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.