the-capacitive-reactance-in-an-rlc-circuit-is-determined-to-be-45omega-when-the-inductive-reactance-

Question

The capacitive reactance in an RLC circuit is determined to be 45$\Omega$ when the inductive reactance is 65$\Omega .$ (a) Is the generator frequency $\omega$ higher or lower than the natu-
ral frequency $\omega_{0} ?$ (b) Is the phase angle $\phi$ positive or negative?
(c) Calculate the phase angle $\phi$ if $R=33 \Omega .$

João Gabriel Alencar Caribé · Accepted Answer

before restoring this question. Note that the question is referring to the angular frequency omega and not to the frequency off, which is given by two pi times the angular frequency. So you warned about it. Now for the first item, we have to determine if the resonant frequency is bigger than the frequency right now in that circuit. Let us do that. We begin this question by remembering their following relations for the react. Ince&#x27;s The capacity of reactors is equals to one divided by the frequency times. The capacitance wild inductive reactions is given by the frequencies times they looked at us. No note the following the resonant frequency. It&#x27;s such that the reactor&#x27;s is out of the same. So they are equal a newness situation given by the problem. They are not the same, so the circuit is not running at residence. In orderto achieve residents, we have to lower the inductive reactions while you&#x27;re increasing the capacity of reactors. And to do that by looking at these equations in these equation, we conclude that we don&#x27;t have to lowered the frequency of the circuit because by lowering the frequents off the circuit, we are increasing the capacity reactors while decreasing inductive reactors. Then we conclude that the frequency of the circuit omega is bigger than the resonant frequency off that circuit for the second night. And we have to remember that detainment off the face angle is given by the difference between the nuclear reactors and the capacity reactions divided by the resistance of that circuit, and now knows that the resistance is obviously bigger than zero. So the only thing that can be smaller than zero is the difference between the react, Ince&#x27;s and disease. What that reminds the side. No off the face. So this is what that their minds if the fate is bigger than zero or smaller than zero and note that in the current situation we have Excel will cost you 6 to 5 on that, C goes to 45 and these is it goes to 20 and 20 is bigger than zero, then the tangent off the phase is bigger than zero, and because of that, we conclude that the angle&#x27;s off. The phase is bigger than 02 in the final light, and we have to evaluate the faith&#x27;s angle for a given value off the resistance. So for our equals to 23 year olds. What is the value off that face angle? So we just have to use this relation that we had analyzed in the last item. Then it goes as follows. The tangent off the figs angle is it goes to 20 which which we had already done. The calculation divided by 33 and this yell DS and facing Lou that is given by the inverse tangent. So the tension my nose one off 20 divided by 33 needs is approximately 31 degrees.

João Gabriel Alencar Caribé · Answer

before beginning this question. Not that it is asking about the angular frequency and not about the frequency that is. He goes to two pi times the angular frequency. So be advised about it. No, we can begin your question in the first item. We have to deter mined if the frequency of the circuit is bigger than or smaller than the resonant frequency for that same circuit. To do that, we have to remember three things. The first storm is the condition for resonance. So when we have resonance, both react. Ince&#x27;s are equal to one another, and then we have to remember how to accomplish the reactors. Is the capacity reactors is He goes to one divided by the frequency times, the capacitance and inductive reactors? Is it close to the frequency times the doctors now let us analyze the data given by the problem, so we have that the capacity reactions is a coastal authority war gnomes, while the inductive reactors is, it goes to 16 girls. So get prisoners. We have to increase the inductive reactors while decreasing the capacity of reactors and by analyzing the expression from the reactant, says we concluded that in order to do that, we have toe increase the frequency off the circuit, then we have to increase to get closer to resonance. Therefore, the resonant frequency of that&#x27;s for a quid is bigger than the current frequency off the circuit. For the second item, we just have to remember that the tangent off the face angle is given by the difference between the inductive Andi capacity react. Ince&#x27;s divided by the resistance. The resistance is already bigger than zero. It&#x27;s always bigger than zero. In any case. Why, oh, the only thing that can be negative in his expression is the difference between the reactors is now. Note that in the current situation we have 16 year olds fronting looked reactors 9 31 gnomes for the capacity of reactors. And these these eagles to minus 15 which it is Mahler than zero, then the tangent off the face and look. It is smaller than Syria that Air Force, the phase uncle itself uses more than 02 Now, on the last item, we have to calculate the face angle. So we just used the previous expression. We have already seen the tangent off that face and hope is the course, too. The difference between the reactors is divided by the resistance, and the resistance is given on its secrets to 12 terms. While the difference between the reactant says we had already seen, that is, that goes to minus 50 noes. Then our look is he goes to the tangent minus one. The ingress tangent off minus 15 divided by 12 reaches approximately miners 51 degrees.

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.

Salamat Ali · Answer

given problem for about A, B and C. We are given the different frequencies for which we have to find. Impotence is represented by Z Speaker, which is I and the fence and knowledge is why, In order to find easy, we use an incursion that easily impedance is equal. Teoh Square root off our square resistance were plus Dubai are Don&#x27;s l minus one over to buy F C Square Square. Root is all the way here for a frequency off. For what? A frequency over 3000 herd&#x27;s. We&#x27;ll plug the resistance off 50 Holmes and inductions or for 3.3 times gentle ar minus three. Henry, um, where we have a capacitance is 4.8 Instant of power minus seven. Ah, the rod. So our values for R L and C for about A, B and C will remain sane already. Frequencies will change it. We can see from the question, so only for question will change. Uh, by plugging the value for R l N C F is called the 3000 we get. The impudence is equal to 69 0.53 Holmes for, uh, peak current. We have equation. That is enough he Nord, divided by 60 line impedance, which is 69.53 This will give us a current off zero point their own seven 191 in fear. Then, um, we&#x27;ll find a face. Let me just scroll down. We can find their fares by using equation that he&#x27;s a phase is equal to Italian. Worse off to buy f times l minus one Divided by Dubai If time see, uh, keep Aston&#x27;s divided by our resistance This will give us a face. So if you plugged the value for F 3000 and uh, no RNC, we get their face face or for minus 44 degrees. So this is for the frequency 3000 for about me off the problem, we&#x27;ll use the frequency 4000 yards where everything will remain same. The MF Elements in which is a five walls resistance in doctor and capacitance women. Same only different question will change. So we&#x27;ll use all those questions for Z, Pekar and infi. And, uh, after playing the values for frequency, lnc, we get the first impedance to be 50 or homes. Uh, then we get toe, I be current will be five divided by 50 which is 0.1 in peer fi. And we&#x27;ll get using the frequency 4000. We get a fire here in this case to be zero degrees similarly for party off the problem we have ah, frequency. That is the 5000 hurts. This time again, we will use the same equations I said. Well, you for all lnc and get the impedance to be 62.41 Arms peak Current will be again five divided by 62.41 or homes which will give us their A 0.8 appears. We&#x27;re facing goal for the given frequency will be a 30 seven degrees.

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.

Averell Hause · Answer

you have the magnitude of the phase angle Phi equaling 54.0 degrees. We have the capacitive reactor. Since equaling 350 homes, we have the resistance of the resister. 180 comes and we have the average power delivered by the source equal in 140 watts. Four part, eh, The formula for the face angle. We can say that tangent, uh, fi equaling the inductive reactions minus the capacitive reactant CE divided by our their assistance week and then say that solving for the inductive reactant so this would be equaling 350 homes minus 180 homes multiplied by tangent of 54 0.0 degrees. And so we can say that then the inductive react Ince&#x27;s equaling 102.251 comes for part B. The average power is equaling to the R. M s current squared multiplied by the resistance are so the R. M s current would be equal in the square root of the average power divided by the resistance are so this would be the square root of 140 watts divided by 180 arms, giving us 0.882 amps For part c, The R M s voltage is equaling the army&#x27;s current multiplied by the impotence Z and this would be equaling to the are at mass current multiplied by the square root of the resistance squared plus the inductive reacted. It&#x27;s minus the capacitive reactor is quantity squared and we can say that then the root mean vote rooming squared voltage would be 0.882 amps multiplied by the square root of 180 bums quantity squared plus 102.251 minus 350 quantity squared. I&#x27;m squared. Extend the square root and we find that the roots spread voltages equaling 270 0.1 volts. This would be our final answer for part C. That is the end of the solution. Thank you for watching

Problem

The capacitive reactance in an RLC circuit is det…

Problem 63 Medium Difficulty

Answer

a) the generator frequency $\omega$ must be greater than that of the natural frequency $\omega_{0}$ .
b) positive.
c) $31^{\circ}$

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James S. Walker

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a) the generator frequency $\omega$ must be greater than that of the natural frequency $\omega_{0}$ .b) positive.c) $31^{\circ}$

Physics

Elyse G.

Zachary M.

Aspen F.

Meghan M.

Electric Charge

The Electric Force

James S. WalkerPhysics

Elyse G.

Zachary M.

Aspen F.

Meghan M.

a) the generator frequency $\omega$ must be greater than that of the natural frequency $\omega_{0}$ .
b) positive.
c) $31^{\circ}$

James S. Walker

Physics