Application of the fundamental laws (setup) | Electrical engineering | Khan Academy

All right, now we're ready to learn how to do circuit analysis. This is what we've been shooting for as we've learned our fundamental laws. The fundamental laws are Ohm's law and Kirchhoff's laws, which we learned with Kirchhoff's current law and Kirchhoff's voltage law.

This says that the sum of all the currents going into a node adds up to zero, and the voltage law says the sum of the voltages going around a loop adds up to zero. The other thing we learned was the sign convention. We had a passive sign convention, which was, if I label a voltage like that, then I label the current flowing into the positive end. The positive end and the current go together.

So, these are the tools that we have for analyzing a circuit. I've drawn a circuit here. What we see is we have a voltage source; we'll call that Vs, and we will give it a value of 15 volts. We have a resistor R1 that has a value; we'll give that a value of 4K ohms.

Another resistor, R2, is sitting right here, and we'll give it a value of 2K ohms, 2,000 ohms. Finally, there's a current source sitting over here, and this has a value of three milliamps flowing downwards. The point of circuit analysis means what we want to do is find all the currents and all the voltages in this circuit using our fundamental laws.

So, let's identify first. Let's identify the nodes in the circuit. We'll give them letter names. We'll call this node A, and that's the junction between R1 and Vs. We'll give this one a name; this is a node where all three of these components join right about here. We'll call that node B, and that's one of the nodes. Down at the bottom here, there's the third node, which is this distributed node here. It connects the voltage source, the resistor, and the current source, and this is all; we'll call that node C.

Now we can also label some voltages on here. Here, we'll label the voltages; we'll do that in orange. Okay, we'll call this V1, and we'll give it a plus sign here and a minus sign here, and that's the voltage across R1. We'll give R2 a name; we'll get the voltage here; we'll call this plus minus V2. That's the voltage across R2; it's also the voltage across the current source. It's the voltage between node B and node C.

Now let's label the currents. Let's label the currents in this circuit. We have a current coming through R1; we'll call that I1. There's another current going through R2, and we'll call that I2. There's a current going here through Is, and we actually already know that; we'll just call that Is. And that's all the unknown currents in our circuit.

If we stare at this, we're not going to be able to tell just by inspecting this what's going on. We have to come up with some solution technique, and we're going to solve this by what's called application of the fundamental laws. Here's our laws over here, and the whole technique is based on solving simultaneous equations. That's the skill of circuit analysis. Circuit analysis means setting up and solving simultaneous equations.

So, let's write down some things we know about the circuit. The first thing we're going to apply is we'll apply Ohm's law to the two resistors. So we can say V1 = I1 * R1, and we can say that V2 = I2 * R2. All right, that's not a bad start; we have two equations.

How many unknowns do we have? Um, I2 and V2 are unknown; I1 and R1 are unknown, so we have four unknowns, and we have two equations, so we're halfway there. Now we need to come up with some more equations. I'm just going to stare at the circuit, and what I'm going to do is apply KVL around this loop here. That's going to be my KVL loop, and after we get that equation, what we're going to do is write KCL.

We're going to write the current law at node B. That's the two equations we're going to develop here. So, let's do KVL. Let's start at this corner of the circuit and go around clockwise. What we see first is a voltage rise, plus Vs. Next, I see a voltage drop, so it's minus V1 going around this way, minus V1.

I'm at this point now; I'm going to go through R2, and I see a voltage drop of V2, minus V2 = 0. That's Kirchhoff's voltage law around this loop: one rise, two drops, one rise, two drops. Now we're going to move up here and do Kirchhoff's current law at this node right here.

So let me draw a few more arrows. This is I1; it comes right through that resistor, and this is Is. So, Kirchhoff's current law: let's count the currents going into node B. The current going into node B is I1. The currents going out; we'll set that equal to the sum of the currents going out of node B, so that's equal to I2 plus Is.

So look, now I have my four equations. Here's my four simultaneous equations, and this is what we have to solve. So, let me move the screen up, and we'll start doing that. Let's do a double check. We had four unknowns: V1, I1, V2, I2. Here's V1 and V2, and here's I1 and I2, and I have four equations, so we ought to be able to do this.