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A capacitor of capacitance $5 cdot 00 mu mathrm{F}$ is charged to $24 cdot 0 mathrm{~V}$ and another capacitor of capacitance $6 cdot 0 mu mathrm{F}$ is charged to ...

Question

A capacitor of capacitance $5 cdot 00 mu mathrm{F}$ is charged to $24 cdot 0 mathrm{~V}$ and another capacitor of capacitance $6 cdot 0 mu mathrm{F}$ is charged to $12 cdot 0 mathrm{~V}$. (a) Find the energy stored in each capacitor. (b) The positive plate of the first capacitor is now connected to the negative plate of the second and vice versa. Find the new charges on the capacitors. (c) Find the loss of electrostatic energy during the process. (d) Where does this energy go ?

A capacitor of capacitance $5 cdot 00 mu mathrm{F}$ is charged to $24 cdot 0 mathrm{~V}$ and another capacitor of capacitance $6 cdot 0 mu mathrm{F}$ is charged to $12 cdot 0 mathrm{~V}$. (a) Find the energy stored in each capacitor. (b) The positive plate of the first capacitor is now connected to the negative plate of the second and vice versa. Find the new charges on the capacitors. (c) Find the loss of electrostatic energy during the process. (d) Where does this energy go ?



Answers

A 20.0-$\mu$F capacitor is charged to a potential difference of 800 V. The terminals of the charged capacitor are then connected to those of an uncharged 10.0-$\mu$F capacitor. Compute (a) the original charge of the system, (b) the final potential difference across each capacitor, (c) the final energy of the system, and (d) the decrease in energy when the capacitors are connected.

Go. So the total charge here on the combination of capacitors is the sum of the charges on the two individual capacitors, since there's no battery connecting to them to this power supply to add additional charge. And there's no neutralization of charged by combining positive and negative charges. The voltage across teach capacitor must be the same after they're connected. And since each capacitor plate is connected to a corresponding plate on the other capacity by a constant potential connecting a wire. So use the total charge and the fact that equal potential to find the charge on each capacitor and the common potential difference. So the total charge here Q will call it Q of T is equal to I Q one initial plus you two initial, which is equal to Q one final close Que tu final. Okay, well, uh, to one initial plus que Tu initial is equal to compact. Since capacitance see one times the potential V one initial plus C two times V to initial and then the final is C one times V final, but the final first to one final and the final for Q two final. The potential V is the same. So this is C one plus C to we can just pull that potential out front or out back. We're gonna multiply it by Visa. Beth. So solving for Visa Beth, this is equal to C one times V one initial plus C two times V to initial divided by C one plus C two. Okay, well, see one is equal to 2.5 times 10 to the minus six in the unity airfare at Since it's capacitance, this is gonna be multiplied by the one which is 746 volts plus C to which is 6.8 times 10 to the minus six fare ads, oh, times V two, which is 562 volts V to initial divided by C one plus C to which comes out to be 9.3 times 10 to the minus six fair rats. So we find that the final then is equal to 6.11 volts Quicken box set in this part of our solution to the question. Okay, we can also then find Q one final. Uh, this is pick you one final, which is going to be equal to see one times V final since the final is the same for Q one Q two final. So playing in C one and the final, we find that this is equal to 1.53 times 10 to the minus three columns. Oh oh, and then the charge of on the other one in the final state. So Q two f was going to be equal to C two times VF. So playing in the value for C two and VF, we find that this is equal to 4.16 times 10 to the minus three close when we can box that heart in is our solution to the last part of the question.

We have seen givens. We have cease of one. The first capacitor has a capacitance of three point seven zero micro cool arms. Or we can say three point seven times ten to the negative six. Ah, fared starts. Micro Fareed's might my qualities, and this is when it's charged. Um, and we have the equals twelve votes and see so to equalling five point zero micro Farid zor weaken, say five times ten and then give six pairs. And again, this is on church. So party is asking us for the stored energy Ah, before the two capacitors are connected. So this would simply be equal to p e equals one half cease of one V squared. So this would equal one half times three point seven times ten to the negative. Sixth twelve squared. And we find that the stored energy before they're connected is going to be equal to two point six six times ten to the negative forthe Jules. So this would be your answer for party. This would be the stored energy before the two capacitors are connected for part B. They're asking for the stored energy after two capacitors are connected. So at this point, we know that the total charge is going to be equal to the capacitance times the capacitance of one times the voltage. Now this is going to be equal, Tio three point seven times ten till negative six times these. So that would be simply twelve. And this is equaling four point four four times ten to the negative fifth. Cool ums. Now, at this point, we know that cues of one the charge in the first capacitor a sequel to see someone fee And then we know that the charge and the second capacitor is ceased to be. So we can say that the charge in the first about about the charge in the second is going to be equal to the charge. Sorry. The charge and the first divided by the capacitance in the first will equal the charge in the second, divided by the capacitor in the second. And we know that this is going to be good to Q total minus que ce of one divided by ceases to So we know that Kyu won. He's going to be equal to the Q total times c someone plus c said to and as see someone is in the waiter. So this would be the the formula First cease for accuse of one. And then we can actually solve and say that this is going to be a four point four four times ten to the negative fifth. And then it will be three point seven times ten to the negative sixth and here, eight point seven times ten to the negative sixth. We find that this is going to be equal to one point eight eight, eight times ten. So the hey, negative fifth cool arms now too soft. Recuse of two. This is going to be equal to the total minus que ce upon. So this will be a four point for four minus one point a times ten to the negative fifth and this is going to equal two point five five, two times ten to the negative fifth. Cool arms. Now, this is important to note as well as this values important. So at this point, we can find the potential energy total. So this will equal the potential energy from one plus the potential energy from the second. And we have a queue of one squared over to see close cues of two squared over to see and we can we say that this is going to be equal. Rather, let's get a new line. So essential energy total Give me equal to one point eight eight eight times ten to the negative Fifth squared developed by two times the capacitance. This will be see one BC to so here it would be three point seven times ten to the negative sixth. And then we'LL be plus two point five five two Time's tenth And they had a fifth squared divided by two times five times ten to the negative sixth. And we find that the potential energy total after the two capacitors are connected is going to be equal to one point one three times ten to the negative fourth. Jules. So this would be our answer for partner for Part B rather now for part. See, they're asking us for the change in kinetic energy, so this would be simply peace final minus p initial. This would be equal to one point three rather one point one three three minus two point six six four times ten tonight of fourth and we find that out the p e, the change in Connecticut and potential energy and stored energy would be negative. One point five three times ten to the negative forthe jewels. So the system is losing energy in part. See, that will be your answer. For Parsi, that is the end of the solution. Thank you for watching.

Hey, so in this problem we start out with a 20 micro fair and capacitor, and it has a potential difference of 800 folds. So if we wanted to, we could find the charge on it. I'm guessing we probably will have to. So that's 20.0, times 10 to the minus six fads. And the voltage is 800 volts. And then this capacitor is then connected to another capacitor. That's uncharged. And it has a 10 micro frag capacity, so see two is equal to 10 uh, times 10 to the minus six fans. So here's redraw. All See one here. See, too. And then basically, the questions is I mean, how much charge is gonna get on this other capacitor? So, um, and then the final energy of the system and how it changes on. So first we want to get the original charge in this system. So for part, a sees cure V. So, um, he was cute by right. Be so Q is equal. Two. Ah, see one v. So Oh, I could do that. One of my head. So that's 16 times. Make sure that was 20 and not too. Yeah, so 22 times eight is 16. That's 10 of the minus five times 10 to the two. So that's times 10 to the minus three. Cool ums. It's a lot of charge and part B, huh? It's here, So quite be asks us to find the potential difference across each capacitor. So what's gonna happen when we connect the used to charge capacitors? Um, are gonna now have the same potential difference. So we can say the wine equals B two. And so, um, the voltage across either is gonna be the charge, uh, divided by the capacitance. Never had a race that who oversee, and then that's gonna be true for both of them. And then we know that they're gonna um actually, no, we don't know that they're gonna be sweating the charge, but this is gonna tell us the ratio of the charges. So we know that, um, q one it's gonna be Q. So Adam Brickley solving this equation for a Q one gets equals that it's equal to Q two times, see one divided by sea to and let's see. So how did their capacitance is? Compare to see one has double the capacitance off see too. So therefore, um que wise Could be two Q two. No, excuse me to you too. And so basically, it's gonna be if you could divide this total charge of the thirds and Cuban will get 1/3 and then cue to look at 2/3 of it. So then I'm gonna continue this on the next page. So the cute total was equal. Thio, I think it was 16. Um, c give me one second. So 16 times 10 to the minus three cool ums. Therefore, Q one is gonna get tau 16 divided by three. What? So it's gonna get 10 point uh, seven. We'll worry about the Sync fix later, and then Q two. It's gonna get half of that. So, um yeah, it's just gonna be 5.33 Millie Coolum And next we want to get the final energy of the system. So this is still be so if we want to get the final energy. Um, we just want to evaluate you, which is equal to 1/2 C V squared. Um, let's use one with charge. So see ISS, not voltage. So v askew overseas. So that's 1/2 Hugh squared over a C square time. See, gives 1/2 Q squared, divided by sea. So you want. Okay, I'll have to use a calculator for this one. But I mean, yeah, I'm just gonna be putting in Q one squared, divided by sea wine. And then 1/2 Hugh two squared oversee, too. And then I'm gonna go ahead and pause the video. Thio do this calculation. Okay, so I put everything into a calculator, and for you one, I ended up getting 2.85 jewels. And for you, too. I ended up getting 1.4 to Jules, and then d asks youto compare this energy to what it was originally so originally. Um, let's just use the 1/2 C B squared formula, because those are I guess you could use either one. I like to use the things that are directly given if, um, possible. So yeah, I'm just plugging in this C one and then this b s this seat 1000. Let me just double check. That's not 800 0 800 makes war actually used 800 not 8000. I did use 800. Okay. Excellent. And so that's 6.4. All right, Jules. So therefore, the energy lost between the initial and final configuration is, um it's gonna be this 6.4 minus you one minus you, too. And then when I put that into a calculator, I got 2.13 drawls.

So it means this question. We have to pastors what is cheap in seven U F. And it was initially charged to 475 votes and less. Where is for us, and it is initially trash to 525 votes. So these impostors are disconnected from the batteries, and the positive place it's a service is ultra disrespected is supposed to exist. Apology in place are now connected and so that plays are connected. So what will be is a potential difference across each custard. What he's a charge on each. So the total charge off the combination of depositors is a sub off the charge onto individual clusters because it's absolutely system, so there will be no Oh, there will be no you should either by combining costume and negative charges So the voltage across the impostor must be the same. Options are connected because each depositor is connected to your correspondent place on the other posture by a coaster potential. So he used a total church and the fact that people potentials, uh, to find charge pastor and the Carver contingent of fists. So let's first, uh, find so it'll charge. We have initially were cute. Total equals one plus cute. You, Hugh, is Sitarski. So this equals to see where you want plus c to meet you. It also equals C When the final plus C to talk speech. You find it. Okay, so this gives us be final because, uh, find when they stabilized the one that final and the final will be equal because on sicker. But this is a prostitute. So we finally waas see what everyone initial plus c to beat you. That is the initial total charge to buy that by C one prostitute. So that is cheaper. Set up traps tantussi, just six fire attempts. 475 volts. Last foot Which there was your statues inactive since parliament times 500 volts divided by, uh, steel and process. You do that? It's 6.7. I'm Stan choosing Egypt's exports. This is about 100 and five volts. This equal studio where final and this equals to meet you finally and actually foot touch that. So after that you have an indifferent if you want you to after or it's too close to our final equals C one final see what tops few more vital. Uh, thank you, Chief. I know. Equal. See Cheers us each file in this because But she went seven from strange electric sex boat parents class over five foot is this equals four times 10 to his next of six. Forage on. Can't has 505 votes. So this is what me through six lapsed into protective circle. This is too. I have separate us very well. So this is a charge capacitor wanted to after they're attracted. So parties is what will be the voltage in charge for each capacitor if place of offset science are connected. So what happens if we Maxim Cicely? So, uh, the first thing has seen is that for your connect place off defines what what happened is a charge for float isn't quite mutual eyes a little bit because the total time without bees of difference of charge for the true place. In other words, here total becomes your total becomes a difference off Cuba and cute you initially And it's, uh whichever star tresses that's absolutely 30 queue up my schedule and it is still equal to Q one final last. You define it. So, uh, this is see what you are minus each of you to absolute value equals C will seat you. China's the vital. So this times we have me finally equals C When you want minus secure feed you divided by C one. Prosecute again. We have the exact same equation. If here. Except that we changed the minus. So that's a plus sign to fight us. And here we will actually end up getting on subsidies 150 boat. So you can see it's lost dollars as unfortunate reproach and we confer. And Cuba at the kitchen is the same way. This is Lucy. What's up? Speed up. Which is so, uh, pastures. Monster watch 120 boats. This year's st sequence three stages Negative for this is chp up? It was full for others 10 to the negative six types of her 20 boats. This gives for quenched by times. T z left it for who For which Okay, so is that it sounds like a party and party


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