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Anderson Video - Capacitor in AC Circuit

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