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Physics31. Alternating CurrentCapacitors in AC Circuits

But big reactants means small current. Right, because V equals I times X sub C. So, this is the voltage that's supplied by the source, this is the current in the system, this is the reactants. If the reactants is big, that means the current is small and hence the light bulb is dim. So in fact, what you want is just the opposite, you want high frequencies to give you low reactants, and that gives you big current. So when I think about that circuit it's gonna look like this -- resistor is basically what's in a light bulb. Here's my capacitor C, and what I want to do is I want to minimize the voltage drop across the capacitor. I want to minimize the reactance. I want to make that as small of a number as possible, and so if I want that to be small I need Omega to be big. Big Omega means X sub C is small and therefore the available current is big. More current, brighter light bulb. So one thing that is good to think about in these circuits is what happens to capacitors and inductors in the limit of very low frequency and very high frequency? So let's say we do the following: let's say we have a voltage, AC voltage, let's put a resistor and a capacitor, and now let's look at the two limits where Omega is very big versus Omega is very small. What does the circuit look like in those two cases? Well in the case where the frequency is really really high, the capacitor reactance goes to zero and so this effectively looks like this. It's like the capacitor goes away, but in the case where Omega is small that reactance gets very big, and now it looks like an open switch. Okay, it looks like you have broken the wire in that case. This should tell you, right off the bat, whether you're dealing with high frequency or low frequency. Is it a high pass or is it a low pass? Okay. So, what about inductors? We know that inductors respond like Omega times L. Let's draw the circuit for an inductor, we'll go with the pink. An inductor we have a resistor, we have our inductor, and now let's look at the two limits where we go for big Omega or very small Omega. If it's really big, the inductor doesn't like that, right? It doesn't want to change its frequency, and so the effective circuit just becomes this resistor and then the inductor acts like an open switch. It's just like you broke the wire. Whereas if Omega is small, the inductor doesn't care and so it's like it's just a complete circuit now, it's just a wire. So those are the two limiting cases, right? And you can see that they're exactly the opposite. If Omega is big, the capacitor goes away, if Omega is big here, the inductor becomes a break in the circuit, and just the opposite behavior for when Omega is very small. Okay, how do you put all these things together, now in something really complicated like an LRC circuit? Let's take a look.