Hello everyone, I'm Jesse Mason and in this episode of the Teach Me series we'll learn the basics of Kirkaf's rules and see how they're applied to circuits. Kirkaf's rules, sometimes referred to as Kirkaf's circuit laws, are a pair of rules used typically to analyze DC circuits. The first rule that we'll examine is Kirkaf's junction rule. The junction rule states that the sum of the currents flowing and yes I know that current flow is a bit redundant, leave redundant. Anyway, the sum of the currents flowing into a junction is equal to the sum of the currents flowing out of said junction. Mathematically speaking, current in equals current out. Sounds simple enough, right? Let's take a look at a circuit diagram for a junction to elucidate this rule. We'll take a simple three-way junction and label it J1. We'll draw current flowing into J1 from the left, call it i1, and current flowing out the right leg and down the vertical leg. i2 and i3 respectively. How exactly did we decide the directions and labels for these currents? We'll address this very good question momentarily. So applying the junction rule to J1 we have current in, that's just i1, equals current out, which is i2 plus i3. And that's it. That's how the junction rule is applied to a junction. Before we move on, I'm impelled to point out that Kirkaf's junction rule is just a consequence of a more physically significant principle, namely the principle of conservation of charge. So we can sort of think of J1 as a fork in the road, where the cars, I mean the charges, either continue traveling to the right or turn and move downward. Got it? Good. Now let's examine Kirkaf's other rule, the loop rule. The loop rule states that for any closed loop the sum of the voltage lifts is equal to the sum of the voltage drops. We'll define a closed loop as any continuous path in the circuit, which ends where it started. The loop rule stated mathematically is, the net voltage for a closed loop equals zero. Okay, now let's look at a simple circuit to see how we apply the loop rule. Here we'll have a voltage across the source, V sub S, and a voltage across the resistor V sub R. Since it's a simple circuit, we'll have a singular current and its direction of positive charge flows clockwise due to the orientation of the voltage source. Next we'll label our circuit loop, loop A. Note that for most circuits, currents and loops won't coincide and need to be explicitly labeled separately. Okay, to apply the loop rule to loop A, we'll travel clockwise around the loop, summing voltages. Starting on the bottom left, we'll have positive V sub S, a voltage lift, and then moving around to the other side, we'll have negative V sub R, a voltage drop. We set that equal to zero, and that is how we apply the loop rule. By the way, Kirchhoff's loop rule, like the junction rule, has its physical roots in a conservation law, namely the principle of conservation of energy. Okay, now let's discuss the conventions associated with Kirchhoff's rules. The first two conventions relate to the loop rule, and identifying voltage lifts and drops. Before moving around a loop, and we travel through a battery, while summing voltages, and we go from low to high, which is to say going from the negative terminal to the positive terminal, then the voltage of the battery is treated as a positive voltage, which we'll call a voltage lift because of the increase in electrical potential. If instead we travel through a battery high to low, that is positive to negative, the voltage is treated as negative, which we'll call a voltage drop because of the decrease in electrical potential. So for voltage sources, low to high, we have a positive voltage. High to low, we have a negative voltage. It turns out that the sign of the voltage across a resistor also depends on the direction of our labeled current. So if we follow a current, while summing voltages, through a resistor, then the voltage across the resistor is negative V, or invoking ohmslot, negative i times r. If instead we oppose the direction of the labeled current as we pass through the resistor, then the voltage across the resistor is treated as positive i times r. So for resistors, follow the current negative i r. Oppose the current positive i r. Now a lot has been said about the directions of currents and loops. How are these directions initially decided? This is the best part. The directions of loops and currents are assigned and labeled arbitrarily, with absolutely no preference and direction. So long as the circuit is correctly analyzed, using Kirchhoff's rules, the actual direction of positive charge flow will be revealed in our results. So it's kind of like, choose your own adventure in physics land. One final convention relating to labeling our circuit diagram. Typically, we'll use one more loop than the number of junctions in the circuit. So be sure to have enough of them labeled before applying Kirchhoff's rules. I'm Jesse Mason and I hope you found this video helpful. If you have any suggestions for future Teach Me videos, or just want to say hello from your part of the world, please do so in the comments below. And as always, happy learning!