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Consider an AC power supply with the frequency f = 80 Hzconnected to an inductor (L = 0.2 H), capacitor (C = 2e-05 F) andresistor (R = 30 Ohm) in series. The maximu...

Question

Consider an AC power supply with the frequency f = 80 Hzconnected to an inductor (L = 0.2 H), capacitor (C = 2e-05 F) andresistor (R = 30 Ohm) in series. The maximum current in the ACcircuit Imax = 0.2 A. What is the maximum applied voltage?

Consider an AC power supply with the frequency f = 80 Hz connected to an inductor (L = 0.2 H), capacitor (C = 2e-05 F) and resistor (R = 30 Ohm) in series. The maximum current in the AC circuit Imax = 0.2 A. What is the maximum applied voltage?



Answers

A series RLC circuit has a resistance of $25 \Omega,$ an inductance of $0.30 \mathrm{H},$ and a capacitance of $8.0 \mu \mathrm{F}$. (a) At what frequency should the circuit be driven for the maximum power to be transferred from the driving source? (b) What is the impedance at that frequency?

First, we should find the inductive reactant ce. This would be equaling two pi times the frequency times the induct inst al This would be to pi times the frequency of 600 hertz multiplied by 6.0 times 10 to the negative Third Henry's This is giving us 23 arms and then we have the capacitive reactor. It's this would be willing one over two pi times the frequency time See the capacitance and this would be equaling one over to pie time 600 hertz multiplied by 25 times 10 to the negative Sixth Farage's and this is giving us 11 homes. So here the impotence Z would be equaling the square root of R squared plus accept out minus X of sea quantity squared. And this is giving us the square root of 25 homes quantity squared, plus ex of al 23 minus 11. So I would be giving us 12 comes quantity squared and this is giving us 28 comes so this would be the impotence rather. And from this we can then say that four part eh, the voltage across the resistor would be equaling the arm s current multiplied by our and this would be equaling the our mess Voltage divided by Z The impotence multiplied by our and so this would be 10 volts divided by 28 homes multiplied by 25 comes and this is giving us eight 0.9 volts. So keep this in mind and then the voltage across the induct er would be equaling the R. M s current multiplied by the inductive reactant ce. And so this would be again 10 volts divided by 28 comes multiplied by 23 arms. And this is giving us 8.2 votes. Keep that in mind. And then the voltage across the capacitor Equalling our mass times the capacitive reactor since again 10 volts divided by 28 arms multiplied by 11 homes. And this is giving us 3.9 volts. So, as you can see no for your answer for car day, the some of all of these we can say 8.9 volts plus 8.2 votes plus 3.9 volts is equaling actually 20.9 volts. And this is of course not equal to 10.0 bolts. So no, and then, for part B. We can say that the power delivered Howard delivered to the resistor would be the greatest note. There are no power losses occurring in an ideal capacitor or an ideal in Dr. And So in this case, the power delivered to the resistor would be the greatest. And then for part C, the average power would be equaling. The R. M s current multiple Army's current squared multiplied by are the resistance. And so this would be equaling 10 volts. The armistice voltage divided by the impotence of 28 arms quantity squared, multiplied by 25 homes. And this is giving us 3.2 watts. This would be the powers the power delivered to the resistor. That is the end of the solution. Thank you for watching.

Belongs to the alternating current chapter in which we have V. RMS equals to 1 20 world. And frequency F equals to 60 hertz of an Rlc series circuit. Having resistance R equals to 1 50. Home inductions. L equals to 1.20 million Henry. And capacitance equals to 33.5 micro ferret. Okay so for the part of the question we have to calculate the reluctance of the capacitor XC and for the conductor L. X. L. Okay so The X. C. It will be equal to one x 2 by F. See so substituting values so we get one by two pi multiplied by frequency 60 hertz and capacitance is 33.5 micro forever. That is 10 to the power minus 6 30. So from here we get exceed that is equal to 79 point double two home. And similarly excel. That is equal to two pi F. L. So two multiplied by frequency is 60 Hz. And in defense L is 1.20 into 10. To the power minus three Henry. So from here we get X. L equals two. G 0.45 double two home. Okay so this becomes the answer for the part that is capacitive leah tense and that is inductive resistance. Okay now moving to the part B in which we have to calculate the impedance Jed and which will be equals two. R squared plus X. L minus X C. Holy square. And this under oath. So substituting values so we get Jerry equals two our which is 1 50 home. So Holy Square plus XL which is 79 point double two minus X. C. Which is 0.45 double two. And this holy square and this understood. So from here after solving impedance jed this will be equal to 1 69.4 home. So this becomes the answer for the part B. Now for the party we have to calculate the peak current so it will be equals two. We not by jail. And we know it can be written as under two times of the RMS divided by gender, so substituting values. So under the tumor we note which is equal to 1 20 Volt. They were major, which is 169.4 home. So from here we get peak current. I not equals to nearly one point double zero mps. So this becomes the answer for the part C.

So after a significant time is past, We know that the name of circuit which is given this trial bulls busy putting the pee current off, zero going to and piers multiplied by the resistance in the second are and hence we can rearrange this and find good assistants are. And if we do that, we get that resistance is 60 those And knowing that existence, we can calculate the inductions. Since we know at the time constant the circuit tool is equal to our over our where Palestinian doctors. And if we really into this you see that Oh, physical too tall Times on on the time constant We know to be five. I m just into the minus four seconds much better by the resistance to get our doctrines. Resistance is 60 bones and forget and inductions off circuit to be but t many. Henry's

We have re l equals I excel. It was I for maker l now v Aziz s so not over the Omega l equals s They're not only got over with the value of z e in which is I'm split us. Well, maybe I added my savana. What already got c squared now for visas to be minimum use d v l d Omega equals zero on solving this, you will get omega l equals you. You one over Squared off one over, forming an r squared minus half our square. See squid where will make a knot equals one over as e under the square in now the watch that cause the in dr will be given by v l equals I x l It was absolutely not oversee times over I got when we have you Not over z times Omega, not l. So this is when omega equals omega. Not that's when we have this value because we have substituted omega. We don't make a not and that comes out as absolute. Not over. Z times squared off l or C. It was General one Denver over. Want home l equals one micro Henry divided Recap Astiz is one micro fatted So that comes out to began Village. So in order to have if Max we must have, we'll make a n equals one of what? Living on our sled minus half I swear C squared raised the bar off native half equals putting are the brothers in. This will come out to be 1.414 times tend to their six ready in for a second now impotence at this frequency will come out to the Z equals sweated off our scribes ours omega as and thus minus minus one over or made a l. C squared. And this will come out to be 1.2 to 5. Oh, and the voltage will be excellent not over z times omega l l on putting are the numbers in This would be living for 55


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