Electric Circuits

Let's talk about electric circuits. What is an electric circuit? Well, an electric circuit is one or more loops of wire that connect a bunch of circuit elements. They're usually, a current can flow all the way through the circuit. If current can't flow all the way through it, I'm not going to call it a circuit. Alright.

Now, circuits are usually driven by a battery. The way that we represent batteries is we've got a long bar like that, that's the positive side of the battery and then we've got a short bar, that's the negative side of the battery. Resistors are the other circuit element that I'll be talking about in this and they're represented by this little weird squiggle. So the important thing about drawing the squiggle is that you should go below and above the straight line. The straight line just represents a wire. Doesn't really do anything except for connect circuit elements. So it doesn't have any potential difference, it doesn't have any resistance or anything like that. It just connects the different circuit elements. Tells you where are things connected. Alright. So the purpose of a battery is to drive the circuit where the purpose of a resistor is to use energy.

So what are some example s of resistors? Well, essentially, anything you want to plug in is a resistor. Light bulb, resistor. Television, resistor. Car, resistor. Microwave, resistor, they're all resistors. Anything that you plug in to use energy is a resistor. That's the way it will be represented in a circuit diagram like this. Alright. So let's see how we can actually solve a circuit.

So suppose that I've got a circuit that looks like this one. Alright. I got a 20 volt battery. Notice I didn't put the plus and the minus. I put a long and a short and you're supposed to know that the long is the plus and the short is the minus. And I want to know, what's the current through this circuit? Alright. We're going to do this in two different ways. The first way is somewhat straight forward and it will give us a pretty quick answer in this case. the second way is a little bit more involved but it's much more broadly applicable. Alright. So let's do the first way.

So what I'm going to say is, look. These wires are perfect conductors, that's what they represent. So that means that there can't be any potential difference across them. So if there's no potential difference across them, the potential difference here is 20 volts, then the potential difference here got to be 20 volts. So now it's time for ohm's law. So we'll say, delta v equals minus ir, potential difference -20 volts equals minus i times what is it, 4 ohms divide and we're done. i equals 5 amps. So we got 5 amps of current that's going through this circuit. Alright.

Let's do the second way. The second way involves something called Kirchoff's law. Kirchoff said that if you go around a loop in a circuit and you keep track of all the potential differences as you go around, by the time you get back to where you started, the net potential difference, got to be zero. Alright. So we'll start off and we'll start right here and we're just going to go round the circuit in the direction of the current. So go across the battery, what's the potential difference? Well, I picked up 20 volts, so I got +20. Alright. Go across the wire here. Nothing happens. Go across the resistor, now ohm's law tells me that I get a potential drop of ir. So it's minus ir and so now I'm here and then I go across the wire again. And again nothing happens. Now I'm back to where I started. So that means that the whole thing got to get me zero. So now I'll move this guy to the other side of the equation and I'll divide. So 20 volts equals i for ohm's and I'll divide and I'll get 5 amps equal i. Same answer I got before of course it's got to be, can't have two different valid methods giving you different answers. Alright.

So why do I care about this Kirchoff method? Well, it's much more broadly applicable to other situations where I can't make these kinds of real simple potential difference arguments. So let's look at this circuit here.

I got two resistors here. So now I want to run a light bulb an a tv, right? And I want to run them on the same circuit. Alright. So I'm going to use Kirchoff because I don't know how to make these potential arguments yet. Alright. So we'll start off and we got 16 volts, nothing, minus 5i minus 3i. And now we're back to the beginning so we've got zero. Adding the 5 and the 3, we got 16=8i and therefore the current is 2 amps. Bur that's not what the problem asked for. The problem did not ask for the current. It wants to know what's the potential difference across the 3 ohm resistor? Jeez, I don't know. Well, now I got the current 2 amps. Potential difference across any resistor's given by ohm's law, delta v equal ir. So 2 times 3, 6 volts. And that's the way that those circuits go. They're essentially all very very very simple but you'll learn that there are ways to combine these resistors that make it even easier.

However, Kirchoff's law no matter how complicated the circuit is, Kirchoff's law will always allow you to write down the equations that describe the circuit enough to give you every single piece of information you could possibly want out of it, provided that you want to spend the time solving all those equations.

Alright. That's electric circuits.