Anderson Video - Kirchoff's Junction Rule

Professor Anderson
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Okay, let's talk about Kirchoff's rules. Kirchoff's rules are the following: the first is called the junction rule, which says at a junction the current in has to equal the current out. What does that mean? That means if I have a wire and it suddenly splits into two wires, whatever current is coming in here, let's say it's ten amps, it has to go somewhere out of the junction. So it could be five amps going that way, and five amps going that way, or it could be seven amps going that way and three amps going the other way. Whatever current is coming into the junction has to go out of the junction. Namely, charge doesn't build up there, charge isn't depleted from there, there's no net buildup of charge and so any charge coming in has to go out. which means the currents have to match up. How does that work when we're dealing with a circuit? Well, let's go back to our parallel circuit for a second. Let's say we have a battery and now we're going to split into two different paths. R1 and R2. This thing right here is a junction. A junction is anywhere the wire splits into two or more wires. So that's a junction right there. And at that junction we have to have current in equals current out. Current in is going to be I. Current out is whatever goes in that one plus whatever goes in that one. So we'll call it I going in, I 1 to the left, I 2 to the right. So, I equals I 1 plus I 2. But we know what I is. I is the same as voltage over equivalent resistance of the whole thing, which is R parallel. Because that circuit we can draw like this, I 1 is whatever voltage is across R 1 divided by R 1. But it's the same voltage. Right, this is a wire all the way to the top of R 1. And so that wire is an equipotential and so the voltage across R 1 is the battery voltage. But likewise, the voltage across R 2 is also just the battery voltage. And so this is what we were talking about earlier, we can cross out all the V's, they're all the same, and we get the parallel series- or, the parallel resistor rule which says 1 over R p equals 1 over R 1 plus 1 over R 2. This is a direct result of Kirchhoff's Junction rule.
Okay, let's talk about Kirchoff's rules. Kirchoff's rules are the following: the first is called the junction rule, which says at a junction the current in has to equal the current out. What does that mean? That means if I have a wire and it suddenly splits into two wires, whatever current is coming in here, let's say it's ten amps, it has to go somewhere out of the junction. So it could be five amps going that way, and five amps going that way, or it could be seven amps going that way and three amps going the other way. Whatever current is coming into the junction has to go out of the junction. Namely, charge doesn't build up there, charge isn't depleted from there, there's no net buildup of charge and so any charge coming in has to go out. which means the currents have to match up. How does that work when we're dealing with a circuit? Well, let's go back to our parallel circuit for a second. Let's say we have a battery and now we're going to split into two different paths. R1 and R2. This thing right here is a junction. A junction is anywhere the wire splits into two or more wires. So that's a junction right there. And at that junction we have to have current in equals current out. Current in is going to be I. Current out is whatever goes in that one plus whatever goes in that one. So we'll call it I going in, I 1 to the left, I 2 to the right. So, I equals I 1 plus I 2. But we know what I is. I is the same as voltage over equivalent resistance of the whole thing, which is R parallel. Because that circuit we can draw like this, I 1 is whatever voltage is across R 1 divided by R 1. But it's the same voltage. Right, this is a wire all the way to the top of R 1. And so that wire is an equipotential and so the voltage across R 1 is the battery voltage. But likewise, the voltage across R 2 is also just the battery voltage. And so this is what we were talking about earlier, we can cross out all the V's, they're all the same, and we get the parallel series- or, the parallel resistor rule which says 1 over R p equals 1 over R 1 plus 1 over R 2. This is a direct result of Kirchhoff's Junction rule.