- [Voiceover] Now I wanna use a diode in a circuit,
and we'll see how we solve circuits that include
these nonlinear diodes in them.
So I have a circuit here with a battery and a resistor
and a diode here, and it's gonna be a special kind,
it's gonna be an LED diode,
so it's gonna give off light.
This is a kind of diode that's manufactured to generate
photons of light when it has a current flowing through it
in the forward direction.
They're pretty cool and you see them all the time
in electronic components.
So we're gonna figure out how to use an LED
in a real simple little circuit.
And in our circuit here, we're gonna have a resistor
of 330 ohms,
and we'll make this battery three volts,
so it's like two double-A cells.
And what we wanna find out is
how much current's gonna flow around this circuit.
And then we label this here,
let me label the voltages across our components.
We'll have VD, which is this voltage here,
and we'll have VR, which is the resistor voltage,
and that's that voltage right there.
So now I'm gonna show you a plot of the iv curve
of our diode.
You can see right here, around 0.7 volts,
the current rises rapidly when there's 0.7 volts
across the diode.
And let's start out by analyzing this,
let's start with the same tools that we always have,
which is, let's try to write some current laws
for these two things.
So for the diode, we write a current law
that looks like this.
The current is equal to IS times
e to the qv
on kT
minus one.
So that's the iv characteristic for the diode,
where this is V diode
right there, and the corresponding equation for the resistor
is i equals V resistor
over 330
ohms.
That's just Ohm's Law for the resistor,
and i in both cases is this i right here.
Now if I wanted to, I could set these two expressions
equal to each other and solve somehow for VD and VR,
but what we're gonna do instead is we're gonna solve this
by graphing, by a graphical method.
Here's a graph for the diode,
and this is the VD scale, this is V diode,
and this is i up here.
And so what I wanna do is I wanna plot the resistor curve
around here as well.
I wanna plot the resistor iv curve
on this same plot.
Now, in this expression, I have VR instead of VD,
so let me see if I can work on VR here.
Let me try to figure out VR in terms of VD.
So I can derive VR
as three volts
minus VD.
And let's put this into this i expression here.
The Ohm's Law expression now becomes
i equals,
VR is replaced with three minus VD,
all over 330 ohms.
And let's work on this a little more.
i equals
three over 330
minus VD over 330,
and this is starting to look like the equation of a line.
Let me write this to recognize it as a equation of a line.
Minus VD
over 330
plus three over 330 is nine milliamps.
So this is the equation of a line, and the slope
is right here, is minus one over 330,
and the i-intercept is nine milliamps.
So let's see if we can plot this line.
This is actually called a
Load Line.
That's just a nickname for this kind of expression
that you get when you have a resistor connected
to a fixed power supply above and the resistor is
hanging down from it.
You get this characteristic equation of a line
that has a negative slope, which is really distinctive.
Let's see if we can plot this line.
Now, it's a line, so all we have to do is find two points
that solve the line and then we'll be able to draw the line.
So if I set VD equal to zero,
then i equals nine milliamps.
So here's VD equal to zero, and it'll go through
nine milliamps.
So that's
one point on the line.
But what else can I set to zero?
I can set i equal to zero,
which means I'm on the voltage axis.
And what I'm actually gonna do
is I'm just gonna look at my circuit and figure this out
in my head.
So I'm setting i equal to zero,
and i equal zero means there's no current in this resistor,
which means there's no voltage drop across that resistor.
And that means that this voltage here
is the same as this voltage here.
And I know the voltage here,
the voltage here is three volts,
so that means the voltage here is three volts,
and that's because I know the current is zero.
So let's go over and put that point on a line.
So when i is zero, v is three volts.
So there's another point on the line.
And now we have two points and we can draw a line
between 'em,
like that.
And what we've drawn is the Load Line
for this 330-ohm resistor.
You remember, back over here we said we could solve
these two equations by setting the two is
equal to each other,
and that's basically where do these two lines intersect?
And they intersect right here.
That's the solution to our problem.
So this intersection point is the solution.
It's where the resistor current and the diode current
are the same, and that's that point there.
Now I can just read off my answer.
Right there is about 0.7 volts,
and the current over here, if I read off the current,
just straight across there, it's about
6.8
milliamps of current.
So now we actually just solved our circuit
using a graphical technique.
And what that says is,
let me erase this a bit to clean it up.
Let me take out these two things here.
That was just the resistor Load Line
that we were talking about.
And now for our solution, we have i equals
6.8 milliamps,
and V,
V diode equals about 0.7 volts.
So that's how you do a graphical solution with a diode.