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= 40f8 QuestionsAssignment Score:37.546Resourcesn'HintCheck AnswerQuestion 0 oi e AllemptsQuestion 4of 8You have (70 capacitors; one with capacitance 15.7 and ...

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= 40f8 QuestionsAssignment Score:37.546Resourcesn'HintCheck AnswerQuestion 0 oi e AllemptsQuestion 4of 8You have (70 capacitors; one with capacitance 15.7 and thc Other of unknown capacitance. You connect the two cpacitors in series with voltage of 371 V applied across the capacitor pair: You discover that, result. the unknown capacitor has chargc of 0.00147 C. Find its capacitance C_02 Question Lofe AttemdtsJgtCorrect03 Question Tofo Attcmptsddr100corectQuestion 0 0i e AltempisQuestion 0 o

= 40f8 Questions Assignment Score: 37.546 Resources n' Hint Check Answer Question 0 oi e Allempts Question 4of 8 You have (70 capacitors; one with capacitance 15.7 and thc Other of unknown capacitance. You connect the two cpacitors in series with voltage of 371 V applied across the capacitor pair: You discover that, result. the unknown capacitor has chargc of 0.00147 C. Find its capacitance C_ 02 Question Lofe Attemdts Jgt Correct 03 Question Tofo Attcmpts ddr100 corect Question 0 0i e Altempis Question 0 ofo Altempts Queston Jgt Lofe Attemdts Correct Question 0 ol e Attempts Question 0oie Attempls



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Answer the given questions by solving the appropriate inequalities. The total capacitance $C$ of capacitors $C_{1}$ and $C_{2}$ in series is $C^{-1}=C_{1}^{-1}+C_{2}^{-1} .$ If $C_{2}=4.00 \mu \mathrm{F},$ find $C_{1}$ if $C>1.00 \mu \mathrm{F}.$

Here we have a question about the energy sort of pastors. So we're given uh formula for energy storage capacities and then we're told that we have two different setups um that we can use with two different capacitors with different capacitance. Both have the same e enough for the battery. And first we're just ask qualitatively uh which which uh arrangement can store more energy. So we want to find some inequality which relates the energy and a serious combination uh to the energy in parallel combination. Uh This equal sign with a question mark over. It means we haven't yet determined what this inequality is, but it doesn't mean it's uh these two equal. So let's find out how they relate by individual finding what their energies are in terms of she wants you to be. So the total energy in series is going to be the energy cross capacitor, one less energy on cap capacity to this can be one half C one b one squared plus one half C two B two squared. Where see where everyone is the voltage cross faster one mmbtu supported cross faster too. All right. So now it's right out for the energy and parallel combination. So this is going to be one half C one B squared. Notice not the one to see plus one half C two B squared. Right? The reason it's just V is because in a parallel combination, both of these loops have to have a voltage drop of the across the capacitor. Since christmas google says that when you go around the league, we have to have a net uh changing voltage at zero. All right. So, we know that V is the sum of B one plus B two. Therefore V is greater than both V one and V two. So, since these are greater than these, then as a whole energy and parallel must be greater than the energy series. So the same quality is a less than sign. I suppose it could be less than or equal to in uh ah in a case where one of the capacitors, capacitance was um was nearly zero. But um we're gonna leave that case out. So it's just me a less than sign. Okay. So now in part two of the question, they tell us that the exact value of the voltage uh in the varies is 60 bolts and they tell us that C. One is me respectively to be persistent. See one has a distance of two micro forwards. And so not about that. Micro ferrets and C. Two as a contestant out of four micro pairs. Alright, so now they want to find the energy in serious combination and in the parallel combination. And then we can compare those and see if inequality holds. Right? So let's start with the energy in the parallel combination. So we established that this is equal to one half C one he squared plus one half. See to these. Great, this isn't hard at all. You can just plug in C. One, C. Two and B. We have all the numbers we need we'll just plug goes in and we find that energy in the parallel combination six times 10 the minus 10 jewels. So that was pretty easy to calculate what makes the energy serious harder to calculate that the voltage across each capacitor is not as obvious as just be All right. So maybe the software B one and B. Two, who's there to announce we're gonna need a system of two equations. We will solve this. I still think about what we know about series uh setups. Well, we know that um we can use her cough sleep rule and we know that. So we'll know that the voltage drop across some of these two capacitors has to be equal to the voltage gain across the battery. Which means that B one plus B two is it going to be? Which is uh this equation right here. Uh And then another thing we know about capacitors in particular is that charge on on one capacitor has to be able to the charge of another capacitor and serious of it. I supposed to use that. So that says that basically Q one is equal to Q two or Q one is the charge on the fast one. Duty is charging faster too. All right. So let's find cute in terms of some other variables that we know. All right. So let's remember that the voltage across the capacitor is equal to Q oversee. So then Q must be equal to see time speed. Right? That's not a threat to raise my question. R C R Q is equal to C times B. So now we can we have our second equation. Uh Let's substitute in uh the specifics for Q. So we have C one. V one is equal to C to B. Two. Right? So we have the two equations we're gonna use, let's start by solving one variable in terms of other variables. First let's all for V two. So the two is going to be equal to b minus 51. If we subtract if he wants the other side, let's help you cheat that into this equation. So C 1 10 C one is equal to C two times the quantity of B minus the one. Right now it's all for B. One. So UFC one V. One. Or distribute this C. Two. Uh It's equal to C. To b minus C. T. V. One. Now it's group the terms that would be one. So we had the one times C one plus C. Two. This is equity, C. Q. B. All right now let's get me one by itself. Be one is equal to ctv over C one plus T two. Right now these are all values that we know. So we can quite goes in. We find that everyone right now this makes be chewed releasing software since uh they want cost me two is equal to uh six year olds. So we too must be equal to 20 volts. Right now we can go back to this equation and we can plug in uh those values for V. One and V. Two which we just saw for. And we'll find that the energy in the series arrangements is equal to 2.4 times 10 to the minus 10 jaws. And then finally, we want to compare these and verify our inequality that we saw for the first part of the problem. So the energy and the parallel combination is greater than the energy serious combination six is greater than 2.4, and that holds with our inequality, which said that the energy and parallel combination was greater than the energy in the serious combination. So we're also.

Okay, let's draw the circuit diagram. First capacity of one capacitor X capacitor three and capacitor to so see to si si point a wouldn't be C one on C X and okay. Okay, Now the C one and C X are in Siri's See two and see three out in Siri's and those these two Siri's pairs are in peril, So potential difference across C one and C C X series. It's same as potential difference across you. 23 1 more information that is given is that the baby there is potential difference between point A and B zero. That means point A and point B both at the same potential. This implies that potential because see one is equal to potential across see too similarly potential across. See X is equal to potential across Si si, because if potential across see one is same as potential across see, too. Then the Partovi nut is the depositor equally among C one and C two hands to point A and point B will be at the same potential. Now let's take an advantage off the given information. No, since the two will see, three are in Siri's, You can find the net capacitance off capacity and capacitor to which is equal to see to see three divided by sea to plus C three. Now, if you substitute those values off, see 23 given as 18 microfibers and 4.8 micro fatted respectively. You get the value three point seven eight Michael Barrett. Now you can find the potential across the See two, which is equal to Q divided by sea to know what's the value of Q Q equals C 23 which is Ned Capacitance times. We know this is the charge deposited across C two C three series circuit, which is equal to three point 78 We not so it's used to find. We see, too. We see two is equal to three point 78 Be not divided by value of C two is 18 now. Similarly, we can find BC Three is equal to 3.78 because in Siri's, you have the same charge distributed on each of the capacity. So each capacitor in serious gets the same charge. That's the property off serious circuit. So instead of 18 now we have C three value of C three, which is full point eight. Now we have Easy One, NBC three. No, As in page one here, you can see VC one musical too busy too VC one than equals the value of easy to is 3.78 We not divided by 18 30 point 78 We not divided by 18. Now, what's the value of the C one that can be given by charge deposited on C one? They were divided by value of C one, which is eight point no equals 3.78 We not divided by 18. You know what? Let's not write the value off. See one yet let's keep it S e went 3.78 We not divided by 18. This gives you Q equal to 3.78 c one. We not divided by 18. Okay, what's the use of the value off cue since we know that capacitor C one and C two are in Siri's, So they both have same charge deposited on them so I can use the same thing. Same charge for C X capacitor now charge deposited on the capacitors. See X is given by see X times potential difference across the capacity. See, thanks. No. To use that information, we need to find out the potential across CX, as mentioned before VC X is equal to V. C three on value of V. C. X is BC three now we can make use of that since Josh is given by C x v cx Cute. Now we know Q, which is equal to three point 78 c one. We not divided by 18 equal to see X The value off visit Lee OVC X is given by 3.78 We not divided by 4.8. You can cancel we not on both sides to find out CX equal to C one times 4.8 divided by 18 which is equal to 8.9 times 4.8 divided by 18. So this is equal to two point 37 micro fatted. I hope you understand this.

For this question. We're looking at a capacitor being attached Siri's three resistor in an air missiles. So it's quite a simple set up. We are given all of devalue us Such s T E m f the resistance throw ste contestants or your find is you're power dissipated by our resistance the energy being stored Bioko, Bester and also the power dissipated by the source right tree, different points in time. So the first point in time will be just when the circuit is formed. Night equals zero. When the current just started to fool the mature is 20 is a ghost in finite. So after a very long time and finally ET the point in time is when the church, close to half of its final value gonna start off. If the 1st 1 one MTI close to zero just started. Ah, just out of anti circuit. So the capacity can be ignored. Can assume that it's just a piece of wire. They're still charge. Start in it yet why needing? So we can just ignore and they're 40 power dissipated by oh, resistor. It's just Ah, using pique was to discover our you can take the entire um f off the battery to be the potential drop across the resistor. Give us 246 year old? No. For how much? Um, Sebesta is actually charging at the rip off church. We're gonna use the equation you request to que square, uh, to see and therefore you read off charging what ISS electrical energy is. Do you differentiating this? Ah, the only one that is depend on time is Cuba see so constant so you can keep net differentiating que que square yet to cure security? You know that security is just the current. So this is que times I see No, because that is nor church there is starting a capacitor yet so curious, Cyril. And the 40 Cent I thing is zero parts. We won't find a politician, bater by t source We just see to find what is the current flowing, truly anti circuit. You can find the Yemen power across the sauce by taking p crystal. I feel now the current you can find you think your sister taking the potential difference across the resistor and the resistance in this work for us Can't 246 year old what's now? We move on to the second point in time when t think was within finite. So after a very long time no, he the best er after a very long time will be fully charged. And now sn open circuit, right? No, allowing any current to flow and therefore there is no current and without any current, the powerful the resistor which is a p goes to I square are oi fi pique was civil because it depends on I and also the potential trouble cause it eu sou west Bill course this No, I de still current flowing through it The power I already read off Great off accumulation off the energy in the capacitor since it is dependent or que So you better cue and I if I think zero this entire thing will be to really the power dispute about the sauce is also zero because there's no current for the third point. Really? When did you start effect that are cure? It's no half off you're not. We used to equation you Not one minus absolute sorry exponential negative to you r c this sea equation to find out what is the charge at any point in time The secret is to are a specific point in time when we want que to be half off the maximum value you not We can rearrange Gary off the common factor and financial toe degree T o r c because to oh, now using this, we can actually find what is the current at our interested point time Since it is not times explanation negative t o I'll see. This will be just half off the makesem current and it makes my current of your reverse. The phone is this was 200. Any for five point it Using this current, we can find what it's d participated. Heidi zesa using P equals toe ice cream, huh? The ideas will give us 614. What for? The rich off charging Do you over tea t I know that, uh que right dirty q t t its current. I see we know what is the current but you know what? And you know I see charge is half t excellent church. Then we can find the next one charge based on curie goes toe cv. So this is the teachers I ve heavy is the potential of course Across uh, domestic This case, we can use the potential across our resistor. Yeah, we should need to find based on can use recently power potential costing investors just, um if subdirectory Yeah, this is going to be 120 for this is boats 60 four. Test will multiply this pretty current. Every should get Ah, 61 full 0.5. What? Finally he participated by t source? Yes, Stick I times. Um, if just this case 120 p 12 tree zero what's and I can see? Um, the power despite a power, um f is equivalent to the politics Peter body resistor last year, uh, reads off charging off our capacitor and so it it will be, ah, energy conservation.

Hi. In the given problem, there is a capacitor off capacity and see Let it be C one. Most of the accidents is given a seat. It is charged to a potential difference or we know means we won. We can say Toby Reno the terminals off the charge The capacitor are then connected toe doors often uncharged capacitor as the second one is uncharged. But we can say V two is equal toe zero. You know, this is the first capacitor having capacitance C one it's going to see and the other capacitor and they're terminus are joined together. This was positive. This was negative. So now the charge will distribute over both off them and the capacitance off the other capacitor will see by two means C two is equal. Do half of the first one. So no. In the first part of the problem, we have to find the original charge off. The system means when there waas only a single capacitor. Then, in that case, the original charge off system waas you is equal to we can save. You know he's a quarto. See? One you re one means this is C into we know the bassist. Our answer for the first well off the problem. The old age in a judge over the system. No. In the second part of the problem, we have to find the final potential difference across each capacitor. And the final potential difference across each capacitor will be equal means common as both the capacitors are in parallel. So the expression for common potential, we know is given us seven into even plus C two into a veto. Be invited by C one. Let's see toe. So then we put these values here. There's a C until we not plus zero as a second capacity Ross uncharged, divided by C plus C by two. Or we can say, this is C in tow. We not divided by three C by two. This seat got cancer, so it becomes movie, not by tree. So the sister answer for the second part of the problem the common potential or book, uh, across the periods of both capacitors. So this is the answer for the second part of the problem? No. In the third part of the problem, we have to find the final energy off the system. So in order to find the final energy off the system in per part. This may be given as you do and this is equal toe half into sea in tow, re square. So here it becomes harder for the next capacitance in parallel combination. It will be C plus C by two, as we have found here in this denominator. But this neck capacitance is you see a tree. See, this is three C by two multiplied by the common potential which was truly not by three Yoder ball sweat. So here it comes out to be treated by four C multiplied by four the naughty squared divided by nine. So finally we can say the final energy stored in the system. You comes out to be one by three. See, we know square, This is the answer for that Can't off the problem. No. In the fourth part of the problem, we have to find the decrease in energy when the capacitors are connected means the loss in the energy taking place. We have to find for this. Hopefully we find the initial energy off the system. So yes, initial energy needs human was the energy stored in the first capacity only means this was half See the Not sweat. And finally this is you do which we have found in the her part of the problem. So the loss off energy Delta U is equal toe you one minus you all we can say this is her CV Notice square minus one by tree. See me? Not square. Then we saw it. We get Delta U is going one by six See the not square business our expression or lost in the energy when we join do capacitors? No. In the final last part of the problem they're asking in what form this loss of energy will be Convert it so this los off energy will be opt in in the form off heat the form off heat and life and G in sparking. Then we join the terminals off. The capacitors are sparking will take place. And that is sparking the energy released thing That s parking will be equal toe this loss of energy one by six c v not slept. Thank you


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