an-r-l-c-circuit-has-a-capacitance-of-029mu-mathrmf-a-what-inductance-will-produce-a-resonance-frequ

Question

An $R L C$ circuit has a capacitance of 0.29$\mu \mathrm{F}$ . (a) What inductance will produce a resonance frequency of 95 $\mathrm{MHz}$ ? (b) It is
desired that the impedance at resonance be one-fifth the impedance at 11 $\mathrm{kHz}$ . What value of $R$ should be used to obtain this
result?

João Gabriel Alencar Caribé · Accepted 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

João Gabriel Alencar Caribé · Answer

So this question. We have to remember that to pi times, the resonant frequency is it close to one divided by the square root often do 10 times the capacitance. Then we can solve this expression for the capacitance to get the falling relation to pie times. The frequency squared equals to one divided by yellow time. See, then capacitance is he goes to to pi times the frequency squared times the reluctance divided by one plugging the values. Living in a problem, we get that the capacitance and equals to one divide it by two pi times 1.9 times dead to the turned squared times zero point starting times 10 to the minus tree. Uh, like that and the easiest approximately 54 me grow for its

João Gabriel Alencar Caribé · 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.

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

Zulfiqar Ali · Answer

distance in the R. L C circuit are is equal to 18 kill Oh, or home and inductions in the RLC circuit. L is equal to 20 million Henry 20 minute Millie Henry is equal to 20. Multiply by tend to the power minus three. Henry and Reason and Cree Quincy F is equal Do 4.0 little hearts, which is equal to four points. Ito will took my buying 10 to the power three Hearts, right? No, let&#x27;s do Monty well and you&#x27;re frequency of the RNC circuited. Resonance is omega is equal to one divided by one divided by the route. Elsie route L Times C where l is the inducting. Since he&#x27;s the capacity ins. And this implies that well, Omega is to buy a and Dubai F is equal to one divided by, Ah, look Elsie. Now let&#x27;s so for C or Uh huh Baskins. Then C is equal to one divided by for by square times L. A Times next great, right? No, let&#x27;s substitute values. So Gabe Aston&#x27;s C is equal to one divided by four by square, multiply by inductions will induct NC&#x27;s 20. Multiply by 10 to the dollar minus three multiply by frequency frequencies 4.0. Multiply by 10 to the power three and then we have square and simplifying the best stints is equal to 7 to 9 point to multiply by 10 to the power minus nine Durrant and 10 to the power minus Linus Nano. Therefore, capacitance is equal to 7.7 to 9.2. Nana Faye Rod, Right. Okay. No, let&#x27;s find out. Impotence it reasonings Well, we know that resonances when x l is able to x see here. Right? And impotence is that is equal. Do ah, squared Rudolph are square less x l minus x e Don&#x27;t scare when excel is the inductive reactions and exceeds the capacity reluctance. Right? And this factor, who said is equal to our because, um, X l is equal to x e. Therefore, side is equal to our and r is equal to 18. Que lo oh, mullets to part c Well, for if prime is equal to 3.0 Gilo hearts we&#x27;ll make a prime is equal to to buy if crime right and then we have two pi into free 0.0 killer hearts. If prime is three points, you know killer heart and therefore Omega Prime Musical, too. 6000 already in per second. Right and ended. NZ&#x27;s Zen is equal to square root. Off are square bliss XL, minus X e Old Square and for their that is equal to square root. Off are square less into well X is Omega Ex Eli&#x27;s Omega Prime L minus XY one divided by Omega Prime See all square and no. By substituting values we have, Zach is equal to ah, screen Rudolph um, square root off. First of all, our will re&#x27;s 18 multiply by tend to be powered pre all square bless. We&#x27;ll make a prime will. Omega Prime is, um, 6000. So 6000 multiply by l Well, L. A&#x27;s 20. Multiply bite into the collar minus three, right minus one divided by or make a prime will. Omega prime is, ah, 6000. To multiply, they see and sees 7 to 9 point to multiply by 10 to the power minus line. Right and simplifying. That is equal to um, it in Poland, Uh, and to 18,000 into arms. Right or disc in Britain is that is equal to 18 kill or or bronze

Donald Albin · Answer

Well, this is asking us about resonant frequency. And I know Omega zero, which is the resident angular frequency is a square root of one over l C. We&#x27;re told that our is 20 homes. L is 0.20 Henry, See is four times 10 to the negative 60 ferret. So, um, also Omega is two pi f sub zero. And so, uh, f is going to be 1/2 pi times the square root of one over l C. So let me put that in a calculator went over to pie times one the square root one over L, which is 10.0 is here to see which is four times 10 to the negative six. Power. Rounding that to two significant digits. It&#x27;s 1800 hurts be the impedance of the circuit is the square root of r squared plus omega l squared minus. No, I didn&#x27;t get that right. Sorry. Just at omega l minus one over whips one over Omega Psi squared. Now we do need to know Omega omega is just going to be one over square root of L. A. C or the square root of one over L C. So let me get that. Just have to take the two pi out of there. Give me 11,000 radiance per second. Okay. Square root of our squared 20 squared plus war. Um, Omega Times l 0.2 minus one over Omega. I&#x27;m C four times 10. Do the negative sixth power, and I often forget to square this. I&#x27;m going to square running. Here&#x27;s me. Exactly 20. That was. Oh, and obviously, um, at resonance. Um, the inductive reactions and capacitive reactant will are equal. So I didn&#x27;t even need to do this. The answer was going to be 20. Hey.

Problem

Although an incandescent lightbulb appears to sh…

Problem 69 Hard Difficulty

An $R L C$ circuit has a capacitance of 0.29$\mu \mathrm{F}$ . (a) What inductance will produce a resonance frequency of 95 $\mathrm{MHz}$ ? (b) It is
desired that the impedance at resonance be one-fifth the impedance at 11 $\mathrm{kHz}$ . What value of $R$ should be used to obtain this
result?

Answer

a) 9.7 $\mathrm{pH}$
b) 10 ohms

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a) 9.7 $\mathrm{pH}$b) 10 ohms

Physics

Liev B.

Marshall S.

Zachary M.

Aspen F.

Electric Charge

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James S. WalkerPhysics

Liev B.

Marshall S.

Zachary M.

Aspen F.

a) 9.7 $\mathrm{pH}$
b) 10 ohms

James S. Walker

Physics