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# Introduction to circuits and Ohm's law

Video transcript

Well, we've spent many videos
talking about electrostatic fields and the potential on a
charge or the potential energy of a charge when it's
in one place. But let's see what happens
where, given a potential, what happens when we actually allow
the charge to move? And this will probably be a lot
more interesting to you, because you'll learn how much
of the modern world works. So let's say that I have
a source of voltage. Let me see how I want
to draw that. I'm going to draw
that like that. I'll draw it in yellow. So this is my source
of voltage, often known as a battery. This is the positive terminal. This is the negative terminal. It's a whole other subject, a
whole other video, and I'll make one eventually, of
how a battery works. But let's just say that no
matter how much current-- well, actually, let me explain
in a second, but no matter how much charge flows out of one
side of a battery to the other side of the battery,
that somehow the voltages remain constant. So that's kind of a
non-intuitive thing, because we learned about capacitors, and
we will learn more about capacitors in the context of
circuits, but what we learned about a capacitor is that if we
got rid of some charge on one end, the total voltage
across the capacitor will decrease. But a battery is this
magical thing. I think it was invented by
Volta, and that's why we call everything volts and voltage
and all of that. But it's this magical thing
that, even as one side loses charge to the other side, that
the actual voltage, or the potential between
the two sides, actually remains constant. That's the magic of a battery. So let's just assume that we
have one of these magic instruments. You probably have one in your
calculator or your cellphone. And let's see what happens when
we allow the charge to actually travel from one
side to the other. So let's say that I have an
ultra-good conductor. Let's say it's a perfect
conductor. It's normally drawn straighter
than what I'm capable of doing. And no, I haven't had
anything to drink before making this video. So what did I do here? So in the process of kind of
connecting this positive terminal to the negative
terminal of the battery, I'm also exposing you to common
schematic notation for electrical engineers
and electricians, et cetera, et cetera. So what this is, these lines
here essentially are wires. There's no reason why I drew
it at a right angle here. I just did that to be neat,
those right angles. And it's assumed that this wire
is an ideal conductor, that charge can flow freely
without being impeded. This thing right here, this
scratchy line, this is a resistor, and this is something
that will actually impede the charge. It'll keep the charge from going
as fast as possible. And then, of course,
out here, this is a perfect conductor again. Now, which way will
the charge flow? Well, I think I've mentioned
this before, but in electric circuits, it's actually the
electrons that are flowing. The electrons are those small
particles that are going really, really fast around
the nucleus of an atom. And it's actually the electrons
that have this fluidity that allow it to flow
through a conductor. So the actual movement of
objects, if you call an electron an object, some would
argue that they're almost just notional objects, but the actual
flow is the electrons from the negative terminal
to the positive terminal. But the people and all who
originally created circuit schematics and were the
pioneers of electrical engineering and electricians and
whoever, I don't know who came up with it, they decided to
say-- and I think the point here was to confuse people--
that the current flows from the positive to the negative. So the direction of the current
is normally given in this direction, and current
is specified by I. And what is current? Well, current-- so wait. Actually, before I tell you
what is current, just remember, even though people
say that the current-- and most textbooks do this, and if
you become an electrical engineer, people will often
say that the current is flowing from the positive
terminal to the negative terminal, the actual flowing of
things actually occurs from the negative terminal to
the positive terminal. It's not like somehow these big
heavy protons and nuclei are somehow traveling
this way. Once you compare the size of an
electron to a proton, you would realize how
crazy that is. It's the electrons, these little
super-fast particles that are moving through the
conductor from the negative terminal this way. So you could almost view this
current as, the lack of electrons are flowing
this way. I don't want to confuse you. But anyway, just remember that
this is the convention, but the reality is to some degree
the opposite of the convention. So what is this resistor? Well, as the current is
flowing-- and I want to stay as close as possible to reality
so you have a good visualization of what's
going on. As the electrons are flowing,
you have these little electrons, and they're
flowing in this wire. And we assume for some reason
this wire is just so amazing that they don't in any way bump
into any of the atoms of the wire or anything. But when they get to this
resistor, that's when these electrons start bumping
into things. They start bumping
into the other electrons in this material. So this is the resistor
right here. They start bumping
into the other electrons in this material. They bump into the atoms and
molecules in this material. And in the process, the
electrons essentially slow down, right? They're bumping into things. So essentially, the more things
that there are to bump into, or the less space there
are for the electrons to flow through, the more that this
material is going to slow down the electrons. And as we'll see later, the
longer it is, that only increases the chance that
electrons bump into things. And this is called a resistor
and it provides resistance, and it dictates how fast
the current flows. So current, even though the
convention is it flows from positive to negative, current
is actually just the flow of charge per second. So we could write that down. I know I'm saying this in kind
of a disjointed way, but I think you get what I say. Current is flow of charge, so
change in charge per second, or per change in time, right? So the way you could think about
it is, what is voltage? Voltage is how badly does
current want to flow? So if there's a high voltage
difference between these two terminals, then the electrons
that are sitting here, these electrons want to really
badly get here, right? And if the voltage is even
higher, these electrons want to get there even more badly. So before people understood
that voltage was just a potential difference, they
would actually call this desire of the electrons to
get from here to here the electromotive force. But what we've learned now,
it's not actually a force. It's just this potential
difference that makes the-- we could almost view it as an
electrical pressure, and that's what people used to
actually call voltage, electrical pressure. How badly do the electrons want
to get from here to here? As soon as we give the electrons
a path through this circuit, the electrons
will start traveling. They'll start traveling, and
we assume that this wire provides no resistance, that
they can travel as fast as they want. But when they get to this
resistor, they start bumping into things, and this
limits how fast the electrons can travel. So you can imagine that if
this object right here is somehow the rate-determining
factor in how fast the electrons travel, no matter
how fast the electrons can travel after that, this
was the bottleneck. So even though electrons can
travel really fast here, they have to slow down here, then
they could travel really fast here, the electrons here can't
travel any faster than the electrons through this. Well, why is that? Because if these electrons are
traveling slower, so the current here is lower-- current
is really just the rate at which the charge
is traveling, right? So if the current is lower
here and the current was higher here, we would
essentially end up having a buildup of charge someplace here
while all of the current were waiting to travel
through this. And we know that that's not
the case, that all of the electrons actually travel at
the exact same rate through the entire circuit. I'm going in the opposite of
the convention right now, because the convention is that
somehow we have the positive things traveling this way. But I want to give you a really
intuitive sense of what's going on in a circuit,
because I think once you understand that, once problems
get a lot more complicated, they won't be so daunting. So what we know, and this is
called Ohm's law, we know that the current is actually
proportional to the voltage across the circuit. So we know that voltage-- or
we could view it the other way, that the voltage is
proportional to the current through a circuit. So the voltage is equal to the
current times the resistance, or you could say that the
voltage divided by the resistance is equal
to the current. This is called Ohm's law, and
this is true whenever we're at a constant temperature. We'll go into more depth later,
and we'll learn that if a resistor actually has
temperature increases, then its particles and its molecules
are moving around more, they have higher
kinetic energy. And then it's even more likely
that electrons will bump into them, so actually, the
resistance increases with temperature. But if we assume at a constant
temperature for a given material-- and we'll also learn
later that different materials have different
resistivities. But for a given material at a
constant temperature in a given configuration, the voltage
across a resistor divided by the resistor is
equal to the current that flows through it. An object's resistance is
actually measured as ohms, and it's given by the Greek
letter Omega. So let's do a simple example. Let's say that this is a
16-volt battery, so the potential difference here is 16
volts between the positive and the negative terminal. So it's a 16-volt battery. Let's say that this resistor is
8 ohms. What is the current flowing through-- and I keep
doing it in the opposite of the convention, but let's go
back to the convention. What is the current flowing
through this circuit? Well, it's fairly
straightforward. It's just Ohm's law,
V equals IR. The voltage is 16 volts, and
it equals the current times the resistance, times 8 ohms. So
the current is equal to 16 volts divided by 8 ohms,
which is equal to 2, and this is 2 amperes. Or sometimes they're called
amps, and that's the units for current. But as we know, all current is,
is the amount of charge per amount of time, so an ampere
is just 2 coulombs per second, right? Oh, I'm already at
11 1/2 minutes. So I will leave you there. You now know the basics of Ohm's
law and maybe a little bit of intuition on actually
what's going on in a circuit, and I will see you in
the next video.