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.