Kirchhoff's Junction Rule

by Patrick Ford
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Hey, guys. So in this video, we're gonna talk about a very simple but very helpful rule that you can use to make solving circuits easier. Now, I should note that a lot of professors and textbooks don't cover this until a little bit later on. But we're gonna do it here because it's gonna help you immediately in problem solving. So let's check it out. All right. So the rule is called Kharkov or Kirchoff. However you prefer his junction rule. Okay, Now, remember that resistors in Siris always have toe have the same currents. And that's because if you have a two resistors in Siris like this, the wire doesn't break. So all the current going through this first resistor here, I one let's call it the current through the first resistance called I one and then this current, I too have to be the same because the charges have nowhere to go, so they just keep flowing. Okay, Now, currents will change on Lee if the wire splits into two or more parts. So, for example, let's say if you have this here and then it splits into two wires, right are two or three, so these currents will not be the same. I one will not be the same as I too. And I one will not be the same as I three. It splits now the point where it splits this point right here is called a junction or a node. Okay, so that's the special point right there. And Kharkov or Kerchove is Junction Rule says that the current into a junction is always equal, equal to the current out of the junction current and equals current out. And this flows from conservation of charge. Right? So if this was not the case, then what would happen is that charge would accumulate over here on do you can't have that, because charges, they're just always flowing. So if something like three amps goes in and I know that two amps goes out here, it means that one amp has to be here because the charge is conserved and it has to keep flowing. That's it. This is one of the simplest ideas in physics. Um, this is called his junction rule, but it's also sometimes called current law. Okay, so it's a LaRue. It's a law Junction rule current law. Cool. All right, so Let's do a quick example here. Super simple. What is the voltage across the two ohm resistors? So what is the voltage across this guy here? And I want to remind you of owns law, which is an equation that ties the voltage, the currents and the resistance off a resistor. And the idea of alms life, you remember is that if you know two of these, you can find the third okay, and you'll see how we're going to use it. So let's see. I want to find the voltage of the two homes, so I know the resistance is too. I am looking for the voltage. Is there an equation that ties these guys together? Yes, it's this one here so I can write the equals I R. And the problem is I know are I'm looking for V, but I don't have I. So I can't solve this unless I have I. So is there a way for me to figure out I from the diagram? What is the current going through here? Let's call this I too, since it's going through the two, which, by the way, is the same as I to over here notice that I have four amps going into this node or junction. I have three coming out and I have I to coming out. If four goes in this way and then four have to come out, three is already coming out. So one has to be going this way. That's it. That current is one, so I can do one amp times The resistance. The resistance to homes one and times to homes is two, and the units of voltage is votes. So the answer is simply two volts coat. That's it. Super simple, the super helpful. Let's get going.