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2) Find the total equivalent capacitance of the entire arrangement of capacitors pictured below Then find the voltage across, the magnitude of the charge stored on ...

Question

2) Find the total equivalent capacitance of the entire arrangement of capacitors pictured below Then find the voltage across, the magnitude of the charge stored on the plates of,and the energy stored in the 2.5714 Farad capacitor: [Hint: while finding the total equivalent capacitance, it helps to show a step- by-step simplification of the circuit with pictures drawn for each step. These diagrams can then be used to help find the follow-up information:]ViB = 9voltsqF6.1364F9F2tF9F2-5+14F9FLi F

2) Find the total equivalent capacitance of the entire arrangement of capacitors pictured below Then find the voltage across, the magnitude of the charge stored on the plates of,and the energy stored in the 2.5714 Farad capacitor: [Hint: while finding the total equivalent capacitance, it helps to show a step- by-step simplification of the circuit with pictures drawn for each step. These diagrams can then be used to help find the follow-up information:] ViB = 9volts qF 6.1364F 9F 2tF 9F 2-5+14F 9F Li F



Answers

Find (a) the equivalent capacitance of the capacitors in Figure P26.18, (b) the charge on each capacitor, and (c) the potential difference across each capacitor.

Belongs to the capacitor topic in which we have three capacitors in seven equals to 45 micro fairer and C two equals to 65 micro fairer. And si three equals to 80 microfiber. These are connected in this series. So for the part A we have to compute the equivalent to pass it and see. So for the series we know that the equivalent capacitance is one by C equals to one by seven less one by C two plus one by C. Three. So substituting values. So we get one by 45 less one by 65 plus one by 80. So from here after solving CQ violent will be equal to 19.96 micro ferret. So this becomes the answer for the part of the problem. Now for the part B we have to determine the charge on each capacitor. So since capacitors are in these cities, so charge Q. It will be equivalent will be equal to the equivalent capacitance, particularly potential difference, equivalent capacitance is 19.96 and the connected potential difference, it is 48 world battery. So substituting values. So we will get that charge Q. That is equal to 9 58. My curriculum. So since capacitors are in serious, so Cuban equals two Q two, that is equal to Q. Three And it will be equal to this value. So 958 Micro column. So this becomes the answer for the part B of the problem. Okay, now for the party we have to determine the energy stored in the each capacitor. So you won for the capacitor seven. So it will be equals two Cubans square divided by 27 So Cuban which is this value. So 9 58 manipulated by 10 to the power minus six column holy square divided by two molecular basis even which is 45. Multiplied by 10 to the power minus six federal. So from here we get you one that is equal to 10.2 million jewel. So this becomes the energy stored in the cap set at seven. Okay, now for the capacitor C. To the energy story to it will be equal to that Q two squared divided by two C. Two. So cute to which is again 9 58 Into 10. To the power -6 column Holy Square. They were by two molecular basis to which is 65 microfiber. That is 10 to the power -630. From here you two is equal to 7.06 million jewel. Okay. And similarly you three will be equals two. Again 9 58 into 10 to the power minus six Holy square that is Q three divided by two manipulated by C. Three which is equal to 18 manipulated by 10 to the power minus six third. So from here after solving U. Three equals to 5.74 million jewel. So these are the energies value for the capacitor C two and capacitor C three. Okay, now for the last part of the in which we have to we have to show that total energy you found in the party, so you total that is equal to you one plus youtube plus you three. So substituting values. So you want that is equal to 10.2 million jewel Plus 7.06 million jewel plus 5.74 million jewel. Okay, so we can right here also millie jewel. Okay, so from here total energy you comes out to be 23.0 million jewel. So we have to verify it. It is the same as the energy store with the covenant capacity. And so you it will be equal to one by to see equivalent, multiplied by the square. So one by two manipulated by C. Equivalent which is equal to 19.96 micro fairer. That is 10 to the power minus six. Further. So holy spare manipulated by V, Which is equals to 48 walls of 48 square From here. After solving, we will get that you it will be equal to the same 23.0 million jewel. So this becomes the answer for these questions. So we can say that both energies are same. Okay, so this is verified that energies are equal. Okay.

So here we have the circuit and these are the capacitors, Eight microphone at six microphone to micro fabric and eight microphone connected here. And we need to find out the total capacitance of this circuit. So as these two capacitors are connected in parallel. So we will effectively use the expression or the capacitance is connected in parallel. It will be seven plus C two. And for the capacitance is in series videos 72 by seven plus C two. So as these two capacitors are in parallel. So the net capacitance here will be 6-plus 2, that is it micro for it And this eight and this it at this eight. These three capacitors are now connected in series. So the net capacitance will be now one by C one plus one by C two plus one by C three is equal to one by sea in series. So here we put the value speak. It won by CS as one by eight plus one by eight plus one bite. So in 23 times. So this gives us The capacitance is as here by three. So this is the net capacitance of the given circuit here. Okay, so this is the net capacitance and let us find out on each capacitor what will be the church. So as we have figured out the net capacitance, the total voltage applied here is nine Volt voltage sources nine world. So we know that charge will be CN two V. This is the next charge which will be emitted from the battery. That will be hit by three into nine. That is 24. My curriculum because we have taken in micro parity. So this is the charge which is emitted by the battery 24th micro column. So on this capacity, the charge will be 24 Micro column only. So this display will have plus 20 footers will have -24. Similarly displayed here will have minus 24 my curriculum And here we'll have plus 24 micro column church. And here the charge will be divided And in what ratio it will be divided. Let us figure out that. So basically 24 Micro column charges coming out here and these two capacitors there in Berlin. So if we use the expression Q. Is equal to C. B. So in parallel we have the voltage which is constant. So that means Q. is directly proportional to the capacitance of the branch. That means this 24 micro column, it has to be divided in the ratio of the capacitance is so he had these capacitance is there in the issue three and one it's a judge. We have to send three part of judge Out of 4th from this 24 Micro Cola and through here 1/4 will only flow. So this will be six my curriculum. And this will be 15 micro column. So we get that the charge through six micro for it will be 18 Micro column and just through this two microfiber will be six. My curriculum and let us also computer in the circuit the difference in potential across each capacitor. So once we have figured out the church so let us redraw this quite more effectively. So we had eight micro for it here and connected to six micro for it and here we had to micro ferret in parallel and we had yet micro for it here as well. And this was connected to the source nine world. And the charge that your paint was 24 Micro column deposited on this capacity 24 my curriculum deposited on this capacity as well And then 18 μ Colombia and six My curriculum here on this capacitors. So once we have the value of C. And Q. Then we can get the voltage difference across the capacitor to find the voltage we will use Q. Is equal to C. V. So we have Q N C. So we will be cube. I see. So here cuba I see 18 by six. So that will be three volt. And across this capacity we will have six by two that is three volts because and it should be same because they are in parallel across this capacitor world age will be Cuba. I see that is 24 x eight and this is three bolt And here also it will be three world because total supply was nine world. Three was applied across this capacity. Three was applied across these two terminals total six and remaining three volts will be applied across this capacitors

In the given problem may have been given series and parallel combination of the capacitors. And we have to find the equivalent capacitance off this combination. And here clearly, these two capacitors, most of all, are in parallel. And then this federal combination is in Siris it a turban. Here, this is then micro Fred, this is 2.5 Michel Ferret. And finally, this is just 0.30 micro fatted. So as then, my grow fat it and do 0.5 micro fatted capacitors, uh, in parallel combination. So their net capacitance is given us c b. We can see. So this barrel combination city comes out. Toby 10 Micro fire. It lost 2.5 micro carry. It becomes well, 0.5 micro parrot. No, this city is in Siris, the 0.0 micro ferret. So finally equivalent capacitance off the circuit is equi valent. The accidents see, because now will be to capacitors are in cities. One is this which in in a see P and another is this 0.30 So it will become 12.5 in 20.30 being invited by 12.5 plus 0.30 because they know if only to capacitors C one and C two. Our impact in cities than their neck capacitance is given asked wanting to see two upon us even less C two. So using this relation, the equal and capacitance becomes this micro ferret and then we can let it the final answer. We come out to be zero point. So nine my grow Harding. It's the final arm, so thank you.

In this question we are given this up network of capacitors. So we want to find the equivalent capacitance between points. B so uh to do this question. Okay the first thing that we do is to redraw the kids. Okay so become this. He Okay so we have four micro firing up here to my crew down here in micro ferret. For micro ferret and to micro carrier. Okay, so if you look at this skanky arrangement can see that. Look at these two points cnd. Okay you can probably say that that I V. C. D zero. Okay because uh uh the upper branch you have to for micro ferret capacitors in series. In the bottom branch you have to to my profile capacitors in series and here is in the middle so the potential will be the same. So we don't have zero. Okay, no charge. Uh store in the in microfiber capacitor. Keep. Uh huh. You can remove the eight micro feral capacitor and the city is still the same. Okay. Right so you can read rather flick it again this time without the macro ambassador. Yeah so keep so we have to follow micro fabric on top and to micro Farrant capacitors below. Yeah so the top ranch branch. Okay the capacitance is mm I called a C. One to be one of the four micro parrot. That's one over for micro parrot. You take the recipe about that and you get to micro ferret. Okay and then the bottom branch. Okay I'm going to call it C. Two. So to micro ferret to ferret the recipe for a bit is one group there. And since I. C. One and C. Two parallel. So C. A. B. S. You want to see too? Just remarkable. Okay so this is the capacitance of this level of capacitors. That's all for this question.


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