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.