Hello, I'm Nathan Parrish and this Linear Circuits.
We're going to be looking at some basic linear circuits and some of the devices
that use linear circuits, to give a quick introduction to some of the basics in
electrical engineering. We're going to be starting with looking
at current and charge, and the aims of this particular lesson are to help you
calculate the forces that charges exert on one another, and to calculate the
functions of current and charge. Now you might remember from the previous
class, that there was a different person who was presenting, that was Doctor
Ferri, and we teach this class together. As part of that, she introduced the
course as a broad outline, as well as she covered the basic overview of module one,
which is the background module, giving you the, the bare essentials that we will
need before we can start talking about more interesting things.
To put these topics in context with the rest of the module, we will start by
talking about charge and current. And after we've talked about these
things, we can then start talking about things like voltage, and power, and at
the end of this module we will even introduce you to some basic electric
circuits, so that we can start doing some analysis.
The objectives of this lesson are, to first of all, help you to identify the
forces that charges exert on one another, and then to allow you to calculate a
charge, based upon a current, and a current based upon a charge.
In talking about charge, charge is, a fundamental property of matter, all
matter has charge. And it comes in quantized, discrete
amounts. This amount is known as the fundamental
charge, and it is equal to 1.602 times 10 to the negative 19th Coulombs.
All protons have one positive elementary charge, and all electrons have one
negative elementary charge. You might also remember about neutrons
from basic physics, where neutrons have neutral charge.
Electromagnetism is a fundamental property of matter, and you might
remember that all the protons are held together in the nucleus.
And why is it that they aren't just, pushed apart?
Well, it turns out that there's other forces that work here.
The electric strong force holds the protons together in the nucleus and it's
about 137 times more. Strong than electromagnetic force, but on
the other hand, electromagnetic force is about 36 orders of magnitude stronger
than gravitation. Which means that if you held your cell
phone upside down, it's going to work equally as well as holding it right side
up. When we talk about charge we're measuring
it in units of Coulombs, after Charles Augustine Coulomb, an 18th century French
physicist. And when we represent Coulombs, we're
going to use a capital C. When we use these values in equations,
we're going to use a q, sometimes it's a lowercase q and sometimes it's a capital
Q. It doesn't particularly matter which we
use just so long as the, you know, that q reference is charge.
The electromagnetic force that is exerted on particles can be calculated using
something called Coulomb's Law. Coulomb's Law states that the strength of
the force that charges exert on one another is equal to k sub b times the
quantity q one times q two, divided by r squared.
Here q one is the charge of the first particle, q two the charge of the second
particle. And r is the distance between them.
K sub e is Coulomb's constant. It's a fundamental constant of nature,
and that is equal to 1 over 4 pi epsilon naught.
And it is in units of Newtons meter squared per Coulomb squared.
Here, the pi is the pi that you're familiar with from basic math, 3.14159,
and so on. Epsilon naught is known as the
permittivity of free space, which is something that you're probably not
familiar with. And we'll talk about it more in the
future. But again, this is a constant property of
matter. If you put them all together, k sub b is
approximately equal to 8.988 times 10 to the 9th Newtons Meter squared per
Coloumbs squared. The way that these charges interact with
each other is through something called an electric field.
If we look at electric fields, positive charge is going to have an electric field
that pushes outward radially in this manner.
We use the arrows to distinguish the direction that other positive charges are
going to be pushed. If we look in turn at a negative charge,
it's going to have the same basic behavior, but the arrows point the other
way. Because it's going to attract positive
charge inward towards itself. Now neither of these is particularly
interesting, but if we start putting them together, that's when things start to get
a little bit more interesting. And, the most common configuration for
doing this is in something called an electric dipole.
This is where we take a positive charge and a negative charge, put them in close
proximity and fix them. And when we look at this we get kind of
an interesting field behavior. So here, if we have a positive charge and
a negative charge here, and we place a positive charge somewhere in between
them, the charge is going to be basically pushed straight from the positive, here,
to the negative, here. But it gets a little more interesting if
we put perhaps the positive charge somewhere out here.
Because it's so close to the positive charge, it's going to be basically
trending away from this positive charge. But just because the negative charge is
further away, it doesn't mean it has no effect.
It will have an effect and will start to try and pull it towards it, which causes
this positive charge to be pushed, as it goes outward, slightly over and curving
around. And so it's the interaction between the
positive and the negative that cause this curving behavior.
Now that we know something of electric fields, this allows us to start talking
about current. The way that we define current is by
looking at a material we come up with a cross-sectional area.
And then we count the amount of charge that passes through that cross-sectional
area in a given period of time. But, we would like to know what the
current is at an instant of time. The way that we do that is we take these,
slices of time and make them smaller and smaller, until they approach zero.
You might remember from calculus that what we're essentially doing here is,
we're taking it the limit. And so when we do that, we take the ratio
of charge with respect to time. And take the limit as time becomes
smaller and smaller. What we're essentially doing is taking
the derivative. Hence to calculate the current.
We take the time derivative of the charge.
It becomes very simple then to invert this operation if we desire to know what
the current is. What the charge based upon the current.
We do this by simply integrating but to get a complete picture, we must also add
the initial charge. Now we can measure this current in units
of Coulombs per second, or we can use the unit of Amperes, or Amps, which is itself
a unit. We designate it using an A, and Amperes
are named after again, a French physicist, Andre-Marie Ampere, who was
one of the first people to study current. When we do equations, we're going to be
using the variable i to represent the flow of current.
And the reason we use i, is because in his research, Andre-Marie Ampere used the
term intensity of current. To represent this value.
And so we use the i from intensity to represent the current.
It becomes very important when we're doing these types of calculations to keep
in mind what our reference directions happen to be.
And this is one of the areas that most beginning electrical circuits and
students really start to trip up is by not keeping the reference directions
straight. So, to help you better understand, we're
going to start by talking a little bit about electric charge.
If we have a charge that's slowing, it's actually not generally the positive
charge that's moving. It's the negative charge.
And the reason for this is when Benjamin Franklin, an American, scientist was
studying charge, he noticed that rubbing two materials together caused charge to
be transferred from one to the other. And so he just made an assignment, made
one positive and the other negative, it turns out that the negative ones are the
ones that move. So to start looking at this in
perspective, if we have one Amp of current flowing here, as labeled in the
left diagram. What that means is that we have one
Coulomb of charge, every second, flowing from the top to the bottom.
But in practice it's actually negative one Coulomb of electrons pulling from the
bottom to the top. If we look at this figure on the right
it's basically saying the same thing. We've changed the current from positive
to a negative and we've changed the arrow direction.
But again, it's negative one Coulomb. Of charge going from the bottom to the
top every second. And by keeping your reference structure
straight it will make sure that you don't end up getting strange values when you're
doing you're basic analysis calculations. In summary, we discussed charge as a
property of matter. We discussed how we can calculate the
forces the charges exert on one another. We were able to calculate current by
taking the derivative of charge and calculate charge by taking an integral of
the current with respect to time. We've also emphasized the importance of
being straight with your reference directions when you're doing your
calculations. So for my next class we're going to be
taking a closer look at electric fields. We will present the idea of voltage, and
then we'll actually have a practical example of seeing how voltage behaves, by
looking at how a car battery works. I'll remind you that there are forums
online where you can post your questions. Doctor Ferri and I are both going to be
monitoring those forums. And you are encouraged to go and
participate in the forums and answer other peoples' questions.
It's a great way for you to learn by teaching others.
And it should be an excellent opportunity for us to get together.
That's actually the primary way of being able to, to ask questions of Doctor Ferri
and me. So we look forward to seeing you on
forums, and look forward to seeing you next time.
'Til then, cheers.