an-r-l-c-circuit-with-r200-omega-l295-mathrmmh-and-c497-mu-mathrmf-is-connected-to-an-ac-generator-w

Name: an r l c circuit with r200 omega l295 mathrmmh and c497 mu mathrmf is connected to an ac generator w
Uploaded: 2020-02-20
Duration: 7 min 6 s
Channel: Numerade
Description: An $R L C$ circuit with $R=20.0 \Omega, L=295 \mathrm{mH},$ and $C=49.7 \mu \mathrm{F}$ is connected to an ac generator with an rms voltage of 21.5 $\mathrm{V}$ . Determine the average power delivered to this circuit when the frequency of the generator is (a) equal to the resonance frequency, (b) twice the resonance frequency, and (c) half the resonance frequency.

Question

An $R L C$ circuit with $R=20.0 \Omega, L=295 \mathrm{mH},$ and $C=49.7 \mu \mathrm{F}$ is connected to an ac generator with an rms voltage of 21.5 $\mathrm{V}$ . Determine the average power delivered to this circuit when the frequency of the generator is (a) equal to the resonance frequency, (b) twice the resonance frequency, and (c) half the resonance frequency.

João Gabriel Alencar Caribé · Accepted Answer

the average power that is delivered to the circuit is Eco&#x27;s true, the R E master voltage kinds, the rmx current times. Their co sign off the fees with No, Remember that, Ari Master voltage, Is it close to the area? Maskell rent times the imperatives then they are a mask or rent is the question the voltage decided by the impudence. Therefore, the average power can be reading mass. Um, I remember squared, divided by the impedance times they call Sign off the face, but the course hand off the phase. Is it close to the resistance divided by the pendants and the average power? Is it close to the R A mask voted squared, divided by the square times the resistance In the first item the circuit is driven out residence. Then remember that at residence both react. Ince&#x27;s are equal and therefore the people&#x27;s easy goes to the resistance. Then, in this case, the average power is it close to? They are a master voltages squared, divided by the resistance. And these is itcause True, 21.5 squared, divided by 20 which is approximately 23.1. What on the next item, free things off the circuit is it goes to two times in the resonant frequency as the resonant frequency is because to one divided by the square, root off L C. Then to this day frequents often a circuit. The videos is equal to the square root r squared. Plus, the difference between both reactors is squared. Before planning anything in this equation, let us take a look at the reactors is the capacity reactors is equals to one divided by the frequency times the capacitance These equals true one divided by well, true times like capacitance times this crab boat off Hell time See which finally, of course, too. The square it off. L divided by two times the square root off. See which then I have off the square root off, Help oversee They looked reactions. In the other hand, is it close to the frequency times they looked at us? We can see close to two times l divided by the square root off health time See And these equals two two times and square it off l O R c e. Then excel miners. That seat easy goes to two times the square root off. They&#x27;ll oversee minus 1/2 in the square it off L A mercy and these is equal to three. House off this Beirut off l oversee. Then we can plug in these results in our expression for the impedance we get. The easy question is quite a bit off r squared plus mine over for me times they&#x27;ll oversee. Finally, we can plug in the values given by the problem to get square root off 20 squared plus nine over four times 295 times 10 to the minus street divided by 49.7 times 10 to the minus six. This is approximately 117 0.3 owns And now we can proceed to calculate what is the average power consumed by our circuit. The average power is equals Truth. The remans for voltage squared, divided by the impedance squared times the resistance as we had seen before. Right you&#x27;re then what? We get 21.5 squared, divided by 117 point treat squared times the resistance which is 20 20 and these is approximately zero point 67 too. What? On the next item, we have the following Sit up now the frequency. Is it close to 1/2 off the resonant frequency which is the cause to one divided by two times the square it off. L time, see? No, the capacity reactant is enclosed one divided by one divided by to the square Root off l time. See Time seat on these. Easy question. Two times the square root off l time See why you open your other hand. Excel is equals to one he wanted by two times the square it off l time see times ill which is equals to 1/2 off the square Root off l oversee And that this time we get Excel My nose XY is equal to 1/2 square Root off L over seats minus two square root off l ever see which is equal to minus street over to express route off L over seats Then the impudence is the cost of the square root off r squared plus mine&#x27;s three over two times the square root off l oversee squared, which is equal to the square root off r squared plus nine were four times l Oversee. Note that way Already have seen his expression right here. So the value off, the impudence will be precisely the same. And then they value off the average power. We will also be the same. So on the last item, the average power is close to 0.672 What&#x27;s as well.

Averell Hause · Answer

So here report A We have residence so we know that then the inductive reactant is equal in the capacity of reactions. And we know that the power is sent the equal in 1/2 times the current multiplied by the voltage times co sign of the face angle Phi. So we can say that the formula for the phase angle Phi would be equaling are 10 of X sub out minus except C divided by our We know that X the again the inductive reactant equals the capacitive reactor. It&#x27;s which means that this value zero Which means that fives equaling arc Tanne 00 This would be equaling 20 degrees, which means that CO sign of Fei is equaling co sign of zero degrees, which is equaling one. And so that would be the power factor of the circuit. And so, for part B, we then know that the current I will be equaling to the voltage over. The impotence is easy. And so and I residents, we have that the impotence Z is equaling are and so I z equaling simply the over our and we can say that then the power is equal in 1/2 multiplied by I he co sign of fine. And we know that CO sign of five is actually one. And so this would be equaling to 1/2 V squared over R At this point, we can solve. And so the power with the 1/2 multiplied by 150 volts quantity squared, divided by 150 arms. And this is giving us 75.0 watts. This would be our answer for part B um four part See, We know that the formula for the average power delivered by the source p equaling again 1/2 times v squared over r multiplied by co sign of the phase angle. If I hear the power factor here is again one. And so the equation becomes again V squared over to our, which is exactly what we had in part B. So the average power delivered by the source will be equaling two again 75.0. What&#x27;s this would be our answer for part C. That is the end of the solution. Thank you for watching

Ze-Han Lee · Answer

for these problem. We have this. Ah, are RCC every circuit and that we know Tow the pyramid is for our ale and see. And also we know the bold. Each amplitude is 1 50 Will 1 50 volts. Ah, and, uh, and the frequency equal to the resident&#x27;s frequency of the circuit. So this this That means that Ah, one over Omega Psi pickle too. Oh, Miguel, in this problem or impotence off the circuit simply ableto are Okay. So for part A what is the power factor? So if Z you could our pal factor course I&#x27;m fi equal Thio are oversee in this case equal to unity. If a part b So I want to find an average of power they diverted by the source. Ah, So the power equal to the average power equal to B r. M s squared over our and we already know the peak value for the ah for the source, which is 1 50 votes so eight will equal to 1 50 over square two squared over our Ari&#x27;s ah 1 50 homes. So the veterans 75 what&#x27;s and for Parsi sees that we have a new cup, Asta, but the frequency is adjusted to the new residents better. So I&#x27;m gonna find out the average power to get a bit by the souls in this case. All right. So biggest the frequencies is a gay in the new residents. Better so he tells us that one over Omega Prime See primes. So only the prime is the new frequency. See, Premise is the new capacitance again equal Thio Omega Prime times L. Okay, so by using this condition waste Do you have ze equal to our So a fact off the capacity still canceled. Always the doctor in that case, the power against them people to B r. M s squid over our and, uh, just give us the same result. 75. What&#x27;s okay?

Khoobchandra Agrawal · Answer

in our series Off in Dr of Register on Capitol Components. Having the bed indoctrinates don&#x27;t really handy Carpets Tinto 1 40. No, no, Forget it. And the distance off. Chief it deal the letter Hasn&#x27;t Aramis bolted up? Want on people on frequency? 1.25 kilohertz. We have to Gallipoli Barber supplied by the generator B but poverty depicted in the register in our in order to see you No average power supplied by the source. The average off source is given. Bite I out of it the famous and do cross fight Bob, but consumed by register art Benry Ice. Where are Emmis? Into what? These two concepts we have to use be required the omelet frequency so we can measure now. Goodbye ever the window. 3.1 ft, 1.25 in tow. 10 to the power three Radian per second. So maybe you will get seven point a 5 ft and 10 to the power three Radian per second. We can fight the reappearance off. Inducted on Capitol as well. You re a paint off in The spirit is on me. Omega is seven. Went 85 ft 10 to the power three on Independence. It continually, Henry, let me check. So 20 in tow tend to be power my industry on solving it. It would be 1 57 0 Andrea prints off campus studies burn up on the way. I do see Omega is seven point it Fight foot she is given. See having the just be 1 14. I know on solving it you will get the get prints off campus. Turtle, be 909 No. Start solving trust. Able to fight the frayed relations between correction. You It would be stand up. Fight. Just give invite. Naturally. A prince of the circuit XL minus xy upon, huh? Except it&#x27;s one piece of it. XY is 90. You know, Night of the distance is 3 50 so we will get

Khoobchandra Agrawal · Answer

I know friends here is given that in a large circuit and see our our LRT meaning is that it it makes no difference. You write l gl RCN CLR. It doesn&#x27;t make it but the state off one trip home and that is having trouble. 175 Indy and abstinence is why zero one. One end, you know, might grow up in it, but I thought it is worth having that amplitude up full days. 1 50 would and frequency people toe regularly reports on the guy&#x27;s photo when we got that bon upon Trudeau. Lt in part, we have to calculate our picture that it&#x27;s got some fight and be part. We have to calculate average power, deliver the average and see but got pissed, etc. Is replaced by under capstone while you 36 might know better and frequency again interested toe regularly frequency. And he did then bodies above average power deliver in. This gets really average no party, uh, a regular frequency or maybe not face difference between courage. In both cases. Zero. Re a paint off in Dr. It&#x27;s going to re offense off tapestry. That is really a pinch of that circuit is zero impudence. It&#x27;s going to what? That is 1 50 or so power factor or some fight having a bit. But on a bus unsaid off a problem his father factories. But in the park, we have to calculate Yeah, every bubble are yet, um it the elements and to cause a fight. Are you had a Mrs? I&#x27;m not by two Be automated, be not by toe power factor is given, but so it can build and I not, huh? It better be. I know with me. Just a moment, please get it in the hub I&#x27;m not defined that we not by yet and get it&#x27;s goingto are for a unit frequency and be not so it becomes be not a square by work Be not is given but people divided by doing toe are is 1 50. So it will be 75 watt under a beeper. No sea parte. See, It&#x27;s just you see this But frequency is also changed to regulate frequency. So impudence will remain Our how are the zero sorry phase and video for our factor will be one. So every Powerball very mean Save that is off 75 point. You know work. They&#x27;re soul for this problem. Thanks for watching it

João Gabriel Alencar Caribé · Answer

in the first item. We have to evaluate the power factor of the circuit. So we have to evaluate the co sign other fees and the music goes to the resistance divided by BNP. This and in this case, the impudence has two contributions, one coming from the resistance and another one coming from they looked at us. So the feelings is it goes to the square it off squares plus the inductive reactors. Where&#x27;d they looked? Reactant is given by two quiet times the frequency times, the induct ins. No, we can plug in the values given by the problem in this equation and get the power factor. We choose the square root off two times, stand to the turns. There is a kilo there squared plus to pi times 1.55 Again there is a kilo times 292 merely squared. This is old under the resistance reaches two times 10 to return and these things approximately 0.5 seven 52 which we can for the approximate to 0.575 in the next item we have to complete. What is the average power consumers by that stir Great the average power is given by the are a mess voltage times the arguments current times the power factor. Now remember that there is a relation between the aromas voltage on the Aramis current and that relation is the following. The remans voltage is of course, to ari mass current. Multiply it biting Peters, then solving for the R. M s current, we get that the Aramis current is equals two The aromatase voltage divided by eating peanuts. No, the average power is then the remans voltage squared divided by they impede us and multiply it by the power factor and disease equals truth. A square root off the resistance is squared. Plus to buy f l squared under a square root under the aromatics voltage squared times the power factor This is just impedance which we have already calculated here. So we know just have to put in their values given by the problem on the power factor that we have completed before To get the following square root off two times 10 to the third squared plus to five times 1.55 time stand to deterred times 292 times 10 to the minus tree squared This is all under 20 points. Eight squared times the power factor, which is 0.575 and disease approximately 0.715 five, which we can write as 71.6. Really, What?

Problem

The intensity of a lightbulb with a resistance of…

Problem 87 Hard Difficulty

Answer

a) 23.1 $\mathrm{W}$
b) 3.94 $\mathrm{W}$
c) 3.94 $\mathrm{W}$

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a) 23.1 $\mathrm{W}$b) 3.94 $\mathrm{W}$c) 3.94 $\mathrm{W}$

Physics

Elyse G.

Marshall S.

Aspen F.

Jared E.

Electric Charge

The Electric Force

James S. WalkerPhysics

Elyse G.

Marshall S.

Aspen F.

Jared E.

a) 23.1 $\mathrm{W}$
b) 3.94 $\mathrm{W}$
c) 3.94 $\mathrm{W}$

James S. Walker

Physics