Welcome back to our series in linear circuits.
Again, I'm Nathan Parish. And today we're going to be talking about
an Introduction to Circuit Diagrams. We'll start looking at the actual things
that are drawn out, and really get your hands in there trying to solve some of
these things. The things we're going to be aiming to do
today is to identify the collection of basic circuit elements.
To be able to identify nodes, identify short and open circuits, and then finally
to identify equivalent circuit diagrams. So from last class, we showed how
currents and voltage interact to let us know the power that's being consumed by
the system. And we showed the basic physical
constraints and equations that allow us to solve for unknown values.
In that case, it was using a known power and a known voltage for example, to be
able to find a current. So now we're going to be taking all of
the things that we've learned to this point and starting to look at how they
come together into an actual circuit diagram.
Which is probably the thing that you most think of when you think about circuits.
In this lesson, our objectives are to identify a set of circuit elements, the
ones that we're going to be presenting, which will be all of the circuit elements
that we'll be looking at in the class. But enough to get us started.
We'll identify nodes in a circuit diagram and recognize which circuits are self
contradictory or circuits that just don't really make sense.
We'll identify open and closed circuits, identify when two circuits are
equivalent, and modify a circuit to give us an equivalent circuit.
So first of all, we just present this circuit diagram.
Now, you don't know what any of these things mean if you haven't been presented
a little bit of information on circuits before now.
But these are all circuits that we are going to be looking at today, and then we
will revisit this diagram after we've been able to see all the individual
components. To see how they come and work together.
So first of all, let's actually define what we mean by circuit analysis.
We kind of use the term a little bit loosely here, but let's kind of pin down
what we mean. And devices that are given some known
parameters and we put them all together in kind of a graphical model.
And we wish to identify the behavior with this device using the known information.
So what we're going to be then doing are making systems of equations to describe
the behavior, and then solving these different equations.
To let us know the unknown values, the things that we're eager to discover,
about how the circuit's going to behave. So the first element we're going to be
looking at, is wires. In the circuit diagram, wires are
presented as lines. And they just connect the devices.
And they hold them all together. Wires are believed to have zero internal
resistance. Which means that current can just flow
through it. And it doesn't really have any impact in
and of itself. It's just a way to show two different
items are connected together. You also have these two terms, nodes and
junctions. By nodes we mean any set of wires that's
all connected together. And a junction is where we see two wires
that actually meet up. So here, this would be a junction, a
little dot. And we'll use these filled in dots to
indicate where these two wires are actually connected.
But all of this is a node, and so sometimes they can be a little bit
difficult to distinguish what the nodes are.
So one thing that can be helpful is color them.
So here we have the red node, everything that is red is part of the same node.
Everything that's green is part of the same node.
Anf everything here that is blue is all part of one node.
So even though we have a couple different junctions here, those aren't the nodes.
The node is everything that's connected together.
And we believe that this node, there is zero voltage.
And if you remember, voltage is created by differences in charge density.
Well, because charge is able to freely flow on a wire, it can redistribute
itself however it see's fit. And so what's going to happen is all the
Charge is going to just distribute itself as broadly as possible.
And so we get no voltage across any different wire.
And it's also possible to have an arbitrarily large current that makes this
happen. We place no constraints on these
particular wires. Now, obviously that's not true for
physical wires. If I tried to stick a very enormous
current through a physical wire, bad things happen.
But as far as our diagrams are concerned, it's perfectly fine.
The next devices that we're going to look at are independent sources.
That these sources are sources where we specify either a current or a voltage
that is believed to constant, no matter what else is going on in the system.
So the first one, where we have the plus and the minus, is an independent voltage
source, where we say that the voltage from the minus to the plus is some
constant voltage. And it's completely independent of
anything else going on in the system, however it might be a function of time.
For example, you might have some type of device variable which is going to go up
and down in time, but nothing else in the circuit is going to be able to determine
what that voltage is going to be. It's kind of a known value.
The same thing is said for current sources, but in this case we're again
going to use an arrow. And these designations, the plus and the
minus and the arrow, correspond to the same pluses and minuses and arrows we
were using before when we discussed both voltages and currents.
Sometimes we don't know for certain what these values are, but they are actually a
function of something else that's going on in the circuit.
So, when we have this happen, we use what are called Dependent sources.
Instead of using circles, we now use squares that are turned on their angle.
So, again, we have, on the left, a voltage source with the plus and the
minus, and then, on the right, a current source, with an arrow.
These will typically be described by using some kind of equation that will be
listed next to the device. Referencing some other measured quantity
in the circuit. And we'll see how that works when we take
a look at our full diagram again. And this is a Resistor.
Now we haven't actually talked about resistors yet.
But they're the most common circuit elements, and in order to have an
interesting circuit diagram, we kind of want to have some Resistors thrown in
there. We'll talk a little bit more in
subsequent classes about exactly what these Resistors mean.
Resistors are drawn by drawing zig-zag lines.
Now the number of zigs and zags varies, and it's not particularly important.
If you see something with the going up and down zig and zag, it's a Resistor.
Other similar devices will be presented and introduced as we encounter them, but
basically, this is just kind of a passive device, it doesn't have any specified,
known voltage or current, it's completely at the at the system as to what it's
values are going to be. This is Ground.
It's, identified by showing a series of parallel lines getting decreasingly
smaller. Ground kind of gives us a point of
reference, when we're talking about voltage.
You remember from the voltage lecture, we talked about how important it was to
know, with respect to what, when we talked about voltage.
Well with Ground, it kind of gives us a zero.
sea level per voltage as it were. Where we say, this is going to be our
threshold, and everything has it in common.
Now, sometimes Ground is actually a physical thing.
You might know lightning rods use a Ground.
It's a wire that goes from a point of a building into the physical ground giving
path for electrons to flow, without having the electrons go through your
house and cause damage. Sometimes you can use something like a
Grounding strap, that would allow the electrons to flow through the Grounding
strap, rather than through some kind of sensitive device.
In these circumstances, this is actually a real ground that is some physical
thing. In our circuit diagrams though,
generally, we're just using it as a point of reference of what is zero voltage.
What do we mean by zero? Now we're going to talk a little bit
about open and short circuits. You hear the term short circuit thrown
around a lot. Something, some device breaks, they often
say oh, well there, there was a short circuit.
Something went bad. Well, this is what these things actually
mean. An open circuit is where we have some
devices where, the two terminals are not connected to anything.
There's no path, for anything to flow. And because it's a circuit, there
probably needs to be a closed loop, in order for anything interesting to happen.
So if we have an open circuit, we just have some dangling ends.
Normally we're going to use these open circles to identify that it's not
connected to anything. Now, sometimes we'll take a measurement
across an open circuit, but we don't see it, any current flowing, so electrically
it's not very important. This is a short circuit.
If we in turn take two points of the circuit element and connect them
together, now current can flow like this, without going through this device.
The reason we often talk about when things break, there being a short
circuit, is that when this happens, usually bad things are happening.
Things are, currents are going where they're not supposed to.
Voltages are not what we expect them to be.
And so that's why often short circuit means that something broke.
But in practice, actually short circuit just means that we are connecting the two
terminals at some device together. Using a wire.
These circuits, are what we call self-contradictory, or they don't make
sense. Remember, that voltage sources specify
what a voltage is, and it's constant. And, we know what it is, it doesn't
depend on the circuit. And, we know that wires have zero voltage
across them, so if we look at this circuit on the left, the voltage source
says that we have five volts from the top to the bottom.
And the wire says we have zero volts from the top to the bottom.
Which one is it? Well, it can't really be either.
It's self-contradictory. It doesn't make sense.
But you might be wondering, it's real easy to connect a wire to the sides of
the battery. That's not hard to do at all.
So why can't we make this? Well, when we actually do that, you might
notice that the wire gets really, really hot.
And the battery loses it's power really, really quickly.
What is actually going on is, the wire is no longer acting like a wire in the
circuit diagram. It's starting to act like a circuit
element itself. So when we have a diagram that's
self-contradictory, it means that we're missing some kind of mathematical
assumption, its not very accurate, and we're going to modify the circuit to be
more representative of the real system. And when we look at the one on the right,
the current source says that we have one Amp of current flowing, but flowing
where? There's no way for the current to go,
because the circuit is an open circuit. The current's stuck, it's not closed.
So again, it's self-contradictory. So when we put it all together, we can
see all of the devices here, put together one big diagram, here we have our
resistor, we have an independent voltage source here and we specify its voltage,
VS, for Voltage Source. Here we have an independent current
source, its current Is is specified, R2, R3, here we have a nice little short
circuit, where we've connected the two ends of this resister, here's an open
circuit, where we're actually taking a measurement of the voltage across it,
here's a dependant current source, and its value is G1 times Va.
So we've measured a voltage here, and we're multiplying it by some G.
If we look down here, we can see where G is.
In this case, G1 is 0.005 Amps per volt. And we have to have this Amps per volt,
because this is a voltage, but we know this source has to be in a current, or
Amps. So we have to do the proper.
Division of Amps per volt here. Here G2 is 1000 volts per Amp.
Again, volts per Amp allowing us to get something in the result that's in a
voltage, even though we're multiplying by a current.
It's possible for us to actually manipulate circuits, to change them into
some different circuit. And this is a particularly confusing
circuit. It's kind of hard to follow.
We notice there are junctions, some places where there are dots, but we also
see that there are some wires that cross. And there are no dots.
They're not connected together. They just happen to overlap each other.
So this circuit might be really difficult for us to analyze.
So let's try moving it around and change it up, to get something that's
equivalent, and maybe easier for us to analyze.
To make it a little bit easier to see, I colored the nodes.
So we'll notice that here, we have this blue node that covers a lot of area in
the circuit, cover, connects a whole lot of different devices.
Let's have a red node, a green node and a pink node.
And so let's take a look at one particular device, and see how things are
connected together. Device A, which is just a square
representing some unknown device, is connecting the red and the blue nodes.
So we know that any circuit that is going to be equivalent to this, has to have
that same behavior. So this would be an equivalent circuit.
A, here, connects the red node to the blue node, everything's okay.
And in turn if we go through each of these individual devices, B goes from
blue to pink, so B from blue to pink. H from pink to blue, H from pink to blue.
If you go through, you'll verify that each of these devices is connected to the
same two nodes. So although somethings are different, the
basic behavior of the system remains the same.
It is a little bit important to notice, however, that if there is a current that
we're measuring across a wire, we might lose it by doing this change.
For example, if we look at the wire between this E and this G, it has no
corresponding wire in this diagram because everything here.
Just kind of bridges up to the same junction point.
So, that's one thing to pay attention to, but as long as you're not caring about
certain values that cross wires, doing this is not a problem at all.
If you find a way of being able to distribute a system in a different way,
where everything is still connected in the same manner, same two nodes are
connected. Then that's perfectly fine, you can alter
it as much as you like. So to summarize we described the concept
of a node and how to identify one. We introduced independent and dependent
voltage and current sources, as well as the dependent varieties.
We introduced the resistor but we didn't describe how it behaves, because that's a
topic for a later lecture. We presented the idea of a ground.
And we showed some examples of circuits that are self-contradictory.
They don't really make sense. And really what that means is that your
system that you've diagrammed is not really representative of the actual
system that you're looking at. And we've described how two circuits can
be equivalent as far as a circuit's view's concerned.
Just by moving things around. So as long as everything is still
connected in the same way. For our next class, we will see another
way that voltages and currents relate, as well as how charges move through
materials. And if there is anything that you were,
found confusing in this class or you have any questions about the material that was
covered here, again I remind you to go to the forums.
Ask questions there, and then, either your students or, fellow students, or
Doctor Ferri, or I, will be able to answer your questions there.
Look forward to seeing you again next time in our next module, where we start
talking about some resistance circuits. Until then, cheers.