suppose-we-would-like-to-change-the-phase-angle-for-this-circuit-to-phi-250circ-and-we-would-like-to

Question

Suppose we would  like to change the phase angle for this circuit to $\phi=-25.0^{\circ},$ and
we would like to accomplish this by changing the resistor to a
value other than 175$\Omega$ . The inductor is still 90.0 $\mathrm{mH}$ , the capacitor is 15.0$\mu \mathrm{F}$ , the rms voltage is $120.0 \mathrm{V},$ and the ac frequency
is 60.0 $\mathrm{Hz}$ . (a) Should the resistance be increased or decreased?
Explain. (b) Find the resistance that gives the desired phase angle. (c) What is the rms current in the circuit with the resistance found
in part (b)?

João Gabriel Alencar Caribé · Accepted Answer

on the first item. Remember that the faith and hope the tangent of the face and gold is equals two eggs l minus x c divided by the resistance before changing anything in the circuit. Their value off the face is my news. 35.3 degrees. By drawing the geometric cycle here, we can sketch attention off minus 35.3 as being somewhere down here we want to change the things and go toe minus 25. When doing that the new tangent, we will be somewhere this please. So what happens here is that the value off the ancient is getting closer to zero. In order to do that by looking at the expression for the tensions of the face and we see that we have to increase the resistance since both they looked in on the capacitance are still the same on the second item, we now have to calculate what is the value off that new resistance to do So we remember we use this equation that we have just mentions for the tangent of the face on. So the tangent off the new face on go minus 25 degrees is equals two eggs. L&#x27;m I know. Zach. See, 33.9. Mine was 177 divided by your value off the new resistance. Then the value of the new resistance is a close to 33.9 miners 177 divided by the tangent off minus 25 degrees. And this is approximately tree 07 homes on the last item. We have to calculate the value off the current after changing the resistance. So we remember on floor B R. A mass is in Costa. Why are a mass times didn&#x27;t see this? And so for the current to get your a mass is equals to be are a mass divided by Z We still the same. So the only thing that changes is the impedance and we get the current eyes. Uh, 120. Divided by the square root off R squared New resistance squared plus excel miners exceed 33.9 miners 177 squared, which gives us a current off approximately 0.354 amperes

João Gabriel Alencar Caribé · Answer

in the first item. We want to increase the face angle for minors 39.3 degrees to minus 22.5 degrees. Remember that the tangent off the face and go is he goes to excel. Mine is sexy, divided by the resistance We want that angle to increase on by increasing in this particular situation the tangent off the face and low we&#x27;ll be closer to zero So we want to decrease this quantity as a world by only mass Mr Frequency Not that you circulate We have XY bigger than excel So this is a capacity of circuit. The capacitance dominates the circuit. If we want to decrease the difference between excel on Maxie, we must decrease exceed while increasing excel Remembering that excel is it goes to two pi times The frequency times they look tense on backseat is equals to one divided by two pi times the frequency times like a past tense We can see that by increasing the frequency way Exactly what we want to go by increasing f we increase excel Why you decreasing XY So what happens is that excel miners XY will decrease has wanted then we should increase the frequency in the second item, we have to find the value off the new frequency. Note that we can do that by using this relation between the ancient off the phase on the property is off the circuit. Two. We got the changing off phase You close to to pie F l f prime here minus on. Also fight crime here one divided by two pi. If prime time See And this is all divided by the resistance are then we have to solve these equations for the frequency and we do it as follows. What you playing both sides by r to get our tangent off. Five Prime is he goes to two pi f prime l minus one divided by two pie. That&#x27;s Brian. See, now we have to cross multiply this fractions to make the eliminator the same to get our times that kind agent off five Prime. Is it close to to pi squared f Brian squared the l C minus one divided by two pi f Brian. See? No, we can do the following. We can send this term to the other side as a multiplication to get our times to pie times see Time&#x27;s left prime Time&#x27;s the Tangent five. Prime is he goes to to pi squared f Prime squared times the all time See my nose one. Then we can put our terms on the same side of the equation to get a second order uh, equation. And by doing so, we get the following to pie squared times l time See times f prime squared minds to pi times our time See times the tangent off five prime left prime miners one Is it cost zero. Now all we have to do so this quadratic equation and we do so by using basket rest formula which goes as follows it is screaming on for these equation Easy clothes, too. B squared. So this term here squared to pie times our time See Time&#x27;s detain Geant fight crime squared miles four times to buy square times l time. You see time&#x27;s men with one Then Delta is equals two to pi squared times r squared times He&#x27;s queer times Detain Geant Square off the new face Uncle plus four times two pi squared I&#x27;m zero time to see Finally the frequency is down equals two minus beat So miners, this term here. So two pi times our time see Thank the tangent off five prime plus or minus the square it off the screaming and to pi squared r squared times C squared times the tangent square lo fi prime It was four to pi squared times l Time see divided by two times to pi squared times l c Then we can plug in the values that are giving the problem to get F Brian is equal stupid to pie Times 175 times 15 times 10 to the minus six times the tangent off minus 22.5 degrees plus or minus the square root off to pi squared times 175 squared times 15 times 10 to the minus six squared Plus uh oh, not yet forgot to change it Times the tangent squared off minus 22.5 degrees plus four times to pie squared times ill which is equals 2 19 time Stan to the minus three time. See which is equal to 15 times. Stand to the minus six and this is all under a square root and finally, this is all divided by two times two pi square times L, which is 90 times 10 to the minus tree times the capacitance, which is 15 times 10 to the minus six. And these gives us two possible frequencies. We tried approximately minus 24 eight point true hurts or 75 point 59 hertz. I know that there are no negative frequencies, so we do not consider the solution. And finally, the new frequency should be 75.59 hertz finally on the last tight. And we have to calculate what is the R. M s current in the circle? It In that case, we can use homes law. The our romance is it goes to I are a mess times the impudence. But not that the following the court sign off the fees is equals. Two. The resistance divided right impedance uniform impudence. Physicals to the resistance divided by the co sign off the face Dan, the current is equals True, the r a mass divided Bye, zee because it goes to Vieira mass times the co sign off the phase divided by our we can then plugging their values that are given in the problem to get 120 times the cool sign off minus 22.5 degrees, divided by the resistance, which is 175. And these results in on Aramis current, off approximately zero point 634 and peers.

Zulfiqar Ali · Answer

well. The foods angle is determined from the react Ince&#x27;s and resistance in the in the system. So five, which is the phase angle, is equal to 18 in worse into Excel, which is inductive reactions minus X e exceeds the capacity of reactive is divided by R resistance. And ah, this can be returnees, Dean in worse into four. My square l time C minus one, divided by to my f uh, are see Well, remember, the Excel is equal to make a time cell and XY is equal to one divided by Omega time. See, So using these equations, we can write Fi, uh, in this far right. So now let&#x27;s substitute values by is equal to team in worse into for my square multiply by ah, 60 square multiply by 0.46 Ah, multiply by 21 multiply by 10 to the power minus six minus one divided by to buy multiplied by 16 multiplied by 150. Multiply by 21 Multiply the 10 to the dollar minus six and then we multiply the whole trump by 1 80 degrees divided by by right. So fine is equal to 17.4 degrees right now. Sue. In the second part, I went from the face angle. We see that the voltages 17.4 degree ahead off the current. So from the phasing the fi, right, Uh, the world teach We is 17.4, uh, degrees ahead ahead off the current Look. The current right. Eso the world data Regis maximum sooner. So we will reach. We will reach it maximum maximum sooner.

Donald Albin · Answer

were given some information. Um, we&#x27;ve got are of 150 OEMs. See is 21 times 10 to the negative six. Power Farid, um, el is 0.460 Henry, um v R m s is 120 vaults. Frequency is 60 hurts. So omega is two pi f. You know that also, V Max is going to be 120 square root of two volts. Okay, where is the phase angle between the current and the voltage? So, in order to calculate that, I need to figure out the impedance which is the square root of r squared. Plus, um, omega L minus one over omega C squared. So just substituting those in gives me the square root of our square. 150 squared, plus parentheses. Omega, which is to Hi, I&#x27;m 60. I&#x27;m l, which is 0.46 minus one over Omega Psi. So it&#x27;s to pay off to pie times 60 and see, which is 21 times 10 to the negative sixth power. That gives me 150 OEMs. The phase angle is the inverse tangent of omega L minus one over Omega Psi. Over our. So why Did I even figure out the impedance in the first place? I don&#x27;t know. It wasn&#x27;t really necessary. Ah, inverse tangent of omega l minus one over Omega Psi. You already have over 150 17.4 degrees. Okay, which reaches its maximum earlier. Is it the current or the voltage? Well, first of all, I have enough to do this. Be I as a function of t is going to be I max sign of omega T minus 17 point four degrees. So I noticed that, um, this current is trailing and therefore the voltage is leading, and so voltage reaches its max earlier.

Ze-Han Lee · Answer

all right, Before these problem, we have the r C series circuit, and we know the face angle is ah, 54 degrees and the source voltage liking the correct. Ah, and the reckons off the combines days 3 50 the resistance resistance is 1 80 So and also we also we also know that every power is 1 40 So for the party, we want to find out that Ah react then something. Doctor, uh, To do this, we can utilize the conclusion. Ah, about the face angle are over easy, equal to course and fi. So this vise the face ankle, which is 54 degrees, and Ari&#x27;s the resistance, which is 1 80 So just plug in the numbers and you&#x27;ve been so forth e puts up, Was he able to 30 sorry. Uh oh. So we can get, uh, this is three old six homes and definition for them. Patents is, uh, square root are squid plus? Ah, I just I just write our ale minus R c. Okay. Hey. So areyou always the reactions of the doctor and our sees the reactions of the pastor And are you just the resistance? So we know are equal to 1 80 homes and ah R C is 3 50 homes. So we camped in. And also we know the voltage legging the current. It means that our c larger then r l Okay, so by using this, this conditions weaken so full the l directly we can Captain R l equal to, uh, 102 hopes. All right, so this is a reactor in something about here. If a party, we need to find out the r m s current. Ah, about the current, we can utilize the ah information about the average power. So the everyday powering the RNC circuit ihsaa p equal to i r M s squid times are right. So I just the current in the series in the search in this series circuit and our is the resistance. And we know this 30 is 1 40 waltz and ours are 1 80 homes. So we can so pull these current directly. We have 10. I. R. M s equal to 0.8819 and peers. If a parsi, we need to find out the arms. Phatu! Ah, for the voltage of the source. So uh, to do that we can simply use Ah, because fault. Because this is a series circuit. So the V r m s for the for the source. Simply put two of the current r M s times Z Z is the voting patterns. Okay? And these Wait, we&#x27;ll find out Z which is, uh, showing here. So an eyes given here. So just plugging their two numbers and we find the final results for the, uh, arms very off the sources to 70 boats. Okay? Yeah.

Mohit Khurana · Answer

Welcome to the from the number forty one point five two. This is a crafty one. I&#x27;ve done it in good saying discourse. We have out and see a circuit and this is being connected to the If he saw us, we don&#x27;t We&#x27;re not given any information about the source, but we have given that the average our discipline it is one fifteen vote and their assistance is a war two hundred dollars. And the evidence off the capacitor is four hundred and indifference we need to find out and were given that the fight after which is the face factor or the factor is forty. So you&#x27;LL use this for my head to find out the XL I reminisce and Jed Bailey, which is the impudence. And then we will find out the Vietnamese. So we have first a using this relation. So this gives us excel equals two are then fly plus XY So we know this valley. So we have two hundred times ten fire which is ten forty Diggory plus four hundred on which is XY. So this gives us Except So this gives us five sixty eight now. You wanted a part B so we need to find out the animus. So using this solution so we have I animus equals two under a lot of power over our So we have our hair. So which is it, counselor? On fifty over two hundred dollars. So this gives us I close to point it. Six six m. P s. So this is that amiss? Current passing to second. We have bouts even need to find out the ambulance. We can use this for my hair so that it tickles too over a close fight losing this election. So we have articles to two hundred and close flies over course for delivery. So using the calculator. So this gives us equals two, six, one. So this is the impudence of the psyche. Now we can use this impudence to find out the voltages. So we&#x27;re using this elation. So we have the Aramis he was too. I aramis present. So we have a point. It&#x27;s six six times two, six one. Remember that this is a coast too Siamese. So Well, this value here. So this gives us or Adolph on Imus. This comes out to be two to six war Now we can also find out the world and Petrovich is because to roof under two times we are miss. So this comes out to be you. Two times two, six, two to six War. It is twenty one. So this is also for this question. Thank you. For what? Watching the video.

Problem

You plan to change the frequency of the generator…

Problem 98 Hard Difficulty

Answer

a) See explanation
b) see work
c) 0.354 $\mathrm{A}$

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Electric Charge

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a) See explanationb) see workc) 0.354 $\mathrm{A}$

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a) See explanation
b) see work
c) 0.354 $\mathrm{A}$

James S. Walker

Physics