Sign convention for passive components | Electrical engineering | Khan Academy

Today we're going to talk about the sign convention for passive components. It's a big mouthful, but it's a fairly simple idea.

So first of all, let's look at this word: passive. Passive is the way we describe components that do not create power or components that do not amplify signals. So particularly, resistors, as we have one here, do not amplify a signal. Capacitors and inductors do not either, so they're both, all three of those, are passive components.

Sometimes we say something like a battery or a voltage source is a passive component because it can't amplify a signal. It does provide power, but it does not make signals bigger; it can't make a voltage larger than it already is.

So we're going to start with a way to label this resistor with its current and voltage. First, we'll resort to Ohm's Law, our friend! Voltage equals current, which is I * R. When we label this device, here's our resistor, so we'll give that a label.

We're going to put a voltage across this; something outside of this is going to put a voltage across it. This end will be positive with respect to this end, and the question is: the question we want to answer is, which direction does the current go?

When there is positive voltage here and negative voltage there, which way does the current flow through this resistor? Does it go from top to bottom or bottom to top? The answer is the positive current goes this way, goes down, so that's I in this, and the current is going into the end with the positive sign on the voltage.

Now, I'm going to draw another one of these, the same sort of thing, and we'll do it a different way. We'll do this one sideways and I'll label the voltage. Here's R, and I'll put a voltage on it. Let's label it this way: let's say we label the plus end this way and label the minus end that way.

The question is, which way does the current go? Well, the current goes in the positive end, so it goes in that way. That's the sign convention for passive components; the current goes into the voltage on the positive terminal of the voltage.

If I drew the arrow over here like this, that would still mean the same thing. It's still going in the positive and coming out the negative side.

So when we draw this for capacitors and inductors, let's draw a capacitor over here. There's C, and if I label this with a voltage, plus and minus V, then the passive sign convention tells me that I label the positive current going in.

I do the same for an inductor. We'll draw our curly inductor like that. We'll put a voltage on this time; I'll put the voltage on this side, plus minus V. Ah, plus minus V. This is our inductor, like that, and the current goes in at the top like that.

So it goes in the same side as the plus, and the current comes out on the minus side. You can draw it either way you want. Let's practice some more.

This time we'll do it with a resistor again. Here's another resistor, and this time I'm going to label the current first. I'm going to say the current goes this way through the resistor.

Now, using the passive component sign convention, how do we label a voltage? I want to label the voltage. Where's the plus sign? The plus sign is on the side that the current goes in. The current is going into this terminal, so that is the plus side of the resistor.

And that's basically the idea of a sign convention for passive components. When we're setting up a circuit, if we have a complicated circuit, we have to give names to all the voltages and all the currents. This is the way you do it to make sure that Ohm's Law comes out with the correct sign. That’s why we have this sign convention.