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Capacitor C, =3pF is charged 6 V Then, the charged capacitor is connected to a closed circuit of two uncharged capacitors, Cz 4 pF and C3 2 pF as shown in figure...

Question

Capacitor C, =3pF is charged 6 V Then, the charged capacitor is connected to a closed circuit of two uncharged capacitors, Cz 4 pF and C3 2 pF as shown in figure. Find the electric energy stored in C3:72pJ8 pJ36pJ4pJ

capacitor C, =3pF is charged 6 V Then, the charged capacitor is connected to a closed circuit of two uncharged capacitors, Cz 4 pF and C3 2 pF as shown in figure. Find the electric energy stored in C3: 72pJ 8 pJ 36pJ 4pJ



Answers

Four capacitors are connected as shown in Figure $\mathrm{Pl} 6.48$ . (a) Find the equivalent capacitance between points $a$ and $b$ (b) Calculate the charge on each capacitor, taking $\Delta V_{a b}=15.0 \mathrm{V}$

So we ever knowns we have our first capacitance of Southern point seven micro ferrets. Or we can save seven point seven times ten to the negative six fair. It's way we have our first velocity of one hundred sixty five volts and we have our Sorry excuse me first philosophy and then Visa two unequal fifteen bolts and we're trying to find ceases to So we know that cute total. There's going to be equal to kyu won half plus q to us, and this will equal C one B one. Now, at this point, after the first capacitor is disconnected from the battery, the charge is going to be constant. So the voltage across each capacitor must be the same when they're connected. So cues of one F would equal cease of one piece of one and then que ce of two effort equal ceases to visa too. So now we're getting that cease of one. These have one plus cease of two. Visa too, equals cease of my apologies, asses, this is going to be Q one final would be cease of one visa too, and like you to final would be ceased to visa too. So here we would have cease of one visa to plus ceases to visa to equal cease of one visa. One. There you go. And at this point, now we console for sees up to and say that cease of two. There's going to be equal to see someone of these of one divided by visa too minus one. And now we can solve. So cease up. Two unequal seven point seven times ten to the negative sixth. And then this would be one hundred sixty five, divided by fifteen minus one, and we find that ceases to. It's going to be equal to seven point seven times ten to the negative fifth thirds. Approximately. So this would be our capacitance sub, too. That's the end of the solution. Thank you for watching.

So again we are given a combination ofthe three contestants. Let me, Joe, the competitors first. So true Capacitors Stephen and see too, uh, connected in Patton to a third. Uh, on this true capacitors are connected to a third competitors. Sit three indiscretion on behalf of a point paint point being with service to this point. So this is my semen. This this sigil on here have city. So I have this trick. Capacitors C one and C two are connected in parallel on DH This intensity capacitors, which is in cities with C one and C two. So this is the combination, the value ofthe the capacitors, different values off each of them. So it's even is given to be six micro fetid. See to it's going to be three micro fetid on better sit three. Is he going to be find my confinement now in the problem? It's given that some potential difference. Crybaby is being applied between the points A and B, which is not given to us the value of the position differences not given to us than we are required to find that some potential difference is applied between these two points B and B on it is given that after the charges on each of the capacitors have reached their final values, the charge on Pastor see too is given to be touchy. I cuckold So the charge on capacity to see to that, said the charge is cute too. On the presidency too is given to be thirty micro clubs. So So we are given the charge on one of the capacitors that it's C too. And in the first part of the problem, we are being asked to find the charges on each of the capacitors, even on city. So charge on one capacitors Setu is already given, which is called cute, too. Thirty Microfilm ferret. On the first part of the problem, we need to find the touch on the first capacitors even and the charge on the turkey poetical century. So if you look at the problem, we see that capacitors even and see toe are connected in parallel on capacitor sit three isn't cities but thiss combination of seven and city which is connected, Balan. So since even and see, two are connected in parallel on DH, we know that for Palin combination of capacitors, the voltage the potential difference across the panel combination of capacitors is going to be equal. So so if I try to redraw the part of the circuit So I'm just trying the part of the circuit where C one and C two well connected. So So we have see one like this on DSI, too. Like this. So the potential difference across this part Peter Andre villain it's gonna be quick because they're connected in Tallinn. So for this to competitors, the potential difference across this took passengers. Be civil and sit with your vehicle, which is a call to even and we do. So we was equals beetles, which is nothing, but it will do on Beidou can be bitterness Q two Divided by CTO from the definition of capacitance. We already know the value of the charge on theta one second competitors, which is cute, which is given to us to be a thirty micro fetid. So I did so you're cuter clothes thirty micro column on DH, divided by sea to the worldly off the capacitance. See to it is, keep it to Bt my Crawford. So this is three kind's Kendra is true negative six. Ferid And there are Luke, um thought to be ten bones. So we found a potential across each of the capacity we want and veto. So having found contention so across even the potential, we have found it to be ten world. Once we know the potential across a capacitor, we can always find the church on the capacity. So the charge in competitors see one is simply given by Q and equals. We will times seven. So my people have already found to be ten rules certain times, the capacitance, they're only up to capacity and see what which is. Six microfiber of six times cameras too negative. Six splendid on DH. Thiss value comes out to be so charge on the first capacitor see one and so to be sixteen micro cooler so that the charge on the first capacity Q and A So we have found the charge on the first capital C Q in charge on the second capacitor is already given to us. We found the charge on the first capacitor. See, when it is called the Pula, which is sixty. Microphone in on DH. Now we need to find the charge on the turkey capacitors. So if you recall that the turkey pass It'LL sit three. So we have our C one and C two electives. So this is Stephen. This is C two on the turkey. Basseterre century is connected in cities but the combination off this competitive Stephen and city so way already found the charges on competitive Stephen and see to to be able to Cuban in Cuba. So if you will recall that in cities combination So if I If I draw the circuit in this world so the net capacitance off capacitor civilian city with a connected in battle and then I'm gonna have the third capacity, which is city. So let's call this net Capacitance equals to see one, too. So for serious combination, the students are on each of the capacitor is indeed equipped to go natured off the circuit. So for cities combination charge on the capacitance Q tree. This ended equal to the sum of the church on each of the sure capacitor C one and C two. So cute request you one last you two. Well, my cure uh, Andi. Kyoto If I ride the sum. So Mike, you and wass sixty micro fetid. So the Cuban Wass thirty Microphone on Be Found That cute, So Q. And it's sixty micro fetid and cue do is thirty microfiber on? If I did this, um, it could have been ninety. Michael Farid. So this is the charge on the upper capacitors Q t. So with this were successfully come to the first part of the problem you have funded. Touched on competitors Q. Three. Cuban on Sergeant Second capacities already went to us. So the second part of the problem is we need to find the equivalent. We'LL ditch the potential difference across the points A and B so for finding the coordination between the points and being so, the financial between the points A and B is simply given by the ratio Off the net are the equivalent start off the circuit. On the Net. They Poland capacitance off the combination of three capacitors. So, as you can see from the first page that thiss trick capacitors to off them. CNNC too are connected in battle to attack a visitor which is connected incidents with the combination of seven and city. So, in order to find the net capacitance, we first need to find the equal in capacitance of civilians into connected infallible. So for that, I'm just gonna write it simply like this that says he went to is take Berlin capacitance off the battle combinations. Human Institute on there We have Century on December points if and b so since evidence the two are connected in Madeline so the maid can presidency went to is simply the sum of the presidents. So it's even less if it is a clone, which it's gonna be. Six micro credit plus three micro fetid. So which is going to be cold? Nine? Might prophetic on if I want to find a Berlin capacitance off this combination. So it's kind of easy equivalent. So since Eve, three capacities see one, too, on dsi three mechanical in Siri's. So the net capacitance off the circuit is going to be one or seek relative wass one order see one too, Plus one hour fifty three. And if the girl Clint, is it gonna be won over nine Micro fetid, close when no fine, the value of which comes out to be around three point to earn my prophetic. So this is the equivalent capacitance off the circuit off the combination off three competitors. C one c to answer, it creates what is the Wellington presidents? Good. So our job is to find the potential difference between the points and be he is given by the student judge they call in charge, divided by Sequent. And if you guys are wondering if we know the value ofthe cook going equivalent have already found that because, as you can see in this part of the circuit the cubicle Eleanor, the total charge between the points A and B, it's going to be going to the church across the capacitance eatery which we already found charges because capacitive victory, which is called acutely, is nineteen microcredit. So we have the Corey Colin touch twenty. Thank you. Derided by they will pass chickens is three point to one like a ferret. And if you take this if you can't let this well, you it comes out to be twenty feet for war. So this is what the baby is. So finally, my V maybe because granted point zero four, this is the potential difference or the potential in applied across the points

All right. We have for capacitors now connected. And I'll draw the diagram just so I can label see one see to C three and C four. These are just my labels, which make it user to follow. Okay, so we want to combine all these into one capacitor, so C one and C two or in Siris with each other, and that branch is in parallel with C three. And that entire combination of capacitors isn't serious with C four. So first of all, I want combined C one and C two and they're in Siris. So, Aiken, take the products divide by the sum that gives us 15 times three over 15 plus three. She comes at 2.5 Micro Fareed's. So now we have something like this with 2.5 on top and six on the bottom. And now those two are in parallels. We can just add them. So six plus 2.5 is eight micro fair words. And now we're down to just two capacitors. If one. This is 8.58 point five and one is 20 and now they're in Siris. We can do the same things we do for the 1st 18.5 times 20 divided by 8.5 plus 20 and rounded. That comes out to about 5.96 Micro Fareed's. So now we have the total equivalent capacitance. And now let's say we want to figure out the charge on each capacitor and we know the potential difference from the beginning to the end of this entire configuration. It's 15 volts and some things that will need to keep in mind to figure out the charge. Any capacitors in Syria's, they're gonna have the same charge. And any circuit components that air in parallel will have the same voltage drop across the entire branch. So first of all, what I can say is that let's look at this last, uh, couple capacitors that I drew, so we know that the charge on each of them is gonna be the same. Yes, we can say que four, this is This is ah, C four from the original drawing. Soak you for it's gonna be, um, the equivalent capacitance of the whole circuit, which is this times the entire voltage drop, which is 5.96 times 15. And that comes out to broach five. Finance six is rounded. So 89.5 micro cool ums. So that is Q four. And it's also the charge on this, which is these two combined. And we know that the voltage drop across both of those branches is gonna be the same. So we can figure out what that is by saying Delta V now I'm gonna go from a to four, which is basically saying from a to so from here to here, that whole bolsters drop. It's gonna be Q four over, uh see, Well, it's gonna be the 1st 3 capacitors. So all three of those this whole configuration there, which is 89 point 5/8 89.0.5, that's 10.5 to 9 volts. So now we know that the voltage for me, the that branch and on this branch is gonna be 10.5 to 9 bolts. So now we can figure out the charge on this bottom capacitor c three, uh, so Q three. It's gonna be C three times Delta bi from 8 to 4, because that's the vultures shop across that capacitor and see three is six micro Coolum or Micro Fareed's and the voltage is 10 point 5 to 9, and that gives us 63.2 micro cool rooms. So 63.2 micro columns is Q three, which is here. And we know that the charge on this entire combination of C 12 and three has to be 89.5 like her cool ums, cause that's what we got from the original part. Then we can say the top branch is just the whole charge. 89.5 minus the charge on C three. So ah Q one and Q two are both going to be, UH, 89.5 minus 63.2, which is 26.3 micro cool rooms. And we know the charge on C one and C two must both be that because they're in Siris. So now we know all four. Q. One is 26.3 micro columns. You two is also 26.3 Micro Coombs Q 3 63.2 Micro Coombs and Q four is 89.5. Biker Coombs. So we had to kind of go forwards to figure out the total capacitance and then work backwards from there all the way back to the original circuit to get the charges on each capacitor

In this question we have a second retreat capacitors. Okay C one C 2. And then this is in series of c. three. He's connected to a power supply which we don't know the footage. Okay. And then we had given that um C one is six micro ferret. C. Two. Yes. Tree micro ferret. See tree is five micro ferret. also given that to one is 40. Thank you too. Sorry you two is 40 micro ferry. Actually passing the question. You want to find Q one Q three And then the rotation apply across capacitors. Okay so okay to find um Q. One. Okay first we need to calculate um be too. Okay me too. He would be using a formula. Can we go to C. V. Okay so we too is you to give up by c. two for the micro cologne? This call on developed by tree micro ferret and you get 13.3 votes and then we want is equal to be too. So 2 1 is c. one. We won six micro ferret Times 13.3 words. We get 80 micro Colombians. Okay so this is the answer of part a hyperion to calculate your tree. So um Q three is going to be equal to Q one task you too because um the trees in series with The parallel combination of c. one and c. two. So uh the charges start on the capacitors in series are the same. So Cuban prosecutors equal to Q. Tree. And we have 120 Micro column. Right? So if that uh we can do part C. Okay so to find a B. Uh the power supply so we can calculate the tree is going to be Q. Tree. They were by sea tree. 120 Micro Kalindi Bye Bye. Five micro ferret. You get 24 woods and the power of the footage of the power supply will be be one class Vetri. We get 13.3 plus 24 37.3 votes. So this is the answer for Patsy and that's all for this question.


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