an-ac-generator-supplies-an-rms-voltage-of-500-v-to-an-rl-circuit-at-a-frequency-of-200-mathrmkhz-th

Name: an ac generator supplies an rms voltage of 500 v to an rl circuit at a frequency of 200 mathrmkhz th
Uploaded: 2020-02-21
Duration: 7 min 6 s
Channel: Numerade
Description: An ac generator supplies an rms voltage of 5.00 V to an RL circuit. At a frequency of 20.0 $\mathrm{kHz}$ the rms current in the circuit is $45.0 \mathrm{mA} ;$ at a frequency of 25.0 $\mathrm{kHz}$ the rms current is 40.0 $\mathrm{mA}$ . What are the values of $R$ and $L$ in this circuit?

Question

An ac generator supplies an rms voltage of 5.00 V to an RL circuit. At a frequency of 20.0 $\mathrm{kHz}$ the rms current in the circuit is $45.0 \mathrm{mA} ;$ at a frequency of 25.0 $\mathrm{kHz}$ the rms current is 40.0 $\mathrm{mA}$ . What are the values of $R$ and $L$ in this circuit?

João Gabriel Alencar Caribé · Accepted Answer

to solve this question, we have to analyze the impudence in each of those situations in situation. One in situation too. Situation one we can complete impedance by using homes. Law v. R a. Mass is the coast. Why every mess times the impedance in situation one which leads to an impedance off Vieri, Mass. Divided by IRA mess. Then the first situation The impudence is equals 25 divided by 45 times, 10 to the minus street, on the other hand, on the second situation. Similarly, in credence, he&#x27;s given by five divided by 40 times 10 minus street. Now remember the following the impudence The situation is equal to the square root off R squared plus Excel squared. Now we can use Z one z two to complete. Both are on Excel How to do that as follows. First Z one is opposed to the square root off R squared clothes to pi times the frequency number one times being booked us on disease squared We already know the value off one Then we solve this equation for l to get the following z one square is equals two R squared plus too pious one times l squared then too pious One times l is equal to the square root off Z one squared minds are squared Finally l A is equal to the square root off 01 squared miners R squared, divided by to pi times F one Then keep these results we now use it to. And so busy too for the resistance Ze truth is equal to the square root off R squared Plus to buy I have two times l and Disease all squared No, no to that Z two squared These equals two r squared plus two pi times at two times l squared and then r squared, which is what we have to know is equals two z two squared minus to pie F two times l squared. Now we substitute these value off r squared these equations for the doctors to get the following The doctor&#x27;s is equals two the square root off See one&#x27;s weird minus R squared which is? It goes to Z two squared Plus because there is a minus minus true pi times two times l squared and these eggs all divided by to five times f one No, we can solve these equations for inducting we get to pie F one l He&#x27;s in close to the square root office. You one squared minus Z chu squared plus two pi f two will squared squaring both sides We get to pie F one hell squared is equal to Z one squared minus z two squared plus two pi f to l squared. We can now but this term on the other side to get to pie F 10 squared my nose to pie F two times l squared is equal to Z one squared minus z two squared Then we can factor out these l to get l squared times too pious one squared minus too pious two squared Is it close to ze world squared minus the two squared And finally the doctors is the course too The square root off z one squared my Z True squared divided by to pipe F one squared minus two by as two squared by plugging the values that we have completed for Z one z two and the vials that were given by the problem for F one And after we got the following square root off Z one, which is egos 25 divided by 45 times, 10 to the minus three. So five divided by 45 times 10 to the minus three squared minus Zi Chu, which is five, divided by 40 times, 10 to the minus three squared. Invited by to pi times F one F one is 20 times 10 to the third squared minus two ply times after you. True was 25. Time Stand to the turd when these is squared and this gives us an in doctors off approximately 608 Me crow Harry&#x27;s. Now we can go back to the expression we had obtained for the resistance squared, which is there&#x27;s one plugging the values that we have right now and get the value for the resistance. So the resistance squared. He&#x27;s equals two. Zi chu squared z True, he was five, divided by 40 times, 10 to the minus tree squared minus to pie times F two times l to pie. Time left to F too is equals two 25 Time Stand to the third diamonds L, which is equals two seeks your wait time. Stand to the mind of six squared So the resistance them because to the square root of this thing, which gives us approximately 81 homes

João Gabriel Alencar Caribé · Answer

to complete the reactors. We only have to remember that I are. A mass is equal to one over the reactor&#x27;s times V are a mess. Then so be for the reactor&#x27;s Get that the reactor&#x27;s Izzy close to V ROMs divided by I a mess. Then, using the data that was given by the problem, we get that the reactors is opposed to 0.8, divided by 0.515 mealy and piers, Um thes is approximately 155 treat homes, and we can write it as being approximately equals to 1.6 kilo Holmes. To copulate the capacitance, we have to remember that the reactant is given by one divided by two pi times the frequency times the capacitance. Then the capacitance is given by to pipe times. He frequents times the reactors. No using our intermediary result for the reactor&#x27;s on DDE. The initial data given by the problem we have a capacitance that he&#x27;s given by one divided by to pie times the frequency where is too kilo hurt times the capacity of the reactors, which is 0.8 divided by 0.515 I&#x27;m Stan put in my industry at the Z Z equals true um, zero 0.515 time stand to the minus tree divided by two pi times two times stand to the third times 0.8 and this is approximately 5.1 times 10 to the minus eight for its and it can be reading us 51. No, no for its Finally, for the last item, we just have to remember that there are a mess. Current is proportional to the frequency of the sewers. So in the first case there frequents off the source is more to play it by a factor of two. Then the R. M s current in this case will be the R. M s current in the previous case to play it by two. So the R. M s current here is two times 0.515 which is equals true. One point. This is the road tree, really m peers. And finally, in the last case, we have a frequency that is 10 times bigger. Then they need show frequency. So the r m s current here, we&#x27;ll be equals to 10 times. They need show every mess current and these easy goes to 5.15 million amperes

João Gabriel Alencar Caribé · Answer

to solve this question. We begin by using the following equation V. Our romance is he goes through i every mass times z where the is the evidence off the circuit. This is a version off homes role that is valued for arson circuits and engaged have forgot impedance off the circuit is given by the square root off R squared plus exceeds squared. These is the resistance on disease. The reactors the reactor&#x27;s is given by one divided by true pi times the frequency times the capacitance. So putting it all together and solving for the current we get I Every mass is. He calls, too. Our romance divided by the square root off R squared plus to pie see under one squared, no plugging their values given by the problem. We got square root off 10 times. Stand to the third because there is a kilo of warm there and I&#x27;ll do the squared plus to pie piously frequency 125. Hundreds times the capacitance 0.25 me crow fired soldiers attending the minor six. Here we didn&#x27;t have one. I already squared is all under the voltage, which is 42.5. No solving that calculation. We got zero point 00 30 seven nine approximately, and we can write it as tree 0.79 Really, m peers.

Mohit Khurana · Answer

welcome to the problem. Number thirty one point two zero. So this it&#x27;s a pretty one ordinating current. We haven&#x27;t allowed circuit the capacitance off the comm pasture and they never turned off uniter. And the assistance of very sister is given. So these are the they&#x27;re loses. This is L. A and C and we have an issue source and this is his source has voltage elements. Is it cost you one twenty world and the frequency of this issue sources one point two five kilo heart. So between the couch. And so this is Serge. So we need to find out the power supplied by the tonality and power dissipation in their sister. And we have the formless here, so we will use these formulas here to find out the parameters. So let&#x27;s find out the first we will find out the and the African searches on mebecause to pay f. So we have to buy times one point two five independence for our three because this is killer hurt. So this concert to be seven point it five for into dangerous to power three. But Etienne, farcical now finding out the exit then, doctor, A reoccurrence which is Omega and and putting the omega and l here. So this comes or Toby one five seven. Remember, this is twenty times than this. So minus three Hendry. And this is a cause to one forty time standards or minus nine. And this is because one I went to five unit and a score three heart now finding are the XY. So we have except cause to one of our own legacy. So we have a maid at this value and see where this wailing. So we put it back in this equation too. Once comes out of nine hundred nine. No. So we&#x27;re done without coming parameters now that find out the average power. So we have then fight the face factor. Which is it cause to excel mine a sexy over our. So this gives us equals two one fifty seven minus nine zero nine. Or were three fifty and taking the Daniel&#x27;s off this value. So fight comes out to be minus sixty five point zero for delivery. So this is over five now going tto find out the dead, which is the impudence of the circuit. So these are in Siri&#x27;s, so we have so these. Aaron says we have Jerry question our square less excel minus x e hold square. So this comes out to be eight to be Joe. Now we need to find out the average power this epic it. So this is because to be Aramis, I reminisce, goes fi because to be anonymous, it&#x27;s where we&#x27;re jet course fight. So this comes out to be one twenty square for what, Jack, which is a thirty cause minus sixty five point zero four degree. So this comes out to be a selling point three two. What? So this is average? Participated. Now we need to find out the average poverty precipitation than a sister and a sister. So which is it cost to I r M s square? Oh, so this comes out to be one twenty square over eight, thirty square times three fifty. So we have vms. It goes to Isaac Otherness. So we have used this creation here to find out the Aramis. So we had our relative fifty own. So this comes out to be seven point three two. What? So this is the inside of this question. Thank you for watching the video

João Gabriel Alencar Caribé · Answer

we begin this question by remembering the relation between the aromas voltage on the R. M s current. So the remans voltage is equals to the art room. Ask current multiply abiding Penis of the circuit. Them they be That&#x27;s that&#x27;s very good is it goes to the arguments voltage divided by the r. M s current. And now we remember that the impedance off the circuit is equal to the square it off. The resistance is cleared plus the inductive reactors squared and they took The reactant is equals two to pi times the frequents times named look tense squared Then we can solve for the resistance to get that their existence is in question. They feed them too. Square miners to five f l squared under a square root No, we can use our previews result to get that the resistance is it cost to the square root off the ari mass divided my eye ROMs squared minus two pi times the frequency times they looked at us squared, then plugging the values, giving any problem we get that the resistance is close to the square it off 25 divided by 0.26 squared minus too high time. 16 times. 145. Really, Harry. So come to the ministry here, square it. And finally, the resistance is approximately 79 hoes. In the second item, the voltage across the resistor is given by V. Hiram s across the resistor. Is he? Of course, too? The current that flows through the residue store times their insistence off that resistor Then the voltage across the resistor is given by, uh, zero 0.2600 years times 79 homes. And this is you close to 20 point 54 votes. The IRA mess Voltage. A crossing doctor is given by the R. M s across the doctor is he goes to the current that flows fruit in Dr Times, the reactive in doctors and this is their clothes too. Zero points 26 times to pipe times the pregnancy, which is 60 hordes times l conductors, which is 100 45 times 10 to the minus street because there is immediately prefix there. And all of this is approximately 14 point or anyone votes? No, we should evaluate the following quantity. The Squires off the are a mass from the resist or squared. Plus there I remember from the doctor squared, these is equal to the square root off 20.54 squared plus 14 points, 21 squared. And this is approximately 24 point 97 which weaken further. Approximate to 25 votes, then square root off V. Hurry mass. Through the reason Stan squared plus the remans voltage for the Doctor Square. Is he close to the remans? Voltage off the source.

João Gabriel Alencar Caribé · Answer

the relation between the aromas, voltage and the Aramis current is the following. The IRA man&#x27;s voltage is he goes to the Ari Mass. Current times impudence. And in the situation, the impedance has two contributions. Contribution coming from the resister, which is R squared, and another contribution coming from the doctor, which is two pi frequents times in luck tints squared. Then we can solve this equation for the current to get i r. A mass is equals two. The square root off our square plus to buy f l squared This is all under the voltage the your mess Now we can plug in the values given by the problem to get ah, you&#x27;re a mess is equals two the square root off 5 25 squared Plus to buy times the frequency 60 time thing Look tense 295 merely Henry squared and this is all under the voltage which is equal to 20. And finally this is approximately 0.37 to 6, which can be written as 37.3. I really am Piers

Problem

An $R C$ circuit consists of a resistor $R=32 \Om…

Problem 92 Hard Difficulty

An ac generator supplies an rms voltage of 5.00 V to an RL circuit. At a frequency of 20.0 $\mathrm{kHz}$ the rms current in the circuit is $45.0 \mathrm{mA} ;$ at a frequency of 25.0 $\mathrm{kHz}$ the rms current is 40.0 $\mathrm{mA}$ . What are the values of $R$ and $L$ in this circuit?

Answer

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