Hi, welcome to Fundamentals! Friday Today, we're going to take a look at one of the most fundamental laws in electronics. As fundamental as Ohm's law. it's called Kirchhoff's Laws or more specifically, Kirchoff's current Law and Kirchhoff's Voltage Law. Now, you've probably heard people, including myself in a lot of my videos just throw away the term Kirchhoff's Law I And you know by Kirchoff's law: bla bla bla bla bla.

And some people don't actually know what it is. but I bet you you're already fundamentally know it, even if you've never heard of it. Now, we're actually going to get into a little bit of math today. But don't worry about it.

Kirchhoff's laws are simple, dead simple. Even simpler than Ohm's law because they're just laws that you don't even have to remember a formula. They're just basically a concept. A very powerful concept that allows us to do some pretty advanced mathematics in electronics.

Although we're gonna stick to some fairly simple stuff today. As with many things in electronics named after the person who discovered it, Gustav Khurana Gustav Kirchhoff in about 1845 or there abouts Now there are two fundamental Kirchhoff's laws. The first one we're going to take a look at is Kirchhoff's current law or KCl for short, the other one is Kirchoff's voltage Law and we'll do that next. So let's take a look at the current laws real easy.

How easy? Let me show you. Kirchoff's current law states in a roundabout wait: the sum of currents into a junction equals the sum of currents out of the junction. Current in must equal current out. That's it.

That's That's the entirety of Kirchhoff's current law. Nothing more complicated than that. So just like the fundamental laws of physics, like the conservation of energy, Effectively, what Kirchhoff is saying here is this is a conservation of charge. If you put charge into a loop circuit, it must come out.

Charged in equals charge out. Or in this specific case, we're talking about a junction point in a circuit. Current in equals current out. It's that easy.

You already know it. It's fundamental. It's obvious. So fundamentally, that's it.

You don't need to know any more than that. You now know Kirchoff's current law. Current in equals current out. It's too simple, but there's some powerful things we can do with it.

So let's take a look at an example, shall we? We've just got a resistor here and two resistors in parallel here that we've got current flowing in I 1 here. Let's just assume it's flowing in here and it's into this Junction You remember we're talking about a junction here, and then we've got two paths coming out. So we've got I 3 coming out and I 2 coming out here. So we can actually have a formula.

We can go. I1 equals I2 plus I3. Remember the sum of the currents into the junction. In this case, we've only got one, but we could have more than one and the equals the sum of the currents out of the junction.

So I1 is in I 2 and I 3 are out. That's it. And if we had another current coming in here, for example, like this and going in and we can call that a zero, it would just be eyes ear o plus I1. Remember, the sum of the currents in equals sum of the currents going out, but sometimes it's actually more powerful mathematically to say this, which is exactly the same.

We're basically just rearranging it. We can go Iza plus I1 minus I2 and I'll explain why in a second. minus I 3 equals zero. It's basically just a rearrangement of that formula.

So what this rearrangement of the formula means, and you typically would write this like directly like this: straight off the bat. and we'll do this in further examples to come: Basically any current flowing into a junction, you define that as a positive current. so I0 is flowing in, so it's positive. I0 plus I1 is also flowing in to the junction, so it's a positive, but I2 is flowing out of the junction.

so you actually define that as a negative current. And likewise, for I through three, there, it's a negative current as well. So you come up with this equation like this and you can write the equation for any number of currents flowing in or any number of currents flowing out of a junction. Even if you've got one current flowing in and one current flowing out, you can still right the basic equation and the thing about this is it's not a formula that you have to remember.

it's just a concept. that current in equals current out. Now, of course, I can build up a boring circuit and actually demonstrate that current in equals current out. But there's no point.

But I'll just give you one little simple example here where you might use Kirchhoff's current law in the real world. for example, to analyze a circuit. Here, let's take an Op-amp We've got an inverting configuration. You should be familiar with something like this.

We've got a positive voltage here, and by Op-amp action. one of the basic rules of the Op-amp is our non-inverting terminal here is at 0 volts. it's a ground. So therefore, the inverting terminal is also at ground.

So we're going to have a current flowing through like this. So remember, look, we've got a current flowing into a junction point right here. Ok, where does it flow? Well, it can't flow into here, can it? Because the input impedance of an Op-amp is supposed to be infinite or an ideal one. So it's got to flow all the way up here like this.

So we've got a current coming out. But in the real world, a practical Op-amp will have some input leakage current in here. Okay, so we've got I L there. for example, leakage.

So this could be say I out and this is I in. So in this case, you can actually come up with the equation that I in equals I out plus I L Because remember, current in must equal current out. We've got two currents coming out of a junction. the one that goes up this resistor, the feedback resistor here, and the tiny little current in there, they must be equal.

And if you've got a practical Op-amp and you've got good enough equipment, you can actually measure the leakage current in there and this current up this resistor. Plus This leakage current must equal the current going in. It's a fundamental law of physics. It's Kirchoff's current law.

and you'll notice that I actually called currents going into the junction positive and those coming out negative. I Put them here in the formula like that. That doesn't have to be the case. You can basically do make them positive or negative.

It makes no difference as long as you're consistent and we'll actually see this further on in the video where we can actually get negative results and things like this. which actually tells us something fundamental about the circuit that we're trying to analyze. So that's it. I Know We went into a bit of detail and we came up with some equations here, but it's just a concept.

Current in equals current out. Got it? Beauty? Let's move on to Kirchhoff's voltage law. Kirchhoff's other law is called Kirchhoff's voltage law or KVL for short, and just like Kirchhoff's current law, it's incredibly simple. it's just a concept.

no formula to remember at all, and you probably already know what. it's obvious and intuitive. really. What it basically says in a roundabout sort of way: the sum of the applied voltages around a loop it always has to do with a memory circuit doesn't do anything unless you have a loop.

so the sum of the applied voltages around the loop equals the sum of the voltage drops around that loop. Simple, right. So if we take a look at the circuit, if we have a voltage source here, II 1 and we have three series resistors like this, As simple as it gets. So just like we did for Kirchhoff's current law, we can make an equation E 1 equals remember this is the sum of the applied voltages.

In this case, we only have one applied voltage. V 1 equals what the sum of the voltage drops around that loop. So of course we're going to. When current flows, we're going to have a voltage drop across.

We're gonna VR 1. Folders' drop across R 2. Voltage drop across R 3. So you can probably do this yourself.

Even if you're not good at math, it's easy. A 1 equals V1 plus. Remember, it's a sum plus V2 plus V3. Bingo.

We have an equation easy so you might be thinking at this point. Well, this is all very academic and obvious. Like, what's the point of this? You're just doing math for the sake of you know, equations for the sake of equations. Well, we'll see later how they actually can come in useful analyzing circuits.

But yes, this is quite an academic concept. and of course, you just use it every day. in circuit theory. Like you know, you don't even think about it.

Go. Of course. Caronian equals current out of a junction. And of course, the voltage drops around a circuit must equal the voltage applied.

It's simple and it is. There's nothing more complicated about Kirchhoff's current law and Kirchhoff's voltage law. And if you just take that away from this video, then hey, you've learnt the concept. You don't necessarily have to get into all the academic stuff of deriving equations and solving circuits and all that sort of stuff, but if you understand the concepts, they're still quite powerful in their own right.

Even if they're bloody obvious like this, you can. at least you know, when you're explaining circus to people. iron just throwing odd because of Kirchhoff's current law, blah blah blah. You know it just makes you sound like you know what you're talking about.

And just like Kirchhoff's current law, we can add more things to this and just expand our equation here. In this case, let's actually be kind of tricky and put in another battery here, but we're actually going to put it a reverse polarity to what we have before and let's see what that does to our equation. Okay, we still got a one. Okay, the sum of the applied voltages? okay.

but because this voltage here, you have to go around the loop and look at. you have to determine a direction of current around the loop like that. And by convention, as we'll see later, we choose a clockwise current like that. So if you go around, you notice this battery is going from positive to negative.

Where is this one? The current is flowing from negative to positive. So E1 will define as positive. but if we define a 1 as positive, then oh sorry, E2 Here E 2 is negative relative to E 1. So E 2 E 1 minus E 2 Eckles The voltage drops.

Aha. So now maybe you might be able to start to see how we can start forming equations and possibly solving much more complicated circuits using Kirchhoff's current law and Kirchhoff's voltage law. But that's it. But hey, once again, we can start doing some silly academic stuff rearranging formulas.

But it's kind of important. so let's do that. Let's say let's just rearrange the formal that we've got here. Let's say we just want a one on the one side.

Here we can go: a 1 equals V1 plus V2 plus V3 Exactly the same as before, but the negative E2 becomes a positive E 2 like that and you can actually see that. Kind of make sense if you think about it. if we're talking about a voltage drop across our one voltage drop across our two voltage drop across our three. But because E 2 is the other direction according to the current flow we chose, it's also a drop.

and the sum of the applied voltages equals this sum of the voltage drops. Bingo. We've got. This one is applied.

All the others are drops. So this voltage source, even though we sort of, we had it as an applied voltage before, you can also think about it as a voltage drop depending on which side of the equation that's on. Like I said. it's academic, but it makes sense.

And just like Kirchhoff's current law, you often see it stated as equal to zero. And in fact, that can be one of the definitions of Kirchhoff's voltage law as well. You don't necessarily have to think about it like this. You can think about it like this: Our Kirchhoff's voltage law is the algebraic sum of voltages around a loop.

Algebraic is just a fancy word for just for taking into account the sign of the voltages. So just like we showed here, that this E to you've got to get its actual sign Correct. That's what algebraic means, It just means taking that into account. So now we can actually rearrange this formula to make this true as well.

We can go V1 plus V2 plus V3 plus E2 Exactly the same as before, but E 1 now becomes minus E1 equals 0. Bingo! We've now got this expressed as an algebraic sum of voltages around a loop and I've probably lost every one Now If all be gone with them. Why? Yes, it's all kind of academic, but this concept of being equal to zero of things adding up around a loop is useful in analyzing complex circuit. And just like Kirchoff's voltage law, here, Kirchoff's current law, which I forgot before, you can actually express it as the algebraic sum of currents at a junction equals zero.

Exactly the same concept. rearrange it to zero and just like Kirchhoff's current law is basically stating the conservation of charge. Kirchoff's voltage law is essentially stating conservation of energy. Voltages applied around a circuit must equal the voltages drop.

You know that. Power in Power out. Conservation of Energy laws. Those basic laws of physics you know can beat the laws of physics.

Captain, you know. Go step smart guy. So I'm actually going to leave it there for this video and let you digest this and we'll follow-on in the next video. Click here to check it out where we actually apply Kirchhoff's current law and Kirchhoff's voltage law to actually analyze some circuits.

and we'll use some of these equations that we've got here. It's a bit you know, too advanced for this video just to explain what Kirchhoff's current law and Kirchhoff's voltage law actually is. because I could have done this video in two minutes. I could have just said the sum of the applied voltages equals the loop and that's it.

and not worried about any of these equations and it's really just stating the obvious same thing with Kirchhoff's current law as well. and you can. As I said before, think of it that easy. If you just take away from the video that current in equals current out and the sum of the voltages around a loop actually equals zero, or the voltage is applied must equal the voltages dropped, then well, that's good enough.

You can use that in everyday circuit analysis, but like I said, it's probably already obvious to you. But the next video will go into what I've got up here in the heading which is looking at some DC circuit theories where we apply Kirchhoff's current law Kirchhoff's voltage law to actually analyze circuits. So if you found that useful, please give it a big thumbs up. And as always, comments down below on YouTube on the blog, website or in the forum link down below as well.

If you want the t-shirt a link in my No Paige down there where you can sign up and get one of these puppies so I'm not sure if it was actually worth 15 minutes explaining this sort of thing. I went into a bit of detail but hopefully as you'll see in the next video, I have actually setting this up so that we can actually use these and it is actually a very powerful concept. The deeper you go into real you know, steep circuit theory, Kirchoff's current and Kirchoff's voltage law x' and how things equal to zero. Very powerful stuff so stick around for the next video.

Catch you next time you.