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In the figure shown, R1-Rz-2 ko?, and C1= 4700 LF: The capacitor is initially uncharged when the circuit is connected to the battery, which provides a voltage of 20...

Question

In the figure shown, R1-Rz-2 ko?, and C1= 4700 LF: The capacitor is initially uncharged when the circuit is connected to the battery, which provides a voltage of 20 V. After 2.5 s what will be the magnitude and direction of the current across the resistor R1?Select one: 11.8 mA to the right5.9 mA to the right11.8 mA to the left5.9 mA to the left

In the figure shown, R1-Rz-2 ko?, and C1= 4700 LF: The capacitor is initially uncharged when the circuit is connected to the battery, which provides a voltage of 20 V. After 2.5 s what will be the magnitude and direction of the current across the resistor R1? Select one: 11.8 mA to the right 5.9 mA to the right 11.8 mA to the left 5.9 mA to the left



Answers

Figure $27-63$ shows an ideal battery of emf $\mathscr{E}=12 \mathrm{V}$ a resistor of resistance $R=4.0 \Omega,$ and an uncharged capacitor of
capacitance $C=4.0 \mu$ . After switch $S$ is closed, what is the current
through the resistor when the charge on the capacitor is 8.0$\mu C ?$

With what we have given. So we have given that this connection is not this connection is made and this connection is broken in the beginning. So this C one charges with the 24 vote so we can find the charge stored on capacitor one that will be this one. So let's denote it as q zero, because that won't be the final charge on C one. So let's do the multiplication. We know that semen is one micro Farid, and we not it's 24. So the answer is 24 micro cooler, not micro fired. I'm sorry about that there. Then let's find out the net capacitance of C two and C three. They are in serious, as you can see here. So the net capacitance C to three here is able to see 23 in verses to see to inverse. Let's see. Three involves soc To is to my professor cities to perform. I repair it. If you perform this calculation, you get C to three inverse at 30.916 So taking invoice again, he will get C to three as 1.91 micro fatter. Now what we do after this is that we break this connection completely on. Then we have this connection made. So we have C to three here in parallel connection with C one. So as you can see, they're in parallel connections, so they must have same potential difference. They say This is Point C. This is pointy potential difference between point See Andy. It's same for both C one and C to three. Remember that Mrs C to three Nazi 23 individually. So let's start with this Q zero, because once you make this connection here, C one deposit some charge on this serious combination on DSI charges depleted on C one, so Q zero is distributed among see one and so C one and C to three. This way. Secure zero sq one plus que trophy on Q zero. We have calculated it in the beginning here on dhe. We also know he want is equal to see when we want also cute to three C to three everyone because, as we said in the beginning, there in parallel connection, so they have same potential difference. So from this, you can find simplify for everyone on substituting the all the values you get 11.48 won't. So that's a valley off anyone now. Next, we are supposed to find the charge on the charge, so we're supposed to find charge. Let's find Q one there. Cuba is equal to see one, the one so we know. See, one is still one micro fired, so and everyone is 11.48 So this gives you simple value. 11 point for eight micro cooler, so that's your cue one on. Then let's find Q 23 and remember that C two on DSI three are in parallel, so they have same charge. So whatever charges here, negative charge goes here again. The positive same amount of charge here again, *** to charge here. So if you find Q 23 is, it is equal to see 23 the one which is equal to as we know. C two threes, 1.91 So that will be multiplication. 1.91 with 11.48 So that gives you 12.52 boat. Oh, sorry, micro cool room. So that's the charge on Cute. Just cue to three under. System off, See two and see three since, as we said before, they have same charges on each plate. Except the alternative positive and negative. So cute to three is equal to que Tu is equal to Q three. Is it well too? 12.52 micro cool. So we are done with finding charges. Now let's find the B two and B three. So we know now you Q 23 right? So Que Tu is equal to see two times we to we can find me, too from this. So the two is it took you to, which is 2.52 Michael Micro Coolum, divided by C two, which is to microfibers. So micro micro councils and you get answer in terms off go it. So the answer here is six point 26 Yeah, sorry about that. So that's your value of the two. Then we are supposed to find me three the same way, which is Q three divided by secretly. So Q three is also the same nest. WellPoint fight one. So except the three his 2.4. So your answer here is 5.218 boot. So that's similar eyes. Now let's see what's everyone, everyone is equal to 11.48 As you can see here, that means it's 11 were keeping only two significant digits. Q one corresponding is equal to 11.48 My cloak alone, which is again 11 Micro Pullo. Then be, too, is equal to seem 6.26 Let's keep it at 6.3 bowls, so Q Q two is equal to 12 point five, so we can approximate it saying it's 13 micro Coolum. Similarly, Q three is 13 micro column on B three, as we found before, 5.2 would thank you.

So over here we have we have uh, still good. Okay. And this is like this one and this year you like resistance on this is like capacity. Okay. And this is going like this way This way. Okay. And the battery it's depend that have a potential difference. That is 12 volt. Okay. And this is switch. And when city switches clothes this existence are having a value of four home And this capacitance have value of four macro fired. Right? And we need to find the third in the circuit when the, when the students have the task, you equals to the micro Poland. Right, Okay. All right. So we know the actor, we know that when we use, when we use the loop law, when we use the kids off slope. Now low blow the tops. Look now That states that the potential difference across some of the potential difference across uh, the circuit will be zero. So when we're going in the clockwise direction, this will be your 12, 12 world. Well world minus of It's currently I is going when cities blood then I are because we are going along the terms of minus of I. R. I. Into four and minus off. We're going from positive to negative side because it's really positive side because this is a political decide To cure one ship because potentially chemical two CV. So vehicle did nothing but screw up on the right and this is equal to zero. So this village 12- of I. Into four into the curriculum. Okay so afternoon to develop -6 Upon this c. c. is for medical in support of the R -6 people to different universities maybe two. So I guess I equal stoop 12- to sustain 10 upon four. So it will do nothing to find five empty. Okay thank you. So they.

We have capacitance even as one microfiber so one into tend to give our minus six fairer and C two is to micro terrors to molecular by 10 to the power minus six Fair initially capsule and Sylvanus and charged So we, at zero time is zero world and capacitance C two is charged with 1 50 world So we do at zero time is equal to 1 50 fold So when switch is closed and equilibrium has been teached, then we can write or even at infinity It calls to me to add infinity equals two we add in Freddie Okay, so now we will write the conservation of charge equation. So from conservation of charge equation, we can write See when we even at zero plus c two we two at g o equals to see when we won at infinity plus C two v two at Infinity Okay, so from here we can calculate we do add infinity or we infinity because we even infinity and we to infinity are equal to v infinity. This will be equals to C to B two at zero, divided by seven plus C two as we even at zero time is equal to zero. So after putting values, we get we at infinity. It calls to see two is to into 10 to the power minus six and we do is 1 50. Divided by seven is one in 2 10 to the four minus six. Plus C two is to into 10 to the power minus six. This will be equal in the unit of world. Okay, so now the value of V infinity from here will be equals 200 fold. So now, energy at zero time or initial energy, which is present only in the capacitance C two as seven capacitance is initially uncharged. So you add zero time is equals two one by two c two we to add zero square. Okay, so you, at zero will be equals 21 by two. C two is to Micro Ferrell's two and 24 minus six, and we do at zero is 1 57. 50 square. From here you at zero will be equals to 22.5 Millie jewels. No energy store act, equilibrium position or you infinity will be equals 21 by 27 plus C two multiplied by read. Infinity is square. Okay, we infinity square. So you add infinity will be equals. 21 by two and seven. Placido will be equals. 23 and 2, 10 to the power minus six, but applied by 100 square. So from here, you infinity comes out to be equals to 15 million Children. So this is the initial energy, and this is final energy. So from these two equations, we can identify the net energy flow, which will be equals two U G zero minus you, infinity. So from here, Delta, you will be equals to 7.5 million. Jewel, this is our answer for that question, okay?

Hi. In the given problem here there is an unknown resistance are put in series with at the president's whose capacitance is 20 micro Farage, This is positive. This is negative. And here this is positive our sell Both of them are connected with a cell having an aim of off 21 year old and the current passing through this combination is I is equal to 20 million and beyond the charges told over the politics of the capacitor is 200 micro column. So the potential drop that grows the plates of the capacitor is we see this will do Q by sea for you this is 200 Micro Kula means 202 tennis partner in the sixth You see, this is 20 micro means again Standish for minus six carat. So canceling all these things we see means the potential dropped across the plates of the capacitor comes out to be 10 wall Here This is the potential drop across the resistor, which is for the timing is missing. As you know, in cities, the net potential means we are plus we see to drop across various elements. The algebraic sum should be equal to the native applied. So here we are will come out to be e minus. We see, or we can say 20 minus 10. Mean Spain world. So for the resistor, you know, the value of the current, the magnitude of the current passing to it and, uh, potential drop taking place across it. So using arm slope R is equal to be by I four v. This is we are which is and rolled divided by couldn't the current remains same in serious combinations. So this is 20 million or 20 into tended bar minus three. I'm here. So it becomes Standish before divided by 20 on Or we can say this is bye 100 all. And here it becomes the answer for the given problem. Thank you.


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