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An RC circuit with C = 42 mF and =21 Q includes U V source. With the capacitor initially uncharged, an open switch in the circuit is closed. a) What is the voltage ...

Question

An RC circuit with C = 42 mF and =21 Q includes U V source. With the capacitor initially uncharged, an open switch in the circuit is closed. a) What is the voltage across the capacitor immediately after the switch is closed? b) What is the voltage across the resistor immediately after the switch is closed? c) What is the current in the resistor immediately after the switch is closed? d) What is the voltage across the capacitor after the switch has been closed for 1 s? e) What is the voltage acro

An RC circuit with C = 42 mF and =21 Q includes U V source. With the capacitor initially uncharged, an open switch in the circuit is closed. a) What is the voltage across the capacitor immediately after the switch is closed? b) What is the voltage across the resistor immediately after the switch is closed? c) What is the current in the resistor immediately after the switch is closed? d) What is the voltage across the capacitor after the switch has been closed for 1 s? e) What is the voltage across the resistor after the switch has been closed for 1 s? f) What is the current in the resistor after the switch has been closed for 1 s?



Answers

Consider the circuit below. The capacitor has a capacitance of $10 \mathrm{mF}$. The switch is closed and after a long time the capacitor is fully charged. (a) What is the current through each resistor a long time after the switch is closed? (b) What is the voltage across each resistor a long time after the switch is closed? (c) What is the voltage across the capacitor a long time after the switch is closed? (d) What is the charge on the capacitor a long time after the switch is closed? (e) The switch is then opened. The capacitor discharges through the resistors. How long from the time before the current drops to one fifth of the initial value?

Hi in the given problem. In And see our circuit. The value of capacities is 40 micro far it And the resistance is 6.0 oh the voltage of the source supplied across these two Is 24 volt. Now, in the first part of the problem, as initially the capacitor is not charged just to help close the switch of the circuit. So initially charge over the capacitor is zero. So the potential drop across it. B C. Is equal to given by cuba. I see that will be equal to zero, hence all the potential applied means all the applied voltage will be dropped across the resistance only. Hence the answer for this was part of the problem. The potential drop across the resistance will be equal to be not means 24 volt, which is the answer for this first part of this problem? No. In the second part of the problem, at the same time, we have to find the potential drop across capacity are also and that we have already discussed in the first part only that the potential drop taking place across capacity will be zero. Now, in the third part of the problem, at the same time, we have to find the current passing through this circuit. So using the equation for current in a charging capacitor, I is equal to I not into minus T. By how Well now is the time constant of the cr circuit. So for the beginning then we just Switch on the circuit. The time is zero hands. I will be equal to I not Into each department zero means it will come out to be I not only which will be given by me, not by art, so I not so I is equal to 24 x six means the current passing through the circuit in the beginning is 4.0. And beer, which is the answer for the third and the last part of this problem. Thank you.

In this problem. We have a circuit that looks somewhat like this. We have a switch here. Battery here. A passenger here, here, here. And we have two resistors here and we are asked to draw one An equivalent circuit with all the capacitors and resistors combined are one IHS 25 homes are too. Is 33 owns. See one IHS 46 my girl fair, it's too. Is 12 micro ferrets and C three is 23. My grow carrots C two and C three hour are parallel. So we do 12 plus 23. We get 35 micro ferrets And since C one and see our Siri's, we do the reciprocal 1/35 plus 1/46 and we get the overall capacitance is 19.9 Michael ferrets. The resistors are in Siris, so we just add them together. 25 plus 33 equals 58 homes. So are overall diagram is going to look like this and I resistant is 58 homes. This is a for the next part. We have to find out what the charges. After a long time it's past. We will use the formula charge equals capacitance times changing voltage. We're trying to find the charge at the 12 Micro Fareed conductor in voltage six, we multiply those remember 12 times, 10 to the negative, six times six and we get 72 times 10 to the negative six. Cool arms has our answer for be We have to get the time constant for C So our time comes to formalize this So are resistance for the overall circuit is 58 homes and our capacitance is 19 0.90 Micro Fareed's so again. 58 times 19.9 times 10 to the negative. Six. 1.15 times 10 to the negative three, That is C for D. We have to find out how much time for the voltage across combination of the capacitors is 50%. So the formula we're going to use is this b equals one minus the active T over time constant and we plug in those numbers the over oh cools more in minus e negative t over the time Constant. We're trying to find 50% so we get 0.5 equals one minus e to make tea over the time constant, which is 1.15 times 10 to the negative three we saw for time. Can we get 8.4 times? 10 to the negative for seconds.

For this circuit. Ah, we have. At the start, the switch is opened. Now the initial parts where the switch is close, the COMESA X s a kind of like he shot circuit to our since and he starts. It actually contains no charges. So current is free to flow Trudy capacitor very easily. And so the current who take a more favorable path through C one chess, Almost zero resistance or negligible resistance. So in this case, the overall resistance which the circuit or experience is just are too. And so we will be able to find initial currents based on the total vote fish or Yemen for the battery divided by the total effective resistance which is just are too. So 24 hours by 30 cloves is your point. Eat Milly impious mix to find the current when the capacitor is a carefully church. So when it's fully charged now the capacitor excess a well could suck it so it's a no currents can flow through it and the current clearly feel true one. So now the effective resistance off our new circuits would just be I want plus two anti soapy 40 kill homes and so the current new current that it's passing through are too now, is he Same? Um, ift but divided by I want plus two. So this issue 0.6 million times no b 12 open this reach after he has been close. So now the COMESA is fully charged and now we want open this reach. So what happens is 30 left site off The circuit is now ah broken circuit. And the only current they can floor from the Sebesta is on the look on the right. All right, so the capacitor work, he have currents flowing true Ah one only because that is the only close duke with Alka Bester. And now we want to find what if the current that is throwing to we won't find What's the time taken for the current that is flowing through our one to reach half the value. So the only interested in the left portion off our circuit right now right after it is fully charged. The left hindsight we can just ignore because no current floor it when it is opened. So for this particle circuit, you need to find the RC constant. You know what er is just are one. So there's 10,000 cease all contestants which is 10 micro 10 micro ferrets. And this will give us 2.1 seconds next to find me to find the time taken. We used to be our equation for the decay for current foreign RC circuit. So this I issue close to my not times like financial negative T o r c. We want to find the time when I issue close to half the initial value. So that's half off. I not so we can cancel the eye not on both sides of the equation. You are left with half physicals to exponential. Negative to you waas. We take long off both sex and every multiply negative R c over to D left. Financing for tea is your points your 69 sick. It's so this time required, you know, after the capacity is being charged and opened and the circuit is allowed to flow and the current would drop to 50% of its initial very

In this. Um, we need to calculate the charge on first as well as the second capacitor. Oh, we're going to forego cities off steps here. Notice was right that sista p in an r c circuit groot off the charge in I took you in circuit is small. Kill isn't going to kill zero because any should charge one minus is to minus t upon how that is Our secret is a time constant. It's market as aggression one. No, we need to find the charges given and cute doing capacity or see within See to respect Terry to know Billy Boyd says their districts which are shown in the circuit, are in pattern combination. So therefore, will first concrete battle combination So which is given by the question as Arvin Artoo upon on went, Bless I do. That's right. The values two kilo multiplied by its weeklong and treacle home last Uchino. So here we get the value asked, Well, under domes. This is the value of father combination that we haven't done so for this show on So capacity does it's even and c do are in battle in I repeat the capacitors even and see two are also imbalance, so we'll take the equivalent as C p. So when capacitors are in battle, their combination is getting Eric. So this, even Placido See even value is to include senators to minus six France Bless three microphone that is seeing good editors to minus six. So therefore CPSC will do five into tennis to minus experience. This is the capacitor equivalent value that we did. No, that's more to the second beach to step. Be now to calculate time constant That is so sure right here that how is required to our intimacy. But in this case, it will be our pee into a city that is equivalent values that we have already got in step away, which is equal to 1200 warms multiplied by five Micro Fred's So here. By my application, we get six into tennis two minus three seconds, which is a value for time constant that we get here Now We need to make use of equation one so right here using Equation one here, which is small. Q is equal to kill monkey, played by one minus. It is to minus T upon toe, but the six, including is to minus tree. But at the same time small Q is equal to key one plus killed too. So therefore, let's put this immigration while what we get as key one plus Que tu is equal to a few times. One minus is to minus t upon six in group analyst to minus three. Let's mark this as immigration, too, which we are going to use further. No steps See, since Stephen and C do are in Palin that you already know so by the formula that is really easy going to you want a bonus even and at the same time reconsider for second said That is cute too. Aw, phone CDO Therefore, can we say Cuban upon see one is equal to cute to a policy, too. That's wide. Therefore we get it. Ask you to music will do C two upon us. Even monkey pride back You won. That's for the value of C two, as three include Dennis to minus six on this even is to include entities to minus six multiplied by Cuban that we have So therefore, finally we get que tu is equal to one foreign five times Cuba. It's mark this as decoration. Three now many to substitute the value of cute too. Any questions? Do right here. Substitute the value off que tu in equation too, because we need to get the value 40 You are so therefore, what we get here as q one plus 1.5 times kyu won because you're a subsidiary in the value of Cuba, for that is equal to Q times one minus etess to minus t upon six include entities to minus three. No, that's all this father. Therefore, 2.5 times Cuban, we simply air that is equal to Q times one minus eat is to minus D. It is minus minus T upon six into generous to minus three. So therefore, finally begin it ask you one is equal. Joe CEO born full time skew and one minus It is, too. My honesty A Bone six in group and is to my industry. Let's mark this as equation for no, we'll do this step, Dina, since we know that cute too is 1.5 times Kyu won should put this value of key one from a question three. So therefore, 1.5 times we get the value off the one from Equation three. So what? Aggression? Three says as it is going to be boring for Q. Again, we have one more packet here that is one minus. Eat is to minus T upon 16 to Dennis to minus three. Therefore, finally, we get on six times Q multiplied by one minus. It is to minus T upon six in good. And it is to my ministry it's mark this as a gration five. No. Thus, what we know already is Q is equal to C B into absolute. Q is equal. Do see be mean to have slowed by using the same formula? So value CB that were already God is find Reynolds to minus six. Finance and value of Absalon is given as 1 20 world that is a battery wordage. So it is 16 to Dennis to minus four Leones next markers. No, what we're going to do is we'll substitute the value of Q in the question for in fire. So right here, substituting value off cue in the Immigrations four and five. So what we get here as Q one first, which is 0.4 times Q multiplied about one minus. It is to dynasty upon six included, and it is two minus three. So therefore 2.4 in good earnest to minus four Gloans and the Bad Amigos we're here remains the same. So my Nestea a bone six in Cook and his to mine industry now fork you too. The question is born six times Q. And one minus eat is to minus D upon six in progenitors two minus three. So what we're going to do is subsidiary the value of Qs six indoor endless to minus four groups. So 0.6 into six into tennis to minus four columns, and the bracket remains the same six into Dennis. To my mystery, it's calculated this and will come as 3.6 into generous Your Highness, for good arms multiplied by one minus. It is too dynasty upon six imprudence too minus tree. So this particular aggression is charge one Thrace capacity. We're right here, John. No, for his capacity. And this particular question is like car John, I think incapacity. This is what we can, right?


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