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Capacitor of capacitance C 4.07 mFis connected in series with switch; resistor of resistance R=3.1kn and battery of emf E = 2.25 V: The capacitor is initially uncha...

Question

Capacitor of capacitance C 4.07 mFis connected in series with switch; resistor of resistance R=3.1kn and battery of emf E = 2.25 V: The capacitor is initially uncharged. The switch is closed at time =0.What is the amount of energy stored in the capacitor after 1.5 time constants have elapsed?Calculate the energy in Joules Round off your answer to 4 decimal places but DO NOT enter the unit here

capacitor of capacitance C 4.07 mFis connected in series with switch; resistor of resistance R=3.1kn and battery of emf E = 2.25 V: The capacitor is initially uncharged. The switch is closed at time =0. What is the amount of energy stored in the capacitor after 1.5 time constants have elapsed? Calculate the energy in Joules Round off your answer to 4 decimal places but DO NOT enter the unit here



Answers

You connect a battery, resistor, and capacitor as in Fig. $26.20 \mathrm{a},$ where $\mathcal{E}=36.0 \mathrm{~V}, C=5.00 \mu \mathrm{F},$ and $R=120 \Omega .$ The switch $S$ is closed at $t=0 .$ (a) When the voltage across the capacitor is $8.00 \mathrm{~V},$ what is the magnitude of the current in the circuit? (b) At what time $t$ after the switch is closed is the voltage across the capacitor $8.00 \mathrm{~V} ?$ (c) When the voltage across the capacitor is $8.00 \mathrm{~V},$ at what rate is energy being stored in the capacitor?

All right. So for this question, we know that the current on the passenger and the right ask you go too. The fastest times, the M F times one minus it to the native t over our city, right? Yeah. Meanwhile, the current can we write us the year f over our having to the negative TFRC. So we know at this moment, the current a one, two, three, three emperors, right. And charge is equal to forty has tend to the native six. So this is a cool and this is him. So from the second question, when they know that around the these first two questions second question second question, we can know that the IMF taps into the negative of RC. You see, I want to three star, which is thirty six great, thirty six votes. And from the first question, will you know that? So if we divide the the Damascus on both sides, so the yeah minus Yeah, I'm letting it over r c if they go to forty times ten to objective six over big basket, which you will give us eight. Great. So IMF minus this part that this part which is three are, which is thirty six secretive eight bullets, which will give us the IMF going to eight nine plus thirty six go to forty four. Felt So there is the IMF off the battery. Okay, that's for questioning. No question. Be again frying cushion to say that Yes. Forty four. As to the day he over r C. You want to thirty six? Great. So we can have that two. They take the natural on both sides. You're going. He was our C no. I never overnight and are still say's five times ten to the negative six lot natural eleven. Overnight flooding The calculator. You can have the correctness in, you know, Sex, Cristian. See? So at this moment, the voting age on the capacitor should be the f I was into elective Teo varsity. So Hee chul a t e times ninety over r. C. We already know that from here is secret, too. I'm having over night over eleven. So it's forty four. Time's now over eleven. Or you can see from this equation. Is he going to thirty six? That's the voyage, Ambassador. So the power on the capacitor I see. So the current times, the voltage, which is gonna be three times this number. So eighteen, one hundred await four wrote. And for the battery. Should we put you into current times, The total vote, which is to the IMF so is three times forty four is gonna give us, um, one hundred thirty two votes.

Everyone in document circuit Kappa Stan having the tapestries find micro parity. The distance is pumped onto you. E m f of poverty is 36 1. In the first part, we have to file the current in the circuit pain potential across campus to to be eight words In second part, we have to find the time and potentially across campus to to be eight point in third part. We have to find rate of energy store. Yeah, in the capital. Ben potentially across it to be able to chart is storing the catastrophic is given by e into C one minus explanation of minus to your point here and current flowing through It is given by he upon our exponential of minus city upon here and potentially cross cap foster will be Q upon seat that is E minus into one minus explanation of three points here now from equation three. Mm, yeah, we will get V. C is given a PMF is 36 1 minus exponential of minus key upon here. So from here, explanation of dynasty upon CIA having the value seven by nine. Yeah, no current is to find us e upon our explanation of minus T of bonds. Er e is 36 r is given quantum d o and 7.9. So currently you will get 123 MP. This is part of a Now, in part, we using equation three b c is eight 36 1 minus exponential. Up to you. She is five micro. Um, and ar is one country so below of the u one gauge. Okay, Yeah. 2.5 10 to the power minus four seconds. Mm hmm. This is answered. Nazi part energy. Storing the capital is defined as chewy square by sick. That is he square. Sue. Yeah. She square up into C one minus exponential of minus. Do your policy here. So rate off dissipation of the rate of the store of energy in the capital. Baby is square. See into zero minus two and two. Mhm. One miner's explanation of two CR into develop on cm. Mhm. Yeah. Mhm. Mm. So it is to wish to e square. My, uh, bon minus. Uh huh. Into no substitute. 30 60 square. Papon 1 21 minus explanation of 2.5 10 to the four minus school of one one. Don't take into five into 10 to de power minus six into group 105 10 to the par minus. Pull upon one country and took 10 to the power minus six. So raped off. Storing the energy in the cattle step people catch right? Yeah, Actually, please, I have to make a correction here. Mhm. So it is to be. And why 20 age June per second. That's all. Thanks for watching it.

In the first part of this question, we're going to kill Claire. The time constraint. Let's find this dog with the equipment no equals two RC were seized the contestants off the capacitor. Let's call it a question one writing the values for this RNC iniquity in one we will get, though, equals two 75.1 to play tennis for three. Micah into 25.0 multiplied by tennis part minus seeks federal. So this will give us toe equals two. One point did. Second, In part B of this question, we need to find that total charge The charge on the capacitor a time d equals Toto, that is, Do you at the time where this time equals Toto. In order to complete this cure, we ride the Formula Two equals to go not into 0.632 where the securities maximum store charging capacitor and it is equals toe seeing to see where this is the potential difference off the battery. Now, using this well, you we can write this equation has two equals toe see into 0.632 Now setting the values off the sea and into this equation. We will get two equals to 25.0 multiplied voters for money. Six. Ferrari into 1 to 12 10 World in tow. 0.632 This is a coastal to it was too. 1.90 multiplied Butters part minus focal. So end of the question.

C. circuit. We were told that the resistor has a resistance of 75 Times 10 to the three homes. The capacitor you have a capacitance of 25 Times 10 to the -6 parents. And the m for the whole package of the battery. He's given us 12 votes. And so we want to calculate the time constant of the circuit for part A. And part B. Want to calculate the charging the capacitor after one second. So to find the time constantly. Just use the equation for time constant which is how is equal to the resistance. Time to capacity it we know both of those values. So we just plug them in to get the value for the time constant. And to find the charge on the capacitor after one second. For part B. Who is the equation for the charge on the capacitor as it's storing charge which is Q. Charging the capacitor is equal to capital Q. The maximum charge that the capacity can store times one minus E. To the minus T. To verify the time constant all time. See? Yeah and here capital Q. The maximum charge that the capacity can store is equal to the capacitance times the voltage of the battery. And you just plug that in. And we can see that we'll have all the values after we calculate the time constant in part A. So we're just poking our values and we get the answer for The not to charge after 1/2. So A. We're looking at the time constant our time. See So we're just poking our values 75 10- 10. 3 times 25 Times 10 to the -6 We get Time constant is 1.88 seconds now. Part B. We're looking for the charge on the capacitor after one second. So we have t to put in one second and we said that equation is little cue the charging. The capacitor is equally capital Q. And the maximum charge which we said is capacitance C terms of altered at the battery. And this is multiplied by one E. To the minus T. Divided by our time. See. Mhm. So we can just plug in what we know. So capacitance 25 10 to -6 Voltage in the battery 12 and then one minus E. To the minus 1 40 Divided by Art EMC which we found as one Mhm. Mhm. So we get Q. Is equal to one point two for attempts 10 to the minus form problems of change. Yeah.


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