to simplify part of a circuit.

Â For example, we look over here.

Â I could have a circuit that's really messy, lots of resistors,

Â lots of sources in there.

Â It could be very messy.

Â And I got these two terminals coming out, A and B.

Â I want to replace this entire circuit with one that is much simpler.

Â It's just got a voltage source.

Â One voltage source and one resistor.

Â 0:35

And the behavior of the circuit is the same

Â across those two terminals as the original one is.

Â So we use Thevenin Equivalent Circuits again when we want to simplify

Â part of a circuit to simplify our analysis.

Â The other reason we use Thevenin Equivalent Circuits is to find the load

Â that will maximize power to the load.

Â So in other words if I wanted to put a load resistor across right here or

Â to the original circuit right there then I would want to find

Â the Thevenin Equivalent Circuit and

Â that would tell me what load will maximize the power.

Â How do we build our Thevenin Equivalent Circuit?

Â Well it's shown over here, we're going need to define a few terms here.

Â We define V Thevenin, which is the voltage source here.

Â The R Thevenin is the resistance rate here.

Â Those are the elements of our Thevenin Equivalent Circuit and then I short

Â circuit or i sub sc is the current that relates these two through Ohm's law.

Â Now how do we find these from an actual circuit?

Â So if I took an actual circuit and I had my terminals coming out and I measured

Â the open circuit across here, and the open circuit voltage, that would be V Thevenin.

Â The other way I can find the other thing I need to find is the, I short circuit,

Â which is shorting out or just putting a wire across this and

Â measuring the current across those terminals.

Â That's i sub short circuit, and those two are both necessary in finding here.

Â And if I found those two through measurements, then I just can come back

Â through this relationship Ohm's law and find R Thevenin.

Â A lot of times in actual circuits it's easier to find

Â R Thevenin maybe analytically by doing a simple method here.

Â What I have to do is go to my original circuit,

Â this might be my original circuit.

Â I zero outsources

Â 2:28

And this method only holds when no dependent sources are present.

Â So if there are no dependent sources, I zero out those sources.

Â And by zeroing out sources, the voltage source has to be 0,

Â that means it's shorted.

Â 3:04

And I open circuit the current source,

Â now I want to find the equivalent resistance.

Â In this case I've got 2 in parallel with 4 in series with 10 and

Â that is 11.33 ohmes.

Â Now to find V Thevenin I actually draw the same circuit here because what I'm

Â trying to do is find the open circuit voltage across here so let me draw that.

Â 3:35

So we've drawn it and now I want to find this voltage right here.

Â And that's V Thevenin.

Â In this particular case, all the current will flow through this,

Â since this is an open circuit.

Â All the current flows through here, that means I know this voltage.

Â If I know this voltage and these current matches right here,

Â that means all this current goes in this direction and I know this voltage.

Â So I know this voltage, this voltage, this voltage, I can do a KVL around here and

Â solve for V thevenin.

Â It's going to be equal to two thirds volts.

Â 4:09

And similarly I can draw the circuit for i sub sc.

Â In this particular case, I draw the same circuit, but

Â in this case I draw a line across here and I short it out and

Â then I saw through this current right there I sub S C.

Â So if I did that in this case I would get 0.0589 amps.

Â 4:40

And I only really have to solve two of these three circuit problems because I

Â can use Ohm's law for the other ones.

Â So I can relate V Thevenin to R Thevenin and

Â i sc through Ohm's law right there.

Â Now once I solve this I can draw the V Thevenin and

Â that is 2/3 for V Thevenin,

Â R Thevenin is 11.33 omz, and

Â that's the Thevenin equivalent circuit.

Â So, this circuit here, is the same as the original circuit.

Â 5:43

In this particular case I short out this resistor,

Â so that R Thevenin is equal to 2 ohms.

Â I want to show a couple of examples of finding

Â V Thevenin in this particular case,

Â we want to find V Thevenin which is the voltage across here.

Â Since this is an open circuit there is no voltage drop across here.

Â That means that the voltage from here to here that's a plus and

Â that's a minus is V Thevenin, that means I just have to voltage devider lock R2

Â over R1 plus R2 times VS is equal to V thevatin.

Â And then I solve for R thevanin the same way we've been solving for it.

Â Let me show an other example very similar, finding V thevenin.

Â Again, I want to find this voltage right here.

Â But it's kind of messy to do this, so sometimes it's easier to find

Â i short circuit and then use Ohm's law to find V ThÃ©venin.

Â And we'll show that here.

Â 7:10

So that's why it makes it easier.

Â So all I have left with is this circuit right here.

Â R1, Vs And this current right there.

Â So, I can solve for i sub sc from this simplified circuit, and

Â once I solve for i sub sc and I solve for R Thevenin,

Â then I say V Thevenin is equal to R Thevenin, and Times i sub sc.

Â So in this case, it just turned out easier to solve our i sub sc first and

Â then use Ohm's Law to find V Thevenin.

Â So one of the other uses of the Thevenin Equivalent Circuit that

Â I mentioned all ready was to find the maximum power transfer.

Â So if I've taken a circuit that I've already reduced down to its Thevenin

Â equivalent, I want to say, well what sort of resistor can I put across here

Â when I call it a load resistor, that would maximize the power?

Â Well the answer is the Thevenin resistance.

Â If I've already solved for that Thevenin resistance, then this particular value of

Â resistor, the load resistor, maximizes power to this.

Â Now let's go ahead and show the derivation of that.

Â 8:19

It's based on a power analysis.

Â Power is equal to voltage across here, so we're trying to maximize this power.

Â So it's a voltage across this resistor times the current in here.

Â And I can go through a little bit of analysis, substitute in for i.

Â From Ohm's Law and then right here, substitute in for

Â V sub ab and that comes from the Voltage Divider Law.

Â And I have something now, the power is equal to this.

Â From this equation I can find the optimum R sub L maximize the power.

Â Now where is this useful?

Â Sometimes it's useful in matched impedances.

Â Sometimes you've got cables, and you want to maximize power at the load

Â end of the cable, and we call things like matched impedance or matched resistance.

Â 9:06

So the key concepts that we've covered so far, is the most important thing being,

Â this is what the Thevenin equivalent circuit looks like.

Â And we showed how to find the V thevanin and

Â the I short circuit when we short circuit this across here.

Â 9:20

The usages we remember that the uses when one part of our circuit is fixed and

Â we want to take something fairly complicated like this and

Â replace it with something very simple.

Â So then if we wanted to add something else like a resistor here

Â then we don't have to reanalyze the entire circuit.

Â And the other use is when we want to maximize power to the load.

Â