Ideal circuit elements | Circuit analysis | Electrical engineering | Khan Academy

We're now ready to start the study of circuit analysis and to design circuits and analyze circuits. One of the things we need to do is have something to build circuits with, and that's what we're going to talk about in this video. The idea is we're going to have three circuit elements. The circuit elements are called resistor, capacitor, and inductor. Okay, these are the three passive or two-element components, or circuit elements, that we're going to use to design a lot of different kinds of circuits.

We're going to first... I want to introduce a symbol for each one of these so we can talk about it and draw make drawings of it. First is going to be the resistor. The resistor symbol looks like this: it's a zigzag line like that, representing current going through and being resisted, having to do some work. Another symbol for resistor looks like this, used in other parts of the world besides the United States and Japan. That's what a resistor looks like, and the symbol we use is R.

Now, for the capacitor, the capacitor symbol is actually... capacitors are built from two conductors or metal objects that are placed close together. Most capacitors sort of look like that when they're actually built. The symbol for a capacitor is C.

Finally, for the inductor, we'll do inductors like this. An inductor is actually built from a coil of wire, and so when we draw an inductor symbol, we draw a little coil of wire like that, and the symbol is L, which is a little odd. It could be called I, but the symbol for I was already taken by current, which is from the French for intensity, and we couldn't use C for current because the C is used here. So, it's a little quirk of our nomenclature.

All right, each of these components has an equation that goes along with it that relates the voltage to the current. Now, I'm going to go back here. I'm going to label the voltages and currents on here in a very important convention for drawing circuits. Let's do that. When we talk about the voltage on a component, we can label it however we want: plus-minus V.

And we draw the current going in; I'll just label a little I there, and we'll do it on all these. The current goes into the positive terminal. The current goes into the positive terminal, so that's V on the capacitor. Finally, and the current goes in, and we're going to be very consistent about this, and that's going to keep us from making mistakes.

All right, so let's go back to our resistor, and we're going to do the equation for a resistor. What is the IV equation for a resistor? IV equation means what relates current to voltage, and for a resistor, it's V equals I times R. So, the voltage across a resistor is equal to the current through the resistor times this constant of proportionality that we call the resistance. This has a very important name: this is called Ohm's law, and you're going to use this a lot. So, that's Ohm's law right there: this is Ohm's law.

Now, for the IV relationship for the capacitor, the capacitor has the property that the current through the capacitor is proportional to the rate of change of the voltage—not to the voltage, but to the rate of change of the voltage. The way we write that is current equals C, which is the proportionality constant, and we write dV/dt. So, this is the rate of change of voltage with respect to time. We multiply that by this property of this device called the capacitance, and that gives us the current. This doesn't have a special name, but I'm going to refer to it as the capacitor equation.

So now we have two equations. Let's do the third equation, which is for the inductor. The inductor has the property—it's very similar to the capacitor—it has the property that the voltage across is proportional to the time rate of change of the current flowing through the inductor. So, this is similar but opposite to how a capacitor works. The voltage is proportional to the time rate of change of current, and the way we write that is voltage equals L di/dt. The voltage is proportional; the proportionality constant is the inductance—the inductance of the inductor—and this is the time rate of change of current flowing through the inductor.

So, this gives us our three equations: here they are. These are our three element equations, and we're going to use these all the time. Right there, those three equations. One final point I want to make is— for both these equations of components, these are ideal, ideal components. That means these things are mathematical perfect things that we have in our minds that we're going to try to build in the real world, but... and we'll come close; we'll come very close.

We now have a wonderful set of equations: V equals I R, I equals C dV/dt, V equals L di/dt. These are going to be like poetry for you pretty soon, and these ideal equations will produce all kinds of really cool circuits for us.