Chapter 25, Problem 067Your answer is partially correct.capacitor of capacitance C1 03 mF is connected in series with capacitor of capacitance Cz 2.93 mF; ad potent...

(III) In Fig. 19-66, suppose $C_1 = C_2 = C_3 = C_4 = C$. ($a$) Determine the equivalent capacitance between points a and b. ($b$) Determine the charge on each capacitor and the potential
difference across each in terms of $V$.

Okay. So relation between the charge capacitance on the voltage is given by charge equals capacitors time. Voltage. Now we are given that charge on each capacitor plate is 2800 micro cooler on dhe. We're supposed to find capacitance, and we are also given the voltage applied, applied to the capacity capacity. Now, Walter, just 9 30 world. So from that, you can easily guess the capacitance equals. Give me some time to type judge divided by mortage. Since charge is equal to 2800 micro Coolum, that is zero point zero zero to eight. Cool. Um, Okay. E have converted micro Coolum to cool. Um, just by dividing it by 1,000,000. Now, voltage is 9 30 and that's in the unit. So whenever you do any calculation, make sure that you have all the same units. That means all the SA units or on the sea genius units so that calculations become easy. Then you can convert it to appropriate units you need. So this division gives you the answer off. 0.0 zero 00 three. Oh. Found, which is also three points. You know, micro flattered. I hope this explains how to solve this particular question.

All right, So, uh, for this problem. So we're we're given this circuit. We have the capacity here, and, uh, there is a pastor, and there is extra and see will see three. So this is C three is the C one and the upper ways opera Wednesday too, and a devoted across the circus. And we know the perimeters. See, Wise turn Micro thirties. See, two is ah, five. I see. 3 15 Okay. And the voltage is 100 ports. So the question is, we want to find out the paramedics for to see onesie 23. So basically, we need to find out the voltage across, see 1 63 and the charge stored on them and also the energy starting them. So, uh, to figure this out, we can analyze this. Ah, see, one sea to firstly, because we can see that these two, they're negative. Parallel. So see, 12 were able to see one pussy too. Right. And to them Ah, we can find out the voltage Distributed on C three basic. It's B three. We were able to b times C one, too. Class C three and a new meter O B c one too. Okay, So, uh, this very actually gives you 50 boats and the q three actually equal Thio 33 times, C three according to the definition off the capacity of the capacitance. So this sickle to 7.5 times tend to negative force, Corpse and energy stored in ah, see, three is the U three, which ago to have seized three times of V three split. Okay, so the very is 1.88 times 10 to the negative to Joe's. And similarly, we can find out the bullet across the onesie to because see one sea to the air connecting Carol. So we won. Sorry. Devoted across sea winds B one B one equal V two equal. The times C three see 12 plus C three. Okay, so, uh, this very also equal to 50 warts and you're gonna find out secu one equal. See one times V one. So this video is ah five times 10 to 4 schools and we want you want, which is energy scolding. See, one is off C one times V once quit. So the video is 1.25 times to inter negative too. Jos and this cute too Ihsaa C two times three too, Right. So, uh, the better is, uh uh Well, so the very is 2.5 times turned thio the negative force Joe's and, uh, and a you too equal, huh? C two times Ah, be to squid. Right? So the video is 2.6 point 25 times tend to naval three jewels, okay?

So there's this question. We have a very complicated circuit, as Showalter left hand on the left side. Well, there's secret. No, The capacitor is in a simple parallel of theories relationship with any buzzer capacitors, so we cannot simplify the circuit into parallel in Siri's. So what can we do? So the question Give us a scheme to that. Assume a potential difference. Be a beak exist across the network, creates a potential difference for various past weighs, assumes network from A to B in terms of the charges off the capacitor and the capacitance. So let's try to think about different ways to coast through the circuit. So we had a one pass might be just here. So we asked. The baby equals C two because beach you, plus these three plus before a different path would be this. So it also equals you must close VC. We want house. Did you? And it doesn't pass? Would be Is this so it also equals you Fight Plus before, and I think that's way have that's also possible passes. And then there are also street independent charge relationships. So it's a total charge Cube, baby. So this is a charge and we can see from this French You may be equals cute you plus Q five and it also lead close if he goes this way. Q. And ask you for and another relationship exist in the middle if you want to look it here so they had q t close killer plus Casey, you might argue that you can also say Cuba, excuse your rescue pied, um, put. That is actually, um, that is actually duplicate with one of these relationships because if you say careful equals kiss three I just q five accused three Close um que five his equivalent to saying If we rearrange it So we have killed four equals cute you, plus Q five by and ask you one, and we know Q minus. Q. One is cute Story say we get to the tradition. So that's a start. We're not getting any sin You from the secret. We only have three independent equations for charge and three dependent equations floors above Pidge. So we will need to fire the equipment capacitance from these 60 creatures. So firstly, because you do not know what que vous that's trying to write Cuba in terms of C of e. So this because see, Clinton, that's B A B. Call CTU, reach you plus C +5355 The equipment tense. Phoebe B equals C. What do you want? Plus sleep for youth. Work lightly. Seat you reach you because see, my B one class system. Really? Please me. Okay, now we have a sit off. Six equations that gives a numbness 112 or high six. Could you cover? So these was 60 questions. So, um, it's first train. We will eventually try to in a minute. Or was a numbers that Would you not what say, from equation to equation. Um, five. And questions six. What we can do is we can see sitting homeland types. Feet equals C while you are pressing for before, um, would be one close See for before I even say we want to get a minute. See what? What we can do is instead of you want because they see won Tons. See, baby, why in this feature end similarly, this number five number six Setiabudi will cease three. These three. Let's see. What? See, baby minus b two. Okay, So when I was just trying to do this are trying to eliminate to be one for always easy questions. So using this part and Zan, let's eliminate even more off these more off the cottages Don't say it. I want to eliminate the five so I can use numbers. Three. She eliminated Thief five. So that's seen question for So see, you have done times feed. I I just write me a B a C for convenience. We could see to meet you plus C five v minus before so no, we have one too, sir, for we have a question. One question. 4546 Or this isn't you for the question while the question 4546 and awesome, You got have a few more angry findings, but we can human intimate Morsi's Let's try also eliminating these three using Cushion one and he's really piercing equations. Six. So, uh, jamboree very quickly. Six. Out put to circle sandwich Is that you? CTO Meet you? It cost me three the mind of speech You let us before. Classy one B minus Eugene. So let's rewrite this than see one just said your class ceased three times feet. You plus these three before equals one Plus these three times. G, Give me the chance. This is cracked. See? Will be 2663 feet. You plus is really for equals C because it's late. Okay, so I would causes cover six. So now we have used 1 to 3 to, um, eliminate straight different voltages in 4556 So we have gone from six on no sex equations to three unknowns, three equations, which is a huge, um, progress we have. So now. So ubiquitous we will be using is this is corps. Um, this is five. And this is six on DDE. Thinks so. It was good. It ended messy. I will really like everything because we still have a long way to go before we can finish this problem. If you do not follow, just go back a couple of seconds on the video and make sure you follow every city in the previous stage. Okay, So before I six, this is a pretty speech. Um, and I'd just call be above six to this new bitch. Okay, So our ultimate professor, of course, is to go from sorry equations. Three. No's just one question. One don't know, and we want to make sure that lost. All know we have is secret mint, but now we have three. So let's just eventually is one equation Thio hostages. He hasn't to you and then just keep to exist and simplify. Six. So let's we've eliminated of you want the three of the five that's tried to get him a to B for and you put a piercing close Rick Regis. But so let's trick you use people from four to even let me hug me. Six. From floor we had before equals sea creature like this. You actually plus plus because there is minus saying fun of that and see him, that is before, if we fluxus into the five and the six, you should have been six. We'll get something very messy, but I was simplifies them. So after I think the fire, both of them five and six will be hard, see if I see Cleveland plus Steve Ford C cripple it minus C for C five minus c five c one. See you close the four seats, you minus see. See one pretty because what we have in the mid 1345 so it's only devoted. Just we have left right now should TV and video C five C one sleeps three plus three secret about my list. Sees recieve C five C one seat. You stays three sees three seats. Two. Okay, So what you should do is you should try to fucking before going to be a father, to be six and simplify it. And to see whether you for your four matches mine here and our group's, um, ivy and beat you. Because for the last step, what we want to do this we watch. It eliminates a variable future so that we can we only get the equation off the C 1 65 secret violent and be so that physical. So what we can do is okay. Is Christian five too good to be too many trips off the other numbers and we can cross him here Or equivalently we can divide people. And what can we divide the question? Part in question six. So that's why I groom some sort of obvious on the inside and future is on the right hand side. So that's the division is going to be easier end. So now I divide them and I got equation. But that is kissing he loved by kissing, equals is divided by sis. So if you imagine this is a fraction in the sister's a fraction. This is a pre shell and getting, and we need to again simplify the hosting. Finally, we can see equivalent was left outside and what we get the result is actually quite messy, plus the onesie to see four plus one c two c five. So, as you see this question, it really isn't as easy is just simplifying circuit because you cannot sacrifice sick. It sees you sees three c four plus C h u C for C five plus thes three c four c five hoof. That's just in numerator. Least you have the denominator. We just see one cc c one c four plus one. See C two Caesar is pretty much just the possible combinations. Plus c juicy for plus C to see Fuck plus thes three c for plus See story. See, I all possible conditions, including see Fozzie. But this is the equivalent capacitors off This whole system is This is really a mess. These this is very complicated. And make sure you're Hispanic matches mine because there are 1,000,000 ways to get cases from. And finally we're clogging the numbers. Let me go back to Page fund, Mrs C. Choosing Blake was agency Once he's received a it's four point fine. Okay, I will not bother if you write everything out, But if you really do just put everything into this equation, you will end up getting six my apparent.

For this problem were given a circuit with three capacitors and a potential difference of 100V is applied across them and we want to find the charge voltage and energy for each of these three capacitors. So I've added in that charges typically given by capacitance times voltage and energy is given. Potential energy is given by one half times capacitance times voltage squared down in the bottom left in red. So let's start with the capacitor three. So this is part a uh the charge on capacitor three Is going to be the same as the charge on capacitors one and 2 together. Uh huh. Because Capacitor three is in series with the group of capacitors one and 2 and so they're going to have the same charge which can be found by using the equivalent capacitance times the voltage in the circuit. The equivalent capacitance will be one oversee one plus C two plus one, oversee three in verse. And so when you plug all that and you get that, the charge on capacitor three is 7.5 Times 10 to the negative for cool items for part B. In order to find the voltage, it's pretty easy now that we know the charge, The three is just going to be Q3 divided by C3 And you would get that the voltage in this case is 50V for part C to find the energy stored in capacitor three. That's just going to be one half C three v three squared. And again we know all of that information. So plugging in the values I get 1.875 times 10 to the negative to jules for part D. We are now looking for the charge Q1 on capacitor one but we know now that if The voltage drop across capacitor three is 50V, then the voltage drop across capacitor one, which will also be the voltage drop across capacitor to because they're in parallel has to be 50V because together These have to equal up to 100. So if the voltage drop is 50V which gives us the answer to the next part, we can easily find the charge. He won by multiplying C1 times B one and in this case you should get that the charge is five times 10 to the negative for cool arms. For E. That's where we wanted to find the one which is 50V for s again we're just using that same equation one half C v squared to get 1.25 times 10 to the negative to jules for the energy stored. And we can repeat this process. One more time for capacitor to uh the charge um on capacitor to would be capacitance, two times voltage too, Or 2.5 times 10 to the negative for cool OEMs. For H we already know V two is equal to 50 volts and for I we're squeezing it down here. The energy is one half C two V two squared or 6.25 Times 10 to the -3 jewels.