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(a) 4 52 resistos €yetem Drenz MaconneceosenesVF capacitobattery. Wnat ne Mayimum cnargewhich this capacito_charged when the battery VoltaqeV? (When entering ...

Question

(a) 4 52 resistos €yetem Drenz MaconneceosenesVF capacitobattery. Wnat ne Mayimum cnargewhich this capacito_charged when the battery VoltaqeV? (When entering unitsMcroTor tne metric(b) Initially the capacitor has Zero cnarge,charbme during the charqina process will the charoeFnis cadaciton15.2 VC?(c) Tnc = cnaclior original resistor)fully charged The battcry removcd und the capacltor dischargcd throughWhat willthe capacitor aftcr 0.208 ms? ( Assume that the bulb has ble same resistancecnarde

(a) 4 52 resistos €yetem Drenz Ma conneceo senes VF capacito battery. Wnat ne Mayimum cnarge which this capacito_ charged when the battery Voltaqe V? (When entering units McroTor tne metric (b) Initially the capacitor has Zero cnarge, charbme during the charqina process will the charoe Fnis cadaciton 15.2 VC? (c) Tnc = cnaclior original resistor) fully charged The battcry removcd und the capacltor dischargcd through What will the capacitor aftcr 0.208 ms? ( Assume that the bulb has ble same resistance cnarde



Answers

A capacitor is fully charged using a battery that supplies $V_{e \mathrm{mf}}=133.1 \mathrm{~V}$ The battery is disconnected, and a $655.1-\Omega$ resistor is connected across the capacitor. The current flowing through the resistor after $1.743 \mathrm{~s}$ is $0.1745 \mathrm{~A}$. What is the capacitance of the capacitor?

Not a healthy given problem. The energy initially stored in the capacitor is given by you nor is equal to Cunard squarely by by two times of capacitance. So a student your values for Cunard, which is zero pour into 0069 Coolum swear. Divided by two times off 4.62 times 10 to the power minus six. Fair odds. This Q's US a. 5.15 jewels. Well, well, I'll be off the problem. We need to find electrical power that's pretty resistant just after the connection is buried, which is given by P nod, Um, physical toe I know squarely by times are, which is it called Thio? You know, Lord Squared, divided by R C, which is on Lord Square. So square is outside story. Gums are we substitute the values for q dot sos una 0.0.69 square divided by, um and 50 homes. Times capacitance off. 4.62 times dental power minus six. Farrar, uh, this full square square. Ah, this gives air so hour off to 6 to 4 user walks. What? Sea off the problem, Francie. Now we need to find electrical power dissipated in the resistor at the instant when the energy storing the professor has decreased to the half. Wailing off is calculated in there, but a the charge or the capacitor at any instant is given by a Q musical cue nod. E exponential minus t lead by very TD like they are, See, So these are No. Two minus one minus sign here. The energy stories therefore, can Burton is usable to Q squared right by to see. It's a shooting value of fuel, which is Cunard squared, divided by to see times exponential minus T O R R c this whole square we know you will not square divide by to see Is it called to, you know? So we can write a bovie coach in terms of you know, this with them. Three more Pierre former in the studio like IRC Whole Square, and this requires us to write exponential. It's one inch of minus T Dubai. There are sea is equal. Thio Square is equal to one over half. From here, we can write, then ah e minus T divided by minus T derided by R C, is equal to one over square root off to the current in the circuit is our visible toe. I nod g minus t right by R c So we substituted value for exponential which is I know Bye bye School talk to So the power dissipated in resistance can be written There's ah, our our isn't cool too I know divided by screwed off A two square terms are Then we get the one or two we know divided by our square times are which is equal to one over to you Nod You're right by r C Squared times are is equal to one over r C times Accu Nord square Divide by to see substituting your values we get here This is a call to our, you know, divided by our scene. So we substituted values. You know What we hear is 5.15 jewels divided by age 50 all homes times 4.62 This gives us 13 10 warts

In this problem we have given the capacitance C. Is equal to 15.19 MF. Changing the unit, I can write, it is at 15.19 multiplication 10 to the four minus three F. Now the value of I can be written in p e m F by our multiplication into the power minus T by RC. So just putting the value in this Express and I can write the value of I is equal to 131.1 by 616.5. My certificates I need to be power minus 3.871 by 616.5 multiplication 15.19 multiplication 10 to the power minus three. And for the solving I get the value age 0.213 multiplication E. To the power minus 0.413 which is equal to 0.213 multiplication euro 0.661 Which is equal to 0.1407 He has our answer.

To solve this problem, I will use the formula V e m f is equal to I uh by he to the power minus T by RC. So just putting the value in this expression, I can write the express vintage Euro .1-0 3 Multiplication 6 9 3.5 Bye. He took the power minus six point 615 Bye 69 30 0.5 Multiplication 19.79 multiplication Tend to depart -3. On solving it, I finally get the value edge 83 point 4 3 p by it to the par minus .482. on solving it for the I get the value it 83 point 43 B. Bye 0.617, which is equal to 135 point to be as the supplied EMF.

Hi there. So for this problem we have uh sets. Yeah point for nana Ferraris capacitor and it is being charged with potential difference of 24 bold use. Um And it is connected in Syria's with a coil that has um and in the tense of 0.0 60 sets and negligible resistance. So after the circus has been completed there are current oscillations of course, because of that independence. So part A of this problem is at what instant when the charge of the capacitor. So that problem. Now the charge of the capacity for this part is going to be 0.0. Aid me Crow cole arms. How much energy is the story in the capacitor and in the in doctor. And what is the current? Uh indian doctor? So we need to determine the um the energy indian doctor. They're going to call you of held and the current. So we know that initial energy store in the capacity or is chaired between the induct er and the capacitor. So the mutual energy in the capacity or is going to be used zero. We're gonna call it like that. one half of the capacities times the initial and potential difference. So we plot all of these values that we know 6.49 of our radios. Nano means 10 to the -9 for radios and 24 volt shoes square. So this will give us a value of 1.80 for micro jewels. This energy is chaired between the induct er and the capacitor. So the energy and the capacitor at this new time is going to be equal to the charge store on it over two times the capacities. So we will have that. We plot all those values. We know that the charge, the capacitor is 0.08 me crow Colom's Square over two times 6.40. None of our ideas. So when we plot this into the calculator, we obtain a value of seeds .5 micro jewels. So the energy remaining indian Doctor is just simply the The difference between the initial one and the energy is stored in the capacitor. So that will be 1.80 for micro jewels minus 0.5 mi cro jewels. The energy in the capacitor. So that will be 1.30 for me. Crow Ferrario. So this is the energy um in the in Doctor now and we know that the energy of the Doctor relates with the, With the current by the following four, of the in Dayton's times the current square. So we need to solve for the current this expression. So that will be two times them energy in the in the tour over the conductance and the square root of this. And this will give us the current. So okay of course we need to take the positive value because it is the physical interpretation. So that will be two times U. L. Over the independence. We plot dulls values in here. We know the value that we obtained for the energy which is 1.30 for um 34 times 10 to the minus sits because that's uh micro Over the importance which is 0.0 sits this sits so from this we're going to obtain that. The current indian doctor is 6.33. Yeah 37 times 10 to the minus three emperors. We can also convert this into a million pairs. That will be 6.37 milli amperes because merely is 10 to the minus three. So this is the current in the conductor. Now for party of this problem, we are told at the instance when the charge on the capacitor is the same as before. What are the voltages across the capacity and across the in doctor? And what is the rate at which current indian doctor is changing. So for this part we again have a 0.08 mi cro for areas um column. Sorry. And that's the charge in the capacitor. So when he took tane the potential difference when the capacity or charge is of this value and we found that the energy store in the capacitor is 0.5 mi cara jewels as we obtained before. So from there we can obtain the voltage, the new voltage in the in this capacity or so we will have to remember that this is related to one half of the capacities times the voltage in the capacity of the square. So if we solve for the politician, the capacitor is just simply two times you see oversee which is the capacities. So we plot all the information in here. So that's two times the energy story in there, which is 0.5 mi Cro jewels. That's the value that we obtained before. And with that charge of 0.08 Micro columns and the capacity is 0.40 Nana Farrah ideas. So we take the square root of all of this and we obtain about you for the potential difference of 12.5 bulges. So that's the potential difference in the capacity to read or now. The cross and the potential across the in that drawer. And the capacity tour is the same. So because they are in serious And so the potential of the capacitor is the same that the potential Indian doctors so that it is 12.5 bolts. Now, the next thing that we need to determine is how it's changing the potential and the electric potential in the in dot you are. So for that we used to follow in that the potential in the doctor is given by the um the magnitude of the independence times the variation of the current with respect to time. So we have That from here we can just sold for the variation of the current with respect to time. That's the value that we want to obtain. So that will be the potential difference in the in dr over the in Dayton. So that will be 12.5 balls over 0.0 60 sets. Which is the indulgence of this in doctor. So that will obtain that the um barry ation of the current in this in doctor is going to be 100 89 um Pers per second. So that's it for this problem.


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