So, in this video, we're finally going to 
define voltage and current so we can 
begin to talk about electrical signals 
and how they behave. 
So, we'll define voltage and current. 
It's pretty easy. 
We're not going to use too much physics 
here. 
It's going to be very intuitive, I hope. 
We'll then talk about the circuit 
elements. 
These are elements that act on voltage 
and current in very particular ways and 
these are used to construct real-life 
analog circuits. 
So, what are voltage and current? So, 
voltage is also called electric potential 
and it provides the push for the flow of 
charged particles. 
So, the idea is that you have a region of 
positive to negative voltage and the 
positive part is suppose to represent 
that it has a higher potential, 
electricall potential than the negative 
side. 
So, this is downhill if you will. 
Higher potential where it's positive and 
lower potential where it's negative. 
And so generally, if you just had a 
charged particle, a positively charged 
particle, it would want to go down hill. 
That's what a voltage does, it provides 
the push. 
Voltage has units of volts. 
usually indicated for lowercase v, 
sometimes for uppercase V named for 
Allesandro Volta, the Italian who, this 
is history, discovered the battery 
[UNKNOWN]. 
Current is the flow of positevely charged 
particles in the direction that's 
indicated. 
So, what this means here is that there's 
a river of charged particles flowing this 
way and notice the word current, is 
analagous to the flow of water in a 
stream or river and the current is 
flowing this way. So, the interesting 
thing though is that this is the flow of 
the positively charged particles. 
If you had negatively charged particles 
like an electron flowing in this way, it 
turns out positive current to the right 
means the electrons are flowing to the 
left. 
you can blame this convention of getting 
negative charge assigned to an electron 
to Benjamin Franklin. 
as you probably know, it's the electron 
that's the workforce in electricity. 
And we talk about current here as a flow 
of postively charged particles. 
But the electrons are actually falling 
the other way, but we don't really care, 
we talk what's the actual value of the 
current that we have. 
The unit of current was named for the 
physicist Ampere usually denoted by a 
capital A. 
1 volt is not a very big voltage. 
I'm going to show you some batteries in a 
second and they're typically 1 1/2 volts, 
1 ampere of current though is a lot of 
current. 
typically most circuits you can range 
from the microamp range to the milliamp 
range, 1 ampere occurs in things that are 
coming out of the wall, for example, and 
supply a lot of current. 
That in, out of a power cycle. 
Now, 
how the charged particles actually flow 
to in response to an applied voltage 
depends on the conducting medium. 
We can go through several circuit 
elements there are and, the laws of 
Physics determine how the voltage and 
current are related to each other so it's 
not always true that if you have a 
positive voltage, like I've indicated 
over here, that the electrons all would, 
rather the positively charged particles, 
always flow that way. 
That's not true, 
it depends on what's in between and we'll 
see that in just a second. 
So let's define a convention here. 
So, here we have a generic circuit 
element, 
I don't know in detail what it is but 
there's a very important convention here. 
And that is if you define voltage to be 
plus to minus that way, 
you want to defined the positive current 
as going in the positive side of the 
voltage. 
This is a convention that is extremely 
important to follow while we are getting 
used to circuits and, and have to think 
about them. 
This does not mean that the voltage V is 
going to lined up being positive number 
The way you assign voltage is up to you, 
you could turn out that once you put it 
in the circuit and you figure out how it 
works, the voltage is negative. 
And it could, of course, turn out that 
the current is negative, too. 
But in order to find, what we call, the 
v-i relations, the relationship between 
voltage and current that a given circuit 
element imposes, we must but, go by this 
convention. 
So, let's talk about some rather simple 
circuit elements first. 
At first, there's just a wire. 
So, we notice the word here, ideal. 
This is an ideal wire. 
So, an ideal wire lets any current flow 
that the circuit wants to flow with no 
voltage drop, the voltage is zero. 
The current essentially pushed through 
here with no electric potential being 
required. 
This is an ideal wire, this is, in fact, 
what a super conductor is. 
It allows current flow with no voltage to 
be applied, no voltage drop. 
the real wire has a small resistance and 
does not behave like this at all. 
But this is what we use in circuits. 
This is a model of an ideal circuit 
element what's called, we called the 
short circuit that let's any current go 
at all, but the voltage drop is zero. 
And guess that there's also an open 
circuit which is what I call a dead wire. 
Which, in this case, there's no current 
flowing because it's open, it's free 
space that will be in between, but there 
is a voltage drop. 
And the voltage drop can be anything that 
the circuit, in which this open circuit 
is found, can occur. 
and so the important point here is that 
in an open circuit, there is no current 
flow through the open area, i = 0. 
Okay. Well, let's talk about something 
that actually does something perhaps the 
simpliest circuit element is the 
resistor. 
And here, voltage and current are 
proportionate to one another and the 
constant of proportionality is the 
resistance R. 
So, 1 ohm is a volt divided by an amp, 1 
ampere. 
1 volt divided by 1 ampere is 1 ohm and 
the symbol for an ohm is a capital Omega. 
so, very simple circuit element 
as we'll see when I show you some low 
ones in just a second. 
The capacitor, and, it was a bit more 
interesting. 
the symbol for a capacitor is this set 
of, lines, going into what looks like two 
perpendicular lines. 
The v-i relationship is that the current 
is proportional to the derivative of 
voltage. 
And the constant of proportionality is 
the capacitance, 
which is measured in Farads. 
Farads is named from Michael Faraday, a 
very important 19th century experimental 
physicist. 
Now, how do you build a capacitor? Well, 
it turns out the symbol for the capacitor 
gives it away. 
If you had two parallel plates and you 
put leads to them and apply the voltage 
to it, put it in a circuit, 
what's happened is that charge wants to 
accumulate on this plate. 
and it may, the current actually doesn't 
flow through. 
It doesn't jump across those plates, but 
current can slosh back and forth as if it 
were flowing through the circuit element. 
And it turns out the capacitance C is 
equal to the dielectric constant of the 
mediumness in between times the area of 
the plates divided the distance between 
them. 
So in order to get the capacitance up, 
you have to have a big area and/or a very 
small distance between the two plates. 
Now, I give you an idea about scale here, 
a 1 Farad capacitor is huge, it's 
gigantic. 
And that is the way the units all work 
out. 
typically capacitors are in the 
millifarad, that's a pretty big capacitor 
even microfarad, even nanofarads, and 
even picofarad capacitors are founding 
lots and lots of circuits. 
But that's the way they're constructed 
out of parallel plates. 
This goes back to what I said about the 
nature of the medium for the circuit 
element. 
It defines that the i relationship 
resistor is probably the simplest medium 
and capacitor is an interesting medium, 
too, that has a bit more complicated v-i 
relation. 
And then finally, there's the inductor. 
inductors are the symbol here for an 
inductor is supposed to resemble a coiled 
wire, has an inductance, L, which is 
measured in Henrys, named for Joseph 
Henry, an American 19th century 
physicist. 
And it has a v-i relationship, the 
voltage is proportional to the derivative 
current. 
In some sense, it's the opposite of a 
capacitor. 
And if we use the laws of Physics to 
figure out how voltage and current are 
related when there's a coil of wire, 
we'll discover that at the new 
approximation, the voltage is 
proportional to the derivative of the 
current. 
So 
inductors are found, for example, in, in 
automobiles, when you talk about the coil 
in an automobile, it turns out it's a big 
inductor. 
Okay. So, let me show you some resistors. 
So, here's a photograph I took of the set 
of resistors I happen to have. And I want 
you to notice, first of all, they're all 
the same size, 
no matter how big the resistance is. 
So, this is the actual resistance of each 
of these circuit elements resistors 
rather going all the way from 10 ohms to 
1 megaohm. 
I want to hold up a resistor to give you 
an idea of the size. 
This happens to be the 1 megaohm resistor 
that I showed you in the photograph here 
and you can see, it's pretty small. 
The size of the resistor determines how 
much power you can dissipate. 
These turned out to be 1/4 watt resistors 
and we'll talk about the power 
considerations in a second. 
Well, how did I know that these are the 
values of the resistors? And I don't know 
if you could see it very well but there 
are little bands of color going around 
each of the elements and it turns out 
that brown black orange is a 10,000 ohm 
resistor. 
And this round black red here turns out 
to be a 1 kilo ohm resistor. 
So, I'm reading those colors from the 
top. 
This is called the color code. 
And you can go online and Google color 
code. 
And you'll find lots of calculators, what 
are called calculators for color codes. 
You type in the colors, and they'll tell 
you what the resistance is, or you can 
type in the resistance and they'll tell 
you what the colors are. And you should 
remember them as you get deeper into 
Electrical Engineering. 
but the important thing here is size does 
not determine the resistance. 
The turn is the size of a resistor is the 
most power, it dissipates. 
And I'm showing that in the next slide, 
where I have a much bigger resistor. 
So, here's that resistor and you can see 
it's quite, 
it's much bigger than the other resistors 
I have. 
And, if you look at it very carefully, 
you can see it says, it's 75 ohms and I 
don't know if you can see it very well, 
but down below, what I just the wrote 
over, it says, it's 25 watts. 
So, this will, will dissipate lots of the 
power. 
It turns out it's hollow inside and 
that's there to allow more power to 
dissipate from this. 
So, this is able to put out lots of 
power. 
I'm sure you've seen light bulbs. 
in the US, there's 60- watt light bulbs, 
and they can get very warm, very quickly. 
Imagine at 25 watts can also get pretty 
warm. 
These 1/4 wire resistors don't get very 
warm at all. 
So, let me show you a capacitor. 
And you can see on the left there, 
a 470 microfarad capacitor and it's 
pretty big. 
Here it is. 
And it's a pretty good size, bigger than 
my finger in diameter, and that's like I 
said, a pretty hefty sized resistor. 
On the right, is a 1 nF resistor, and 
which, I mean, sorry, 1 nF capacitor 
[UNKNOWN] a 1 nF capacitor. 
And it's small by comparison and you'll 
find that science capacitor in lots of 
electronic circuits. 
Finally, let me show you an inductor, and 
here's the inductor. 
It's in that photograph. 
It's about finger sized. And if you look 
at it carefully, it is a coil of wire 
coiled around a circular object and I 
want to point out something. 
if you look very carefully at this 
figure, you can see that the wires coming 
out look to be silverish. 
They're not really silver, but they look 
silverish. 
Whereas, they look to be brownish around 
the coil. 
And it turns out the brown does not 
indicate that they're copper. 
That brownish substance turns out to be 
an insulator. 
Because if this wire was not insulated 
right over here, for example, the wires 
are touching each other and it would 
short out the entire inductor. 
Because they're insulated, this coil of 
wire now looks like an inductor and 
you'll find this, it applies very 
consistently throughout Electrical 
Engineering, that when you send to see if 
that kind of color it's indicating that 
it's a insultated wire, 
you can scrape if off if you want to get 
rid of the insulation. 
Also, as you know, there's a plastic kind 
of installation and lots of lines, too. 
But in this special case, it would 
indicate that this is a very small kind 
or, kind of insulator, too. 
Okay, let's go back and look at the 
circuit elements again, because there are 
times when you want to write the v-i 
relations the other way if you will. So, 
instead of v = Ri, you might want to 
write i equals 1 / R * v. 
Well, we call 1 / R is called the 
conductance. 
It's given the symbol G and G is measured 
in Siemens, a name for the German 
inventor of designer of telegraph systems 
in the early part of the 19th century. 
So, the symbol G is for Siemens. 
There are going to be lots of times when 
it's more convenient to think about a 
resistor in terms of its conductance 
reciprocal ohms, Siemens, that it is in 
terms of its resistance. 
And we'll find that out very soon. 
Now, of course, for the capacitor and the 
inductor, those derivative relationships 
turn into integral relationships and as I 
said, all integrals in this correspond, 
definite integrals and they all start at 
minus infinity. 
So, in some sense, a voltage and a 
capacitor has an infinite memory of all 
the previous ties of the current. All 
previous ties of the current, 
now matter how their rose, going back to 
the beginning of the big bang are 
summarized by the voltage. 
Of course, there are a lot of different 
current patterns that are results in the 
same voltage. 
Same thing for the inductor. 
It's the current that contains a memory 
of everything all the voltage values that 
the voltage of the inductors had across 
it. 
A kind of interesting that they have this 
kind of infinite memory, but that's what 
you get when you have a derivative 
relationship. 
Turn it around, it comes in here. 
Okay. 
Let's talk about some different elements, 
namely, sources. And these provide a 
voltage or a current to a circuit that we 
build. 
So, a voltage source is indicated by a 
circle with a, a + to - indicating the 
positive direction for the applied 
voltage, v sub s, 
s for source. 
So, the v-i relationship again, I am 
defining my own voltage v and my own 
current i, going to the top in a 
consistent way, 
is that the voltage is going to equal to 
whatever the source is for all i. So, 
what this means is that the voltage 
source has no constraints at all in the 
current. 
It can supply any current that the 
circuit to which this voltage source is 
attached will want what it does is it 
provides a, a voltage for all of the 
time, 
whatever v sub s is. 
Similar thing for a current source, is 
that this will provide a current no 
matter what the voltage is. 
The voltage could be 0 -100. 
10^-6. 
It really doesn't matter. 
It's going to provide a given current. 
Now, notice the little minus sign here 
and that is because, on this, 
the way I've drawn it, i sub s, is a 
positive current from the way and we 
always want i defining the v-i relation 
to get on the positive side of voltage. 
So, these two currents are going the 
opposite way and that's the reason for 
that minus sign. 
It's just a minor little thing. 
I just want to make sure you're 
consistent in the way you define things. 
Let me point out it is very, very 
important that you, you define voltage 
that way, 
you define current only in the positive 
sign of a volt, very, very important. 
Now, let's look at some batteries. 
So, batteries are a special case of a 
voltage source that produce constant 
voltages. 
And I've got 4 batteries in this 
photograph. 
This is a D-cell, which is, as you know, 
pretty big, 
is gives you a size of scale. 
If you read the label very carefully, it 
says 1 and a 1/2 volts. 
The little button at the top is the 
positive side. 
It doesn't, in most cases, they don't 
label the negative side. 
Once you know what's positive, the other 
end is negative. 
This is a AAA battery and if you look 
very carefully right there, it says, it's 
also 1 and a 1/2 volts. 
So, again, the size of the battery does 
not determine the size of the voltage it 
produces. 
what it does tell you is how long the, 
each battery will provide that voltage. 
Basically, the bigger the battery, the 
more [UNKNOWN] as I like to think about 
it, 
the more [UNKNOWN] it possesses, 
it can last longer. 
Chemical reactions can be sustained. 
So, the AAA battery, in general in a 
circuit won't last as a, as long as a D 
size battery attached to the same 
circuit. 
I wanted to point out, I discovered this 
the other day this is a battery that goes 
into my remote control for my doorlock on 
my car. 
And if you look at it very carefully 
right there, it says, 12 volts. 
So, this actually provides a bigger 
voltage than a triple A and than a 
D-cell, but it doesn't provide much 
current. 
by the way, the 27A that you may see at 
the top of this battery, is a model but 
it does not mean it provides 27 amps, I 
guarantee you it doesn't. 
And finally, this rectangular battery we 
see is clearly labeled 9v. 
And on the side, you can look to see 
which end is positive and which end is 
negative, that's labeled on the side of 
the battery. 
Okay. You can buy these clearly at any 
store. 
They're readily available. 
So, don't forget that when you buy a 
battery like this, 
it's open-circuited, 
there's nothing attached to, between the 
top and bottom. 
There's no, nothing there. 
So, for here, the way it's been pictured, 
the current is 0 because there's nothing 
attached to it. 
These batteries are quite happy to 
produce 1 and a 1/2 volts for these two, 
at least no matter what because they are 
just sitting there. 
Now, how about a current source? Well, a 
current source will provide a current no 
matter what voltage is across it. 
Providing a current means there's flow of 
charged particles going out of this 
device. 
It, if you, if it's open-circuited, where 
are these charged particles, electrons 
going? Where do they go? if it's really 
open, the current source has a real 
problem, it has no place for the current 
to go. 
Remember, an open circuit does not allow 
any current so it's inconsistent. 
So, it is very hard to go to a store and 
buy yourself a current source that's 
sitting here like this. 
It would be perfectly happy if the 
current source were short-circuited. 
You could buy one of those but heaven 
forbid, if you tried to break that wire 
off to attach it to something because 
then it would not be very happy. 
So, current sources are hard to buy in 
one sense and you go back to the voltage 
source. 
So, a voltage source is very happy to be 
open-circuited but it does not like to be 
short-circuited. 
So, this means the current flows, 
no matter what will a short circuit is a 
0 valued resistor, 
so this means that the voltage, in order 
for v = Ri, if we have a positive 
voltage, let's say, provided by this 
source and the resistance is whatever it 
is, it's 0 for short circuit. 
Well, to get a pop and number here, this 
current would have to be infinite to make 
everything work out. 
And so, voltage sources do not want to be 
short-circuited. 
Current sources do not want to be 
open-circuited. 
Voltage sources do not want to be 
short-circuited, fundamentals of 
Electrical Engineering. 
Okay. So, let's talk about power and 
energy. 
Now, the conservation of energy principle 
is that the sum of energies, consumed or 
produced in a closed system, is a 
constant. 
So you can't produce energy from nothing. 
A closed system means there's nothing 
going in or out of this system and 
whatever energy is inside that close 
system is going to be constant for all 
times. 
So what is power? 
Power is the rate of change of energy 
with time. So that's just the definition. 
So, p is usually measured in watts. 
And to be consistent with this 
definition, the energy would be in 
joules. 
And time would be in seconds. 
So, a watt is a joule second, 
joules per second. 
And, but the important thing for here is 
that the power and the conservation of 
energy principle that the energy is a 
constant means that That in a closed 
system, the power, total power in that 
system is zero at all times. 
Inside that closed system, there could be 
parts of it that are producing energy, 
producing power, but other parts have to 
consume it. 
They have to consume that power, so we 
should look in circuits and what I'm 
going to show a little bit later is that 
this law is obeyed by circuits. 
whatever is producing the power is also 
consuming it somewhere else. 
That's just the way things have to be. 
Well, what's the definition of power for 
a circuit? So, definition. 
The instantaneous power, 
the power at time t that is dissipated by 
a circuit element is the voltage times 
the current at those same times. 
Now notice the word, dissipated. 
So, positive power, 
if p is greater than 0, that means you're 
dissipating power. 
If p of t is less than 0, 
that means it's producing power and 
that's the convention, that's the way to 
think about it. 
Go back to the derivative convention for 
relationship between power and energy. 
So, if power is positive that means the 
energy being consumed by the whatever 
elements going up, so it's consuming, 
but it is less than it's producing so 
it's all very consistent. 
What's interesting is that watts is equal 
to volts times amperes. 
So, we measure the voltage in volts, the 
current in amperes, multiply them 
together and you get the power being 
dissipated or produced by that circuit 
element at that time. 
So let's go through the various elements 
and see what the power equations are for 
them. 
So, for a resistor where v = Ri, you can 
put, substitute this into the power 
formula up here anyway you want and what 
you get is that the power is either Ri^2, 
Rv^2 / R, whichever way you want to think 
about it in terms of voltage and current. 
So, one thing to point out, squaring 
always gives a nonzero, non, a positive 
quantity, it cannot be negative and that 
means the resistors always dissipate 
power. And that's why the wattage of the 
resistor is very important to consider 
because it's going to dissipate power and 
you'd better have a physical design for 
your resistor so that it can let the 
power dissipate freely up to its stated 
rating. 
But it always dissipates. So, resistors 
make dissipate power so there has to be 
some other element in the circuit that 
produces the power that the resistors 
dissipate. 
If we look at the capacitor, and the 
inductor things are a bit more 
interesting. So, I, I plugged let's say, 
the derivative relationship in here and 
it will, a little manipulation to show 
you that the power consumed by a 
capacitor is related to the derivative of 
the square of the voltage. 
So now, the square of a voltage, of 
course, again, is a positive number. 
However, it's derivitive can be both 
positive and negative. 
So, there are times when a capacitor can 
actually produce energy, produce power, 
and there are times when it consumes it. 
It depends on the nature of V and it's 
the same for the inductor. 
And, in fact, the way that we think about 
these, these are energy storage devices, 
the inductor and the capacitor. 
And capacitor energy is stored in the 
voltage and an inductor is stored, stored 
in the current. 
and these are results, 
these equations tell you how to calculate 
the power that's consumed or produced by 
these various elements. 
Now, I want to show you how we are going 
to start thinking about these. 
So, 
our fundamental circuit elements are 
going to be the resistor, the capacitor, 
and the inductor. 
We'll use voltage sources a lot. 
Now, we are going to build systems out of 
these elements that's called a circuit. 
Now so, all of these elements will go 
into our system. 
the sources, 
they're the ones that provide the signal 
for the input to the system and we'll 
somehow grab the voltage or currant to be 
the output of the system. 
So, the sources provide the input x and 
we'll all going to, have to figure out 
how you build systems that have been 
resistors, conductors, and capacitors in 
order to accomplish some goal, some 
relationship between x and y that you 
want and then, some voltage or current 
will be in the output. 
That's what's coming next. 
We'll try to build real circuits and try 
to do something useful with them.