In this lecture, we're going to start with some of the fundamentals of electronics. The first idea that will be introduced is that of electric charge. And we'll introduce the Coloum's Law, which enables you to compute the force between electric charges. With the idea of electric charge, we can then go on to discuss moving charges or currents in circuits. Then building on Coulomb's law, we can introduce the idea of the electric field. And from there, we can introduce the notion of voltage or electric potential difference. With these basic ideas behind us, we can then talk about the first simple circuit elements, resistors, which obey Ohm's Law. Then after introducing another very simple circuit element, a battery, we can go on to start using what are called Kirchoff's Laws which are really based on conservation principles. But they offer us methods for finding the voltage and current at any point in a network of batteries and resistors or, later on, more complicated circuit elements. Then, once we have the basic circuit elements and a method for analyzing circuits, we'll start to look at a few specific examples. And particular series and parallel combinations of resistors. And voltage and current dividers, which are important circuits in audio applications. Okay, we're going to start by talking about electric charge. Now, electric charge was recognized quite a while ago. The, it's existence was recognized a long time ago. And in 1783 Coulomb wrote down Coulomb's Law, which tells you the force between 2 electric charges of charge q1 and q2 separated by a distance r. And those quantities charge is measured in coulomb's and the distance if that's in meters this constant is about 9 times 10 to the 9th Newton meter squared per Coulomb squared. And so just to remind you, one Newton is the force required to accelerate 1 kilogram by an amount of 1 meter per second squared. And that comes from Newton's second law. So that means if I take a 1 kilogram mass, and I press with the force of one Newton, it will be accelerated by one meter per second squared. Now, the reason we're introducing the idea of force here, is that you can really understand the amount of charge in terms of force, which is something you can measure. and the way you measure force is by letting it act on a certain mass. And then you can measure the acceleration. So this is something that you can directly measure with stopwatches and meter sticks. And that's a physical thing you can go on the web and measure. So the idea of force is is kind of derived from from that. But then, from the problem here is understanding charge which is kind of a, a an unusual concept. It's kind of hard to put your hands on, but it's really understood in terms of the amount of force between charged particles. So, going back to Coulomb's Law, here's, imagine we do an experiment, where we take two, what are called puff balls. Which are the they used to use the insides of, vegetable matter. Because, it was very, very light material that would hold charge. Now, these days you would probably just use a piece of Styrofoam. But if you take a a small piece of material and you supported by a thread, and you put some charge, say like charge, on two of these things. Then they will repel each other with, the electric force, Coulomb force. And from measuring this angle, you can figure out how much force is between these and then that defines the amount of charge these two objects. Now a charge can be plus or minus. And the rule is that like charges repel, and opposite charges attract. Now you can perhaps from high school, they used a glass rod and a piece of silk cloth. And you could rub the glass rod with the silk cloth and that would leave the glass rod, I think, I believe positively charged. Or the other alternative is you take a ebonite rod, sort of the material bowling balls used to be made out of, and you rub it with a piece of rabbits fur. And that generates a negative charge. And so you can generate static charge and move it around with displays its presence using an electrometer, which is essentially objects that hold charge. And then you can see their repulsion. but so, just to give you a feeling for how much charge one Coulomb is. If I were to take one Coulomb of charge on two objects, separate them by 1 meter, then plug that on. This is 1, that's 1, that's 1 squared. So the force is this constant 8.988 times 10 to the 9th newtons. Now that's a huge amount of force. If you sit down and you calculate that, that would be enough force to levitate about 5,000 locomotives, each weighing 200 tons. So, a Coulomb is one heck of a lot of charge. So, at this point charge, as far as we're concerned, so far, charge is really just a, you can think of it as sort of a fluid. It wasn't until 1897 that J.J. Thompson that charge actually comes in small units or corpuscles that eventually became known as electrons. And it's interesting to bring that up because the experimental setup that he used to, to come to those conclusions is kind of a precursor of modern day vacuum tubes. Now, it wasn't until about ten years later than Millikan discovered, or measured, the charge of a single electron. So they knew that these corpuscles existed but it took some very careful experiments by Millikan to actually measure the amount of charge. And it turns out that one electron has a charge that is 1.6 times 10 to the minus 19 Coulombs. If I take one over that number, it turns out that one Coulomb is equivalent to 6.2 times 10 to the 18th electrons. So that is a lot of electrons in one Coulomb. So here's the first problem I'd like you to solve. So, you know, when you unpack something wrapped in styrofoam peanuts they stick to everything you can't put them down, they stick to your hands and your clothing. And so the question is, how many electrons would you have to put on a styrofoam peanut that's one cubic centimeter in size so it would be picked up by your hand from a distance from 5 centimeters. So we're going to assume that the styrofoam peanut in your hand both have the same amount of charge on them but they have opposite signs so they attract. Now, here's a few numbers you're going to need, the density of styrofoam is about 0.035 grams per cubic centimeter. And the Earth's gravitational acceleration, if you didn't know it, is 9.8 liters per second squared. So, here's the picture of what's happening, here's your force, here's your hand, and we'll assume there's a positive charge on your hand and a negative charge on the styrofoam peanut. And there's going to be a Coulomb force that attracts the negative charge to the positive charge. And, lets say that your hand is 5 centimeters, a couple of inches above the peanut. The peanut has a mass given by m. The force of gravity is mg, and so for your hand, for the Coulomb force to exceed the gravitational force, I want you to calculate how much charge has to be on these two objects. And here are the answers to choose from. Okay, now that we've introduced the idea of electric charge, we're going to talk about electrical current. Now just as a a starting point and an aside more or less. for all of the kinds of circuits we're going to look at, it's really not important that charge is made up of discrete corpuscles or discrete particles. And we're going to treat charge and the currents as, really, more of a fluid that's infinitesimally divisible. Now, also, as just to establish some background, a negative charge corresponds to there being a surplus of electrons. So when I put a, a negatively charged packing peanut, there are more electrons on that in a piece of material than there are positively charged protons making up the entire piece of material. And when I have a, a positive charge, that really corresponds to a deficit to electrons. So electrons are the things that move around in a circuit and when I'm transferring static charge for the most part. But the when I have additional electrons, or excess electrons, that's negative charge. When I have a deficit of electrons, that's a positive charge. Okay, so now to current. So imagine I have a wire, and I look at a cross sectional area of this wire. And I define a direction coming out of the page, that I'm, I'm going to call the positive direction. And current I, which is measured in amperes, is defined as the amount of charge crossing this cross sectional area per second. And one ampere corresponds to one Coulomb of charge per second passing through this surface in this positive direction that I've, I've, it's, it's up to us how we define which direction is positive. But, here it is. Plus 1 amp, is 1 Coulomb of positive charge moving along the positive direction. Now, the, that's what I just said, the plus current corresponds to positive charge moving in the direction that we've chosen to be positive, indicated by the arrow. So, just to make this more clear, hopefully, let's say we pick some direction going to the right as the positive direction. So our, our x axis is, is, increasing, moving to the right. So if I move positive charge in the positive direction, that corresponds to a plus current value. If I move negative charge in the direction that's defined to be positive. That's actually negative current, a negative number of amperes. if I move positive charge opposite the direction that I've defined to be positive that corresponds to a negative current. And if I move negative charge opposite the direction that I've defined to be positive. That's a positive current. So what's happening in a real wire if I say I have one ampere coming out of this wire. That really means that there is one Coulomb per second of negative charge moving in the opposite direction. so what it means when I say that I have one ampere of current coming out of this wire is that I have actually one Coulomb per second of negative charge moving into the wire. So one ampere coming out of the wire means there is one Coulomb of negative charge going opposite the, that direction.