Mesh current steps 1 to 3 Khan Academy English English (auto-generated)

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- [Voiceover] Now we're gonna discuss the second

now we're going to discuss the second of

of two popular ways to analyze circuits,

two popular ways to analyze circuits and

and this one is called the mesh current method.

this one is called the the mesh current

This is actually one of my favorite.

method this is actually one of my

There's a fun spot here where we make up currents

favorite there's a fun spot in here

flowing around in circles inside the circuit,

where we make up currents flowing around in circles inside the circuit and it's

and it's interesting.

interesting so in the mesh current

In the mesh current method, what we do is we define

method what we do is we define mesh

mesh currents, so we need to define that word.

currents so we need to define that word

A mesh current.

a mesh current a mesh current is a

A mesh current is a current that flows in a mesh.

current that flows in a mesh and a mesh

And a mesh is the open windows of the circuit.

is the open windows of a circuit here's

Here's one of the meshes in our circuit.

one of the meshes in our circuit there's

There's another mesh here, it's an open window,

another mesh here it's an open window

and this third one here is another one.

and this third one here is another one

And this will be our mesh current number one.

and this will be our mesh current number

We'll call it i1, and we can define these

one we'll call it eye one and we can

other mesh currents, like this.

define these other mesh currents like this and I'm going to define them all to

And I'm gonna define them all to go around

go around in the same direction they're

the same direction. They're all going clockwise, around our circuit.

all going clockwise around our circuit

Now let me take a second to label the other

now let me take a second to label the

components in our circuit here.

other components in our circuit here

We'll call this V, we'll call this R1, R2,

we'll call this V we'll call this r1 r2

r3 r4 and this has a current source in

and this has a current source in it. We'll call that I.

it we'll call that I that makes it a

Makes it a little bit more interesting,

little bit more interesting and this is

and this is one of the reasons we use

one of the reasons we use the mesh

the mesh current method.

current method the word mesh actually

The word mesh actually comes from like screen doors

comes from like screen doors or windows

or window screens where there's wires and there's

screens where there's wires and there's

spaces between the wires, so a space in a wire network

spaces between the wires so a space in a

is called a mesh.

wire network is called a mesh that's

That's where the name comes from.

where the name comes from these mesh

These mesh currents are kind of interesting.

currents are kind of interesting the in

In some sense they exist, and then,

some sense they exist in but it doesn't

but it doesn't seem like they really do.

seem like they really do how could these

How can these currents be flowing around in circles?

currents be flowing around in circles

Let's look a little closely. It's pretty clear that the current flowing through

let's look a little closer altijd source

our voltage source, V, is equal to mesh current i1.

V is equal to mesh current i1 and also

And also, when we get up here to R1, mesh current i1

when we get up here to our one mesh

is flowing through R1 in this direction here.

current i1 is flowing through r1 in this direction here what happens when we get

What happens when we get to R2? We have one mesh current flowing down through R2,

to r2 we have one mesh current flowing

and another mesh current flowing up through R2.

down through Arts you and another mesh current flowing up

How can this make sense?

through our - how could this make sense

Let me go over here, and we'll draw, redraw R2. Here's R2, and now I'll redraw the mesh currents.

let me go over here and we'll draw redraw our - here's our - and now I'll redraw the the mesh current so here we

So we have a mesh current, i1 going down like that,

have a mesh Colonel I 1 going down like

and we have a mesh current, i2, like that.

that and we have a mesh current I 2 like that

And I'll label on here, I'll label the element current,

and I'll label on here I'll label the element current for our - we'll call

for R2, we'll call that iR2.

that I our - now what's going to happen

And what's gonna happen, this is a really wonderful

this is a really wonderful application

application of the principle of superposition.

of the principle of superposition I 1

i1 and i2 superimposed inside R2 to create iR2.

and I 2 superimpose inside our - to create IR - so if we want it to know ir

So if we wanted to know iR2,

- it would be the sum of these two

it would be the sum of these two currents. Now i1 is flowing in the same direction as iR2,

currents now I 1 is flowing in the same direction is IR 2 so this equals I 1 and

so this equals i1, and i2 is going in the opposite

I 2 is going in the opposite direction

direction, so it gets a minus sign.

so it gets a minus sign and if we

And if we somehow knew i1 and i2, this is how

somehow knew i1 and i2 this is how we

we would compute the actually current

would compute the actual current that's

that's flowing in R2.

flowing in r2 so next since this is a

Next, since this is a method, I want to list out

method I'm going to list out the steps

the steps of the method. The mesh current method is the first thing

of the method the mesh current method is

is to draw the meshes. And we did that over here, when we drew i1, i2, and i3. And the second step is to solve the easy ones.

the first thing is to draw the meshes and we did that over here when we do I 1 I 2 and I 3 and the second step is to solve the easy ones

When we say an easy one, here's an example of an easy one.

well we say an easy one here's an example of an easy one this the current

The current source I, right here, defines what i3 is.

source I right here defines what I 3 is

So i3 is an example of an easy current to solve for.

so I 3 is an example of an easy current to solve for and then the third step in

And then the third step in the method is to write

the method is to write kirchoff's

Kirchhoff's voltage law. KVL.

voltage law KVL write kirchoff's voltage

Write Kirchoff's voltage law equations, for the two remaining mesh currents. And the fourth step is solve.

law equations for the two remaining mesh currents and the fourth step is solve so

So in this video we're gonna do the first three steps,

in this video we're going to do the

and then in the next video, we'll go the full solve.

first three steps and in the next video we'll do the full solve okay so let's

Okay, so let's run our mesh current method.

run our our mesh current method number

Number one, draw the meshes.

one draw the meshes here's step one

Here's step one, happening right here.

happening right here so we can check off

So we could check off, we did step one.

we did step one step two is solve for

Step two is solve for the easy ones. And with think, i3 counts as an easy one. i3 flows down, through the current source, and so, step number two,

the easy ones and we think I three counts as an easy one i three flows down through the current source and so step number two so step two is I three equals

so step two, is i3 equals negative I,

negative I because they're pointing in

because they're pointing in opposite directions.

opposite directions but that's it that's

But that's it, that's the easy one. We've done that.

the easy one we've done that now we get

Now we get to the next step.

to the next step so now let's start step

So now let's start step three.

three we're going to write KVL equations

We're gonna write KVL equations on each of these meshes.

on each of these messages we'll start

We'll start here, and we're gonna go around this mesh

here and we're going to go around this

in this direction and write Kirchhoff's voltage law.

mesh in this direction and write kirchoff's voltage law so the first

So the first thing we come to is a voltage rise.

thing we come to is a voltage rise we go

We go in the minus side and out the plus.

in the minus side out the plus that's a

That's a voltage rise of V volts.

voltage rise of V volts next we get to

Next we get to R1, and R1 has a current flowing through it,

r1 and r1 has a current flowing through

a mesh current, and it will have a voltage on it like that,

it a mesh current and it will have a voltage on it like that because the

because the current's coming in from this side.

currents coming in from this side and

And that will give us a voltage, we go in the plus,

that will give us a voltage we go in the

out the minus, so that's gonna give us a voltage drop

plus out the minus so that's going to

give us a voltage drop of a drop

a drop of R1 times i1.

of r1 times i1 right now we are over to

Right. Now we're over to here, we go around the corner,

here we go around the corner and we go

and we go through R2. Now, R2 is odd because it has i1 and i2

through r2 now r2 is odd because it has I 1 and I 2 flowing into it so what are

flowing into it, so what are we gonna do?

Well we already figured out this element current

well we already figured out this element

is written down right over here.

current is written down right over here

There it is right there.

there it is right there

So if I label the current going down here,

so if I label the current going down

I have a plus and a minus,

here I have a plus and a minus this is

this is gonna be another voltage drop

going to be another voltage drop going

going around the loop.

around the loop so it's going to have a

So it's gonna have a value of R2 times this value here.

value of r2 times this value here I 1

minus I 2 and now we've made it all the

And now we've made it all the way back to home,

way back to home to the where we started

to where we started from, and so that's our KVL equation,

from and so that's our KVL equation

which we set equal to zero. All right.

which we set equal to zero alright next

Next step, let's do the other mesh.

step let's do the other mesh we're going

We're gonna go start here, and we're gonna go

to go start here and we're going to go

around this mesh, in the same way.

around this mesh in the same way first

First, the first term, we're gonna see a voltage,

the first term we're going to see a

oh look, it's a voltage rise,

voltage oh look it's a voltage rise so

so I'll have a plus here.

we'll have a plus here a voltage rise

A voltage rise, and it's the same term

and it's the same term that we had in

that we had in the previous equation. It'll be plus R2

the previous equation it'll be plus r2

times i1 minus i2.

times i1 minus i2 that's the voltage

That's the voltage rise going from here to here.

rise going from here to here now we go

Now we go through R3.

through r3 now r3 just has one mesh

Now R3 just has one mesh current.

current he just has I 2 flowing through

It just has i2 flowing through it. So we could put that there.

it so I can put that there so that

So that counts as a voltage drop,

counts as a voltage drop it gets a minus

gets a minus sign, and it's value is R3 times i2.

sign and its value is our 3 times i2

That's that one.

that's that one now we go over to our

Now we go over to R4. R4, this is the same thing with two currents

for our 4 this is the same thing with

that we had over here with R2.

two currents that we had over here with

So we do the same thing again.

our 2 so we do the same thing again this

This is gonna be a... we'll define this

is going to be a will define this as a

as a voltage drop,

there's the element current.

there's the element current well and

And it's the same form as we had here

it's the same form as we had here when

when we calculated the current for R2.

we calculated the current for r2 so this

So this is gonna be a voltage drop,

is going to be a voltage drop gets a

give it a minus sign, and it's gonna be R4

minus sign and it's going to be our four

times, this time it's i2 going down.

times this time it's I two going down I 2

i2 minus i3. And do we get home?

minus I 3 and did we get home now we're

Now we're all the way home,

all the way home

so our KVL equation is all that equal to zero.

so our KVL equation is all that equal to zero

So these are our two simultaneous equations

so these are our two simultaneous

that represent our current, and we wrote them

equations that represent our circuit and

using the mesh current method, so we get

we wrote them using the mesh current

to check off step three. And in the next video, we'll solve these two equations.

method so we get to check off step three and in the next video we'll solve these two equations

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