consider-an-r-l-c-circuit-with-r1052-l518-mathrmmh-and-c0200-mu-f-a-at-what-frequency-is-this-circui

Question

Consider an $R L C$ circuit with $R=105.2, L=518 \mathrm{mH},$ and $C=0.200 \mu F .($ a) At what frequency is this circuit in resonance?
(b) Find the impedance of this circuit if the frequency has the
value found in part (a), but the capacitance is increased to
0.220$\mu \mathrm{F} .$ (c) What is the power factor for the situation described
in part (b)?

João Gabriel Alencar Caribé · Accepted Answer

in the first item, we have to couple it. What is the resonant frequency off that circuit? The resident frequency is given by one divided by two pi times the square it off the lieutenant&#x27;s times like fascinators, then putting the given values by the problem. We got one divided by two pi times the square root off 518 times 10 to the minus treat because there is a merely perfect here times 0.2 times 10 to the minus six. Because there is a me Crowe perfect here, and these is approximately 494 hurts in the second night and we have the following situation. We have almost the same circuit, but now the capacitance is It goes to 0.22 Negro fires, and I remember that the circle it is running out 494 hearts. We have to complete what is impedance off that circuit. Impedance is the square it off r squared. Plus, the difference between the reactors is squared. No, we will calculate. What are you react? Ince&#x27;s The capacity reactors is equals to one divided by two pi times the frequency times the capacitance So it is, of course, true to buy times 494 times zero points, too. 22 times 10 to the minus six. Because there is a me crow here and this is all under one. Then a couple e the value off the inductive reactors Inducted reactors is equal to pi. Thank the frequency times in look tense, which is, of course, to in the following situation to pie times 494 times 5 1/8 time to stand to the minor street because there is Emilie prefix here. Then we plug in all these expressions on the expression for didn&#x27;t see this to get the following result. The impedance is the course, too. The square root off 105.2 squared plus to buy times 494 times 518 times 10 to the minus street minus to five times 494 times zero points 22 times 10 to the minus six under one on This difference is squared and these is approximately 180 homes. Finally, we have to calculate what is the power factor off that circuit in the situation given on the second item the power factor is it goes to the co sign off the face, which is equal to the resistance divided by the impudence. So these equals to 105 12 divided by 180 on. These is approximately 0.58.

João Gabriel Alencar Caribé · Answer

the first tight and we have to calculate what value often reluctance will result in a resonant frequency off 95 megahertz. Then we begin by remembering that the resonant frequency because to one divided by two pi times the square root off l time see And we can solve this expression for l. And by doing that we get the following expression for the doctors. So two pi times the resonant frequency squared Is he close to one divided by your time, See, and then l e Z close to two pipe times the resonant frequency squared times the capacitance by plugging device was given by the problem. We get the following for the doctrines to pi times 95 times 10 to the sixth squared because there is a mega here times 0.29 times 10 to the minus six because there is a micro here they&#x27;re one on. This is approximately 9.7 times 10 to the minus 12 Harry&#x27;s which we can write us 9.7 PICO Henry&#x27;s in the next item we wanted impedance resonance to be equals two, 1/5 off the impedance at 11 kilo hertz and then we want to know what value offer resistance can satisfy this condition. We begin by remembering that at resonance the impudence is too close to the resistance. Then we get our course to 1/5 off the impedance at 11 kilohertz. Now we do the following. Remember that impedance is equal to the square it off R squared, plus the difference between the reactor sis squared. We now square both sides off this equation to get r squared. Is it close to one divided by 25 times R squared plus eggs l mines like see squared No, We can move 25 to the other side To get 25 r squared equals two wars Where plus excel mine is sexy squared Now we move these term to the other side To get 24 r squared is equals to excel Mine is sexy squared Finally divide by 24 We get our squared equals two exile miners XY squared divided by 24 Then our is equals to excel Miners XY Absolutely I you because there is no negative resistance is divided by the square root off 24. Then we remember that excel is it close to two pi times the frequency times in look tense, which is in close to two pi times. 11. Time stand to deterred because there is a key clue here, times in doctors on Docked Us is. He goes to 9.7 time Stand to my news 12 on Maxie. Is he close to one divided by two pi times f time seat because he goes to one divided by 25 times 11 time stamped with toward times the capacitance, which is you&#x27;re a 0.29 Niekro for its no plugging these values in these equations would get the following for the resistance. Are these equals to that one? Divided by the square root off 24 times The absolute value Off Excel We cheese to pie Times 11 times, 10 to the third times 9.7 Time standard in minus 12 miles. Accede, which is equals to two pi times 11 times 10 to the third times 0.29 times 10 to the minus states under one, and this is approximately 10 owns

Yaqub Khan · Answer

first of umbilical Cleared angler is an inter frequency off RLC series circuit. By using the relation angler present and frequency equal toe. So get a load off one divided by induct ins Times get the stones putting different values here one divided by here Independence of the cities zero point 300 Henry and keep distances 16 My girlfriend it 36 times 10 to the power minus six Fettered this use US angler Resonant frequency equal dough 700 45 Radian Worse again In the next part we want to calculate resistance it residence imprudence off our city circuit is equal dough resistance so we can write recent sequel Toe Imprudence s impotence is a ratio between spiegel days applied source Do you add it by speaker here people Dish of the sources 400 40 world divided by speaker in the circuit is zero point 56 in peer This gives us ready since equals toe 700 and a six home living The last abad of this problem We want to call cleared equal days across register in Dr on the campus ter big wattage across register physical do speak Earn times registers here be current is zero point 5 60 ampere and reticence is 700 and the six home This gives us big, old it across resistor equal toe 400 40 world big old age A grass in doctor is he could do speaker times The intense off in Dr That is it will do. I times the Agence off in Dr Ed ordinances equal toe angler resonant frequency times indoctrinates the physical toe I in tow. Resonant difficulty off RLC series circuit is so good old off One divided by Ellen Do see Excuse us I in tow. So get a load off El Suker divided by L C as we can, right? L equals toe. Secure it off, So get off l So this gives us big will teach across in doctor Equal Toe I into so get it off. L divided by, See? Nope. Electing different values here We currently is zero point 56 and Pierre into secure it off. Ellie. Worried by sea here in doctrine C 0.3 Henry, divide by get distances. Six microfiber date is six times 10 to the power minus six. Fettered. This gives us big voltage across in Doctor equals toe 125. Well, IHS, add resonance but he attends up in Dr Is You could do react prince off Cape Mr So therefore well dangerous in Dr is us ical toe were detected us get Mr So we&#x27;ll take a grass That is big voltage across Get Mr is the US equal toe 100 25 world

Mohit Khurana · Answer

welcome to the program number thirty one point three two. This it&#x27;s a pretty one are done it in government. So in discussion were given lcn psychic. All the components are connected in serious. We have assistance capacitance and an inductive. And this is being connected to the easy source. The values are Elsie are given and we have the maximum of the peak voltage that capacitance can have it because two, six, seven tables, that means this is a word in temperature across the contestants. We have three formats here, or we can use more fullness to find out that parameters of discussion. So we have first in this question, we need to find out that as Aaron frequency so resonant frequency is that frequency at which exit becomes because to accept, which means X equals to accent. So which is it? Close to one over Omega sea calls to me. And this gives us army vehicles to one hour under C. So this is about Omega and putting the value the lnc. So this comes so to one point five four into dentist&#x27;s our four radiant or second. So this is over Romania or that has in frequency and resonant frequency If we look at the former here. So impudence from last this is a coast are square plus XY minus x n old square. So in this condition we have accept calls except that means that becomes close to So we have that recalls are now we have vehicles to Isaac, which is it cause too current And we have current can be equated with V C over Maxie Times ten and zealous because to us so we have be sick over XY. James R. We&#x27;re just like you. So we have omega six equals to one over. So we have actually got a c. So this comes out of one point by four Independence to power, four names point zero one two and it&#x27;s a minus six. This comes out to be five point for one in the tenders to power three supporting this valley so we can find out the V, which is equals to six seventy, which is the world that across the contestants for the water temperature is close to our contestants. Over five point for one into tenders to power three, which is sexy tanked assistance, which is four hundred. This is in Lords. And this is an arm. So this kiss, those costs forty nine point five warts. So this is answer for this question. Thank you for watching the baby.

Ryan Hood · Answer

some party, eh? We want the resident frequency. And so to find this we&#x27;re going to use the formula that don&#x27;t make it on is you go to one more square it the induct inst times of precedents. And so now we can plug in what both these are, since they&#x27;re both given in the problem and we get one point a three times 10 to the third radian per second. That&#x27;s an angular frequency. So if we wanted a regular frequency, we would have to divide by two pi. And when we do that, we get 291 hurts. And so that&#x27;s party and part of you want the phase or diagram. And so let&#x27;s go ahead and draw our actual access here. What&#x27;s their voltage goes off at some angle here? Well, at residence, we know that I&#x27;s gonna be pointing in the same direction. So speedy FBI, We also know that I r is gonna be pointing in same direction, too. And then the other currents are perpendicular to this. So they&#x27;re shooting off in this direction or destruction. So this is ill. The current cross the conductor, This is I C, and that&#x27;s the face of a tiger. So here we want the current amplitude across the source. And so the equation. We&#x27;re going to use this just Isaac Levy over the impedance. This is how you find the current amplitude, given the voltage, the opportunity and the impudence. But when we&#x27;re at residents, we know the impedance is equal to the resistance. And so this stuff is because we&#x27;re at residents and now we know what both these values are. And so this is 1 20 volts over 300 homes. And so this is 0.4 grams now, for part, even want the current amplitude across the resistor Thean doctor and the capacitor. And so let&#x27;s start with the resistance, the current across the resistor it&#x27;s just equal to the voltage or the resistance. But since we&#x27;re at resident frequency, this is just going to be the same. Is this value and so is that. Now I need the current amplitude across the in doctor. And so that&#x27;s just equal to the voltage over the reactions of the in doctor and the reactions of the doctor. It&#x27;s just that you&#x27;re frequency times thie induct in ce. And so now I comply in everything that we know and we know it all. So we can like that and get 0.131 amps. So it&#x27;s a little less than these values here. You know, this one last time for the capacitor. In this case, it&#x27;s volts over the reactions of the question playing what? The reactions, the capacitors, here&#x27;s false omega precedents, and then playing in these values gives 0.131 amps, and so that completes the problem.

Mayukh Banik · Answer

we have frequency F not equal as Omega, not over. Dubai equals one of our Dubai route as C it was to buy square load one over to buy square dude and equally as Brian. Three times 10 to the minus three Henry month, led by the Kappas Ignorance 33 Mandel fad and that comes out to be 50.6 key though hearts Now we&#x27;re trying to find the maximum e m f which is I times e. On. In this particular case, Zeke was ARD so we I i r and the current is given by V C over X c for the Kappa sitter. Times are so that becomes Omega. See v c are putting the numbers in. Oh, my guys. 3.18 times 10 to the five Ready and per second cap residencies 33 times 10 to the negative nine. Fatted voltage is 700 fold. Andi resistance is 325 home. Altogether we get the potential to be 2400 vote

Problem

An RLC circuit has a resonance frequency of 155 …

Problem 67 Hard Difficulty

Answer

a) 494 $\mathrm{Hz}$
b) 180 $\mathrm{ohms}$
c) 0.58

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Electric Charge

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a) 494 $\mathrm{Hz}$b) 180 $\mathrm{ohms}$c) 0.58

Physics

Liev B.

Marshall S.

Jared E.

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Electric Charge

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James S. WalkerPhysics

Liev B.

Marshall S.

Jared E.

Meghan M.

a) 494 $\mathrm{Hz}$
b) 180 $\mathrm{ohms}$
c) 0.58

James S. Walker

Physics