Find the charge and current at time in the circuit of figure 1 in R= 40

Name: find the charge and current at time in the circuit of figure 1 in r 40
Uploaded: 2022-01-04
Duration: 4 min 24 s
Channel: Numerade
Description: Find the charge and current at time in the circuit of figure 1 in R= 40

Question

Mahipal Kumawat · Accepted Answer

even circuit diagram in the question and we have resistance value. 40 conductance is one Henry and the capacitance is 16 multiply 10 to the power minus for Jared And the source voltage is 100 costs 20. So if we compare with the standard equation then we can write that the radiant, the angular frequency Omega is going to be 10 radiant per 2nd. 10 radiant per second. Now in the question we are going to find for the current value. So I. T. That will be given by the source holds E. T. Divide the impudence of this series Rlc circuit. So for a series rlc circuit the impedance JED is given by R plus J. Omega L minus one by omega psi. Now put the values are is 40 M. So it will be 40 plus G. Multiply, Omega is 10. Multiply L is one minus one by omega psi. Omega is 10. Multiply C is 16. Multiply 10 to the power minus four. Now if you solve this then we get around 40 and this This town will be more than this. 10. So it is going to be minus. So it will be -J 52.5. This is the value of impudence. Now we can find the magnitude of the impudence that will be under road 40 square plus 52.5 and it&#x27;s a square. Now if you solve this then we get approximately 66 and the phase of the impedance Z can be written as if you look at this Impedance which is 40 -J 52.5. It is in the fourth quadrant of complex numbers in the complex plane. It is in the fourth quadrant Let&#x27;s suppose this is real access, this is imaginary axis. Then somewhere down this is 40 and somewhere down we have here at this point in the complex plane. So we are talking about the fourth quadrant. So the phase is going to be -10. In verse 52.5 divide 40. So it comes out to be approximately -52.64 degree. Now we can find the value of I. T. That is equal to E. T divide the impedance Z. So 80 is it is given as 100 cores 100 course 10 T divide desired can be written as a model of zero which is 60 and the phase of jed which is minus 52.64 degrees Now 100 divide 66. That comes out to be around 1.51. And this phase becomes cause Dante here in the denominator it is minus. So in the new territories it is going to be plus soap plus 52.64 degree. So we can see here that current is leading the voltage by and phase by by the Phase 52.64 degree. Now uh further indication we are going to find the value of charge charge Q. So charge Q. Is given by integration I. D. T. Integration I. D. T. So it comes out to be put the value of I so 1.51 will be out of integration. Integration cause 10 T plus 52.64 degree and DT now if you further so all this Then we get 1.51. The integration of course that is going to be 10 will be in the denominator And it is going to be signed 20 Plus 52.64°, 52.64°. So this will be the value of charge. There&#x27;s 1.51 divide 10 can also be written as 0.151.

Mohamed Raafat Mohamed · Answer

Hello, everybody. You are going to solve problem number 30. So we have to. Did you? Well, I d t plus 100 que equal, then sign 60 de So by divided by to so the question will be Thank you By the tea loss 50 Q equal life slain 60 t Then the integration factor will be called E to support traditional 50 80 equal. E was a power 50. He and the boy mental blank that factor with given equation so we can get that que off t equals to the power. Negative 50 the, um sir, um, the question will be e support 50 50 dick you by the tea lost 15 multiply it is about 50 t Q equal five e to the power 50. See, um science 60 d So it will be you find out the following e So power 50 t que desk equal five e to the power 50. The sign sickest e d. So, by integration for both sides, we can get that you t equals E to support the negative 15 on punk practice for integration off five e Just about 50 t sign 60 t the the loss. See that will be equal e of our negative 50 de I multiply Five peoples of power 15 The, um multiple E one over 6100 Must deploy 50 sign 60 D one of 60. Whose line? 60 t um, that us c e to the power negative 50. See? So it&#x27;s all be equal. 1/1 to 2. Multiply five sign 60 T one of six co sign 60 d plus c. It was of all negative 50 g and but at zero, uh, but a ducal equal killed zero equal. Negative. 6/1 to 2 plus c. So, um m c equal 3/60 61. Andi on the cure equals Q of T equal five sign 60 T minus six was line 60 C over 1 to 2. Lost three e to support negative. 50 t over 61 is a church at time T where the current as, um uh off t equal take you by the tea. Equal one 1 150 equals line 60 de los 180 sign. Sorry. Sign 60 T minus one 150 m about negative 50. The that&#x27;s over. That&#x27;s all over 61. So

Sherrie Fenner · Answer

question lurking. We start with R equals 20 omega. I&#x27;ll even one each See the room. 1000 which takes the inverse of that. I&#x27;ll get 500 one bite, which will be my son. I have f zero q of zero equals zero and you crying of zero equals zero. So first I want to get my general equation and you can fight him. You double crime plus 20. You crying was 500 equals. Waltz just well, so I used my quadratic formula to solve that. So I have negative Lindy Minus where? 400 minus 2000. Divided by two. Which gives me negative 20. That&#x27;s your money News 40. Aye. Over Jim. Which gives me negative 10 waas or minus money. I So the general form of my equation you e equal See one e no Group 10 p. Sign 20. See you e negative 10 p sahn 20. So I&#x27;m gonna let you me e a Thank you Prime would equal zero as well as a huge double crime. So I would have 500 a equals 12 therefore a equals by whom? Or 500 legion Reduced form is three over 1 25 That&#x27;s my name. So I would add three over 1 25 after cell from I see one and my C two solving for my C one. I put a zero in a qc of tea. I know that signs gonna be zero. So what I&#x27;m really left with is, um I have zero equal. See? One plus 321 therefore see one equals negative cream 1 20 Now to find two, I&#x27;m gonna take my time. So like you crime, I&#x27;m t And this is a lot of the product rule C one negative him. I mean, maybe you can t Who sign 1 18 minus What? Me? C one he negative penalty sign 20 minus e county So am I. Key else one See you e with dignity. So what? I love you. My zero equals zero See grow year and then I end up with negative 10 one waas 20. The shoes equals zero. I plug in my native 31 over 1.5. So I end up with huh? 30 Huh? Over 1 25 Equal money fines see too multiplied by 1/20. And I mean that with thank you Because when I plug in three of a 1.5 that makes a positive, and I expect to the other side of negative. So I&#x27;m not by both sides by 1 20 and I end up with C two bulls. Uh, negative three over too. All right, so my general equation negative three over 1 25 e to the negative. 20. Sign money. T minus. Re over to 50 e negative. 20. Fine. 20 month. Factor out me making him one over 2 50 even six. Sign my three sign one plus three over one. Just my answer, then a song for my bye the by the riveting. So when I take my back to my derivative function and I thought in my Oh, I am negative 10 times too Plus minus 21 And I&#x27;m really only concerned with my sine function because that will give me my zero. And I need to zero because Mikey prime equals zero. So when I take, uh, negative, C two minus 20 C one I end up with Really fits my my He equal three minutes in negative. 10 key. Fine. 2019. Yeah,

Bruce Edelman · Answer

Okay, so does Chapter 26. Problem 93. So it says an RC circuit contains a resistor are of 15 killer homes the the capacitor of 0.3 micro parents in a battery with an E m f nine volts. Starting a time equals zero when the battery is connected. Determined the charge Q on the capacitor in the current I and circuit from time equals t two. Time equals he time equals 02 time equals 10 milliseconds, and it wants to do it at 1.1 millisecond intervals for graphing capabilities. Cool, Cool made grass trimming the charge. Cute. I change with time. Um, from the grafts, find the time at which the charms. Okay, cool. So to figure out how in our C circuit you&#x27;ve always like this. We need to look back at the equations 26 6 a in 26 8 Okay, so what these show us is, they show us the charge as a function of time is given by C E. M f one minus B to the negative t over RC. They also show us the current as a function of time given as e M. F. Over our E to the minus t over RC. Okay, now, from this, we can immediately graft these with graphic capabilities. It&#x27;s about the second part First for a second. So it says, find the time at which the charge of chains 63% of its final value. So if we want the charge to be 0.63 que final. Okay, well, what is Q Final? Just a question to final for charge. You can see as t goes to infinity. This approaches to this c times t m f. So this is 0.63 C times. Now we can display visit time 0.3 micro thirds times line votes That comes up to being 1.7 times 10 to the negative six schools. Mrs R. Q. I&#x27;m gonna call it P for an appointment. Find them a graph. Let&#x27;s do the same thing for current. So I p is now. We wanted to be 37% of the final. Great. Well, again, the final current is given. Oh, sorry. As the initial current final charge with the initial Kurt, the initial current is given by looking at this time equals zero just absolutely over our. So this town become 0.37 slung over our 0.37 nine votes over 15 killer homes. And we get an I P. Of 2.22 times 10 to the negative for wimps. So these are the two points we want to figure out on our cards and current versus time plants. So from these equations are we have to do is get an array of T. If you want to use this and pipeline, you can do some pie dot lynn space 0 to 10. No seconds at a point. One nanosecond in between. This gives you an array, and then you can just evaluate this at each point and then plant it. So I&#x27;m gonna go ahead and sketch what the parts are gonna look like here. So it&#x27;s straw this charge versus time slot. So this is time in seconds. 0 to 10. Mrs. Charge, uh, zero, when I say appears to 0.5 racoons. So we started zero then. This kind of follows this kind of powder. Okay. And if we want to find the time when we just find when this equals R Q p that we found before and we should see that happens at about 4.4 milliseconds. Okay, let&#x27;s plot the other wrong here. So this is the current Oh, sorry. This is still time on the X axis. Of course, this is time in milliseconds from 0 to 10 milliseconds. And now this is current. This goes from 0 to 0.6. This is Miller Imps. Now this We start at 06 kind, uh, decays very slowly along this path and again we should see that I p what we found before, the point that we wanted to find happens at the same time, which is roughly 4.4 no service.

Sherrie Fenner · Answer

and on the 24. Where to see why and when I divide over. Thank you 200. We also know that zero one you crying A zero equals zero. My equation will be too. You double crime. Plus what we were Q two Q equals 12 minutes. So that gives me two or square plus 24 Are what? Using quadratic formula. I have negative. Well, plus or minus square 1 44 Oh, Q Therefore negative. 12 us remind us this were negative to 56 over too. But we&#x27;re over two. That gives. That&#x27;s the equation. We won. Negative six key ain t Well, see you, e negative 16 sign Q T no equal a keep crime. Of course. That zero you devil crime, we&#x27;re equals zero. No, I have C bro equals 200. Hey, no, no, no. Each well equals 200 eh? Oh, here for a over 200 re over 50. Tag that right under the end of this mission. And then I see one put in a 0.0. He was in a replenishes cp and recorded in a row. So that gives me the wine sign. Of course, Would be wiped this whole thing would be worked out. I only see one coast side of eight times zero is one less three over 50. So see one gets me negative. 0.59 Now take the cry of my function ti and do product. Cool. So I get negative. Six time I see one e to the negative power. Oh, sign a C minus eight C one e negative 60. Power sign from 18 minus six. Seeking e with negative six key power sign of eight T unless eight C two e to the negative six. Key power. Oh, sign, huh? You all right, too? Looking it. That of being in my zero for my crime and putting in a zero my p really place I&#x27;m gonna have values is for coach sign. So I get negative six He won plus eight c two because for sign Sign of 00 So zero times that whole thing, which is quite right out. So no row he falls negative six. Thank you, Hero by nine. No ready So c two 472 divided by eight c two Come. So 778 And I haven&#x27;t ate because grounding e making six t sign and going back Thio my You see for me in the known values I get it, huh? One e negative six Coastline E What? Three. Which is my teacher? E negative 60 something.

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