when-an-alternating-current-passes-through-a-series-r-l-c-circuit-the-voltage-and-current-are-out-of

Question

When an alternating current passes through a series $R L C$ circuit, the voltage and current are out of phase by angle $\phi$ (see Section 12.7 ). Here $\phi=	an ^{-1}\left[\left(X_{L}-X_{C}ight) / Right],$ where $X_{L}$ and $X_{C}$ are the reactances of the inductor and capacitor, respectively, and $R$ is the resistance. Find $d \phi / d X_{C}$ for constant $X_{L}$ and $R.$

Luis Mendoza · Accepted Answer

so it is falling. We have an A C circuit in Siris on we&#x27;re told that the circuit has an impotence off 190 year olds dependencies to value. See had that face angle will want to current and the whole dish off the generator. It&#x27;s minus 75 degrees. So first we want to find your assistance are on the capacity. React us off the circuit. So, first of five resistance we can immediately use the definition of the power factors will be part factor. Each is to co sign off the face angle intestine to be resistance divided by impotence. We know the impotence and I know the face. And if I So we sold for R U C 10 schools on a five, he was a resistant off 14 11 49.7 homes. And now that we know the resistance, we can found a positive reactors for the definition of C, remember even a C to find peace way r squared plus exit square. Assume where some The next el serum. Danny. Just a matter of solar for XY, so exceed the capacity reckons you just square root of C squared. We should get by the problem minus R Squared, which was found on Gives a Repetitive Reactors off 185 owns.

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

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.

Averell Hause · Answer

so here for party. The phase angle tangent of Fei is equaling the inductive reactant Sinus. The capacity of reactive is divided by the resistance are we can solve for the inductive reactions. This would simply be equal two 400 homes, which would be the capacitive, reactant CE plus 200 homes. The resistance of the resistor multiplied by tangent of the phase angle tangent of 40 degrees. And so the inductive reactant is 567 0.8 arms, four part to be. We can see that the average power is equaling. The root means squared current quantity squared, multiply, literate by the resistance are the root means. Squared. Current is then equaling to the square root of the average power divided by the resistance of their sister are This is equaling to the square root of 150 watts, divided by 200 homes, and we find that the root means squared. Current is equaling 2.866 amps and four part C. To find the root means Where voltages would be, the root means squared current multiplied by other impotence. This would be the root means squared current multiplied by the square root of the resistance of the resistor, plus the difference between the difference of the capacitive reactant ce from the inductive reactant ce so acceptable minus except see quantity squared and we find that the root means squared voltages equaling 0.866 amps multiplied by the square root of 200 bums. Quantity squared plus 200 homes plus 567 0.8 arms minus 400 arms quantity squared extend the square root and the root means squared. Voltage is equal to 226 votes. This would be our final answer for part C. That is the end of the solution. Thank you for watching.

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

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Basic Technical Mathematics with Calculus