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Sign convention for passive components

Video transcript

- [Voiceover] Today we're gonna talk about the sign convention for passive components. It's a big mouthful, but it's a fairly simple idea. Well 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. Does not amplify a signal. Capacitors and inductors do not either. So all three of those are passive components. And 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 gonna start with the 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 times r, and when we label this, when we label this device, here's a resistor, so we'll give that a label, and we're gonna put a voltage across this, something outside of this is gonna put a voltage across it and 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 the positive voltage is here and the negative voltage is here, which way's 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, it 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 gonna draw another one of these, 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, and the voltage let's label it this way, we label the plus end this way and label the minus end this way. The question is which way does the current go? Well the current goes in the positive end so it goes in that way. And that's the sign convention for passive components. The current goes into the voltage on the positive terminal or 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, and there's c, and if I labeled this with a voltage, plus and minus v, then the passive sign convention tells me that I label the positive current going in, i. The same for an inductor. We'll draw a curly inductor, like that, we'll put a voltage on it this time. I'll put the voltage on this side, plus, minus v, this is our inductor, like that, and the current, the current goes in 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 gonna label the current first. I'm gonna say the current goes this way through the resistor. And now, using the passive component sign convention, how do we label the voltage? I wanna label the voltage. Where's the plus sign? Plus sign is on the side that the current goes in. The current's going in to 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're setting it up, we have to give names to all the voltages and all the currents. And 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.