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26. Capacitors & Dielectrics

1

concept

11m

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Alright, guys. So for this video, we're gonna be working on how you solve problems with capacitor circuits. Let's go ahead and check it out because we saw that in circuit problems. We could figure out what the equivalent capacitance is that the entire circuit. But now you're gonna be asked. Things like one of the charges and voltages across some combinations of capacitors is you're gonna need to know how to figure that out. So we saw from the last video that if you have serious connections, you configure with the equivalent capacities is by using these rules, we have the for serious connections. We have the inverse some rule where you basically take the inverse of the equivalent capacitance and is equal to the inverse subs, sums of all of the additional of all the individual capacitors. Right? So if you have all of these capacities that in a line like this, remember that these capacitors mean that there are some charges they're building up on the plates between them, there's negative and positive charges. They're separated by some distance. What is it happening is that one of the capacitors builds up a charge, and it transfers that charge to the next one in line and that when transfers the one next one in line as well. So basically what happens is that capacitors in Siris will share charge with each other. So that means if you have a capacity that has three cool homes of charge built up between the plates, then that means that there's three columns on the next plate and also in the next capacitor. So all of those charges basically pick up three columns each. And it also means that when you condense this down to one equivalent capacitance C e que then that would also have a three Coolum charge. Some of the words these share charge with the equivalent capacitance. So that's how serious connections work. They always shared the same charge, and that's always going to be true now. We also saw that parallel connections. We could figure out what the equivalent capacitance is, and basically just these sums of all those things. So if you have parallel connections, the equivalent is just is just summing each of the individual capacitors. Now what happens is if you have this wire and you have approached this junction and the wire splits off into these three parts. What happens is you can you can imagine these charges sort of branching off in different directions. So what ends up happening is that the charge is not conserved in the charge is not basically flowing through each one of these things equally, it has to split up. But what ends up happening is that through these points right here from this point to this point at this point, to this point, the potential differences In other words, those V's are equal to each other. So unlike for serious connections that capacitors in parallel don't share charge with each other, they share voltage with each other. So whatever the voltage is across one of the capacitors, so I'm just gonna make up a number. If this is two volts, then that means that that voltage is the same across all three capacitors. They don't share the same charge. So that also means is that when you condense this down to an equivalent capacitor C e que, then that means that voltage is also has to be two volts. So you can actually work forwards and backwards from this kind of thinking, you can collapse all of these down to an equivalent capacitor and know what the voltage is, or you can take equivalent capacitance and expand it back out into its individual capacitors. And you know what the voltage across each of those is, so you can sort of work forwards and backwards. Now, with these rules, we basically have everything we need to solve capacitor circuits problems, and we have a nice step by step process in order to solve those things. Let's go and check it out. So we've been working with the first step. Lots we've found with the A single equivalent capacitor is for a circuit. And, um, now what we have to dio is questions. We'll ask you things like, What is the voltage across a this three ferret capacitor? What is the charge against across this combination of capacitors? So we need to do is once we find these single equivalent capacitance and of the entire system, now we need to do is use the relationships between Q C and D to figure out what the voltage and charge are for the entire circuit. And now what you can do is you can work backwards and sort of expand out again that circuit. So until you figure out the voltages and charges for each of the capacitors that you're interested in, that's gonna be the step by step process. We're gonna reduce everything down to a single capacitor, figure out what they voltage and charges across this whole circuit, and then we're gonna move outwards again, sort of expanding out all of these capacitors until we find the variables that were interested. Alright, To see how all of this stuff works, we're gonna go ahead and do this example together. So what's the charging voltage of each of these capacitors in the following circuit? So we've got three capacitors. We've got a mixture of parallel and Siri's, so we're gonna go ahead and first things first, we're going to find out what the equivalent capacity is of the entire circuit. Now, we've done this before. We have these, uh, capacitors right here that Aaron Siri's. But if you look a little bit more closely, we have this one and two fared capacity that air in parallel, so we need to work from the inside out. So what happens is this system right here? This circuit can be thought of as this more simplified circuit where you have the equivalent capacities over here. And then you have the six Fareed capacitor hooked up to the battery right over here. So we have this 10 volts now, in order to figure out what the equivalent capacity is ce que? All we have to do is just add them because they're in parallel. So the words the these air in parallel. So the equivalent capacities is gonna be two plus one, which is three ferrets. And we also have the original six very capacity right here. So now what happens is we need to figure out the equivalent capacitance. So that's gonna be when we do these capacitors in Syria when we had these things in Syria's together. So this is the same exact things. If I had one equivalent capacity like this and this equivalent capacitance C e Q is gonna be well, I have two formulas in order to solve it. I have the inverse some formula, or I can use this shortcut equation in which I multiply each of those two things together on the numerator and then divide by their some. So that's gonna be six times three divided by six plus three. That's gonna be 18/9, which is equal to two ferrets. So that's the equivalent capacitance. That's basically what all of these combinations of capacitors reduced down to as a single capacitor. We also know that the voltage across this battery is equal to 10 volts. So that's step one. It's done. We figure out what the equivalent capacitance is now in Step two steps to says We need to figure out what the equivalent charge and the equivalent voltage. We already know what the voltage is, so that's okay. We know what the voltage for the whole entire circuit is. So in order to figure out what the charge is, in other words, the Q equivalent we just have to use our relationships between Q, C and V. We know Q is equal to see Times V, so that means the queue equivalent is gonna B C equivalent times V. So what's the C equivalent? It's two ferrets and then the equivalent voltage or set. The voltage is just 10 so that means that the entire circuit has 20 cool OEMs of charge that's flowing through it. But that's not our answer, because we need to figure out what the charging voltages across each capacitor in the following circuit. So we need to dio is we need to work backwards from these charges. These voltages and these equivalent capacitance is to figure out what the charging voltages is on all three of these capacitors. Okay, so let's go ahead and draw at a little table because we're gonna have a lot of different variables floating around it. Zits. Definitely gonna be worthwhile to get organized just so you don't lose track of numbers, things like that. Okay, so let's see, I've got this to Fareed's. This is gonna be one Farid the six Farid and then the equivalent capacitance right here. So I'm gonna be looking for the voltage and the charge, and I know what the equivalent capacity is. Right. So I've got my little table now. We said, for the equivalent capacities of the entire system, we know what the voltage is. The total voltages, 10 volts and the total charge is 20. Cool. OEMs. So that's done. So what we can do is we need to work backwards to figure what the charging voltages across the six Farid capacitor. Okay, So we said that this equivalent capacity right here of two ferrets is the same as these two capacities right here in Siris. What's common about capacitors in Siris? Remember that they share the same charge. So if we can figure out what the charge is on this capacitance, which, by the way, is just the charge of the entire circuit the 20 cool OEMs. Then that means that each one of these capacitors here has a charge of 20 columns. So then already answers our first question. So this charge right here is 20 cool homes across the capacitors right here. Because again, if this one capacitor here is the equivalent capacity, the entire search of the entire circuit and it has a charge, Q e que? Of equal equal to 20. Cool. OEMs. Then that means that because these capacitors are in Siris, they have to share the shame, the same charge as the equivalent capacitor. Okay, so these are 20 columns each. Now, how do we figure out the voltage? Well, the voltage across these six. Cool. Um, our Sorry, this expected capacitor is gonna be using Q equal. CV is just gonna be cute. Divided by C. So, in other words, the voltage is gonna be 20 over on that six. In other words, that's 3.33 volts. So we're gonna fill that into our table. 3.33 volts. Okay, now we have to Dio is we have to get the voltage in charges for each one of these two and one fared capacitors. Now, in order to do that, I need to look at what the equivalent capacity is off. This three fared capacitor because then I could sort of expanded back out into the two and one again. So let's see if I if I know that these were going to be in parallel what's going to be the same about them? The capacitors in parallel share the same voltage, not the same charge. So what I need to do is I need to figure out what the voltage is across this equivalent capacitor. So in other words, V three is going to be que oversee so 20 over the equivalent capacities, which is three. So that's gonna be 6.67 And that's gonna be in volts. Now, remember, if this is 6.67 volts and this capacitor is the same thing as these two things that Aaron in parallel. Then that means that the voltage across each of them has to be the same. So both of these have to be 6.67 So we have 6.67 volts and we have 6.67 volts. Now, the charges are not the same because they're not in serious with each other. So in order to figure out what the charges across each one of these things are, so basically we have What I wrote down here is that V three is equal to 6. So v two, in other words, the voltage across this one was also 6.67 The vultures across this one was also 6.67 Now, how do we get the charge? Well, remember, with one of the charge across, the two fared capacitor. We just have to do see times V. Now the capacitance is just the So let's see, we have the two Farid Capacitor. Now, the voltage across this one was 6.67 So that means that the que two is just gonna equal. I've got 13.3. So I've got the charges equal to 13.3, and that's cool, homes. And now for the other one I've got Q of one ferret capacitor is equal to He won Ferid times the voltage 6.67 So it's just gonna be 6.67 and that's cool lumps. All right, so those are all of our numbers right here. We have the charges and voltage for all of these things. So you basically just have to work backwards and figure out all the target variables. You've got this. You got these charges. We've got these voltages. Anyway, Let me know if you guys have any questions with this, and let's go ahead and do some more practice.

2

Problem

What is charge and voltage across each capacitor below?

A

Q_{2F}=10 C, V_{2F}=10 V,

Q_{3F}=20 C, V_{3F}=10 V

Q

B

Q_{2F}=9.8 C, V_{2F}=5 V,

Q_{3F}=7.3 C, V_{3F}=10 V

Q

C

Q_{2F}=4.9 C, V_{2F}=10 V,

Q_{3F}=7.3 C, V_{3F}=10 V

Q

D

Q_{2F}=10 C, V_{2F}=5 V,

Q_{3F}=30 C, V_{3F}=10 V

Q

3

example

2m

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Okay, guys. So we're gonna work out a problem involving a capacitor circuit right here. But this is a little bit different than the problem that we've seen so far, because, really, we're only interested in the charge on one of the capacitors that is shown below. All right, so there's a couple of things I wanna point out about this circuit. The first is the fact that this five voltage battery is in the middle of the circuit actually makes no difference at whatsoever to the circuit itself. In other words, this circuit would be the exact same is if the battery was actually on top and five volts, and then you had the other capacities that were in Siris or there were in the same exact sort of placement as they were in the original circuits. In other words, if I had these two capacities like this and then I had this capacity over here and then I basically just swapped these. Then there was the circuit would be no different than how it currently is. So, for instance, if I had this arrangement one ferret, three ferrets and I had the two and the four fared capacitors this circuit would behave the exact same again. The fact that the batteries in the middle makes no difference at all to the circuit. Okay, so how do we figure out what the charge is on? This three fared capacitor. Well, basically, all we need to know is we need to know the capacitance, and we need to know the voltage because we know that queue for the three Fareed capacitor is gonna be related to C. V. We need to know the capacitance, but we actually already know what that is. That's just the three fared capacitor, and we just need to know what the voltage is across this distance. Now, remember our rules for solving ah capacitor circuits right now, right? So we know that any combination of capacitors that are in parallel shared the same voltage across each other and across the equivalent capacity they make up. So what I mean by that is that if we have five volts across this surface right here across this distance, So, for instance, if I have five volts in between here, then that means that I have Sorry. Five volts, then that means that there's five volts everywhere. So There's five volts here, here and here because all of these three are in parallel. All of them share the same exact voltage with each other. So that means that if I have five volts across this capacity right here, then we just go ahead and figure out the charges. So Q is just going to be the three ferrets. Wow, my pen is not working times the five volts, and that's just 15 cool arms, and that's it. So we actually don't have to go through the process of collapsing everything down toe, one equivalent circuit or one equivalent capacitor and then work backwards because sometimes you can use some shortcuts to basically figure out very quickly what your target variable is. All right, let me know if you guys have any questions with that.

4

Problem

What is the voltage of the battery below?

A

V = 0.80 V

B

V = 1.75 V

C

V = 5.25 V

D

V = 15.8 V

5

Problem

What is the charge on the 5 F capacitor? (hint:be careful with series vs parallel)

A

Q_{5}=2.6 C

B

Q_{5}=9.5 C

C

Q_{5}=13.4 C

D

Q_{5}=14.4 C

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