an-rms-voltage-of-222-v-with-a-frequency-of-100-khz-is-applied-to-a-0290-mh-inductor-a-what-is-the-r

Question

An rms voltage of 22.2 V with a frequency
of 1.00 kHz is applied to a 0.290-mH inductor. (a) What is the rms
current in this circuit? (b) By what factor does the current change
if the frequency of the voltage is doubled? (c) Calculate the current for a frequency of 2.00 kHz.

João Gabriel Alencar Caribé · Accepted Answer

in the first item, we have to cock a little r m s current that flows from the circuit. And to do that, we begin by using some sort off owns well, which is given by V or a mass is he goes to Why a rematch? Times impedance. Remember that thing peons off on in doctor is he goes to to pi times the frequency times they looked at us. Then the army&#x27;s current through that circuit is equals two the voltage divided by two pipe times the frequency times the doctor&#x27;s looking The value is giving in the problem. We have 22.2 divided by two pi times one times 10 to the third It is one kilo hurt times 0.2 29 Time stand to the minor street because it is Emilie, Harry And then all these is approximately 12 points too empty years in the second item we have to calculate by what factor does they couldn&#x27;t change is if we double the frequency. So know that the relation between the current and the frequency is the following You&#x27;re a mess. Is the coast v ery mass divided by two piped into the frequency times the victims. No, if we do as going to two times f, then we will have a new current I prime with Zikos too. V r E mass divided by two pi times two times f times inductive and finally dividing these new current by the previous one we get that is he goes to the voltage divided by two pi times two time the frequency times conductors divided by involved in divided by two pi times the frequency times they looked at us simply find everything we can You&#x27;re left with a factor off one over to which is he goes to 0.5 in the last item we have a frequency off too kilohertz So we have multiplying the frequency by a factor of two, we have doubled the frequency. Then we can use our result from the first item and the result from the second item To get that in this case, the current we&#x27;ll be 0.5 times the current in the previous case, which is 12 point to these is equal to 6.1 amperes

João Gabriel Alencar Caribé · Answer

to call it the Aramis current. We just have to remember that all right, R m s is equals two to pi times the frequency times capacitance times They are a mass voltage and then substituted given data in their equation to get I our romance his equals True to pie times wound Kilo hurt times 0.395 me crew for it times 20 0.5 votes. These is equals true, 0.50 87 And for years and we can write it as approximately 15 0.9. Really And piers for the second item. Note that Hi, Ari Mass. Is he close to two pi times the frequency times the capacitance times they are a mass voltage and now lettuce pools that the frequency of the voltage is doubled. So suppose that have is no two times f What is the r. M s current now? Well, the are a massacre. It will be I pride. A mass is equal street to pi times two times f time See times V. R. M s now dividing i prime ROMs by high are a mess. You got to that easy. Easy Close to two pi times Two times after I see times v r a mass divided by two pi times After I&#x27;m c times we ROMs simply find everything we can. We&#x27;re left with these things being equal to two. So by doubling the frequents off the voltage, we got double the current. So in his multiply it by a factor of two in the last item, we have actually doubles the frequency and have to complete What is the current? So let me call his eye prime again. Well, we have just seemed that the relation between I prime and I is a factor of true, so I prime romance. Zico&#x27;s through two times I Ramesses and leaves his equal stoop to times 59. We just finally closed too. 101.8 merely amperes.

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.

Luis Mendoza · Answer

so in this problem would start by considering a new doctor off 30 million Henry&#x27;s on where adultery react as a doctor is to pointing Kill homes. So 1st 1st team we have to do is to find the frequency of the current going through conductor on for time with Simply used the usual definition off inductive reactors so they&#x27;re going to react in Excel is given. We know lt just inducted. We consult for F So f 15 in my piece equation. I believe the numbers with the frequency of 1.11 Tustin before hair it&#x27;s on now, were given a capacitor that has the same reactions as the doctor at the same frequency that we use calculated. So we need to find a good president. So he would have did react Mrs on the same. So write out an expression for his racks tense. So you have these equality here, and you can just sold for C. So also it for C gives out this equation, so C equals one over to buy a two by Transparency Square L. And he&#x27;s just a pregnancy that was calculated here. Told me that being in the value of L gives us our capacity of 6.83 times 10 to the minus nine. Barracks on for the last part we&#x27;re going to do now is we&#x27;re gonna triple the frequency that went in at the beginning of the problem. So now, instead of having 1.11 times, tend to before we have three point to retreat instantly. Four hertz as the frequency of the current on a given to me. Previously, we need to find a new reaction season both in doctor and the capacitor. So we seize their standard definitions. You change the frequency at for F Brian, you just triple off the real pregnancy for the doctor. Well paying 6300 owns on for the capacitor who obtained 700 owns.

Mayukh Banik · Answer

Yeah. Now frequency is given by one of our two pies. World off. Elsie! Andi Putting the values in you will have 1/2 pi squared off. L is $200 gentle minus 30.2 types capacitance C 0.15 times 10 to the minus six under the square root. So we have frequency equals 919 hearts. Yeah, okay, I r equals. Yeah, Aramis, voltage over are I l is rms voltage over omega. L and I see is Aramis full Just times Omega psi. On calculating this, we find the coming through the registries. 1.5 ampere through the in dr 1.6 ampere on through the capacitor 6.73 me the ampere, RMS current. It was squared off I r Square. Plus I l minus. I c squared equals 2.19 ampere and the face angle fy equals are trained it off. I c minus I l over i r equals negative. 46.7

Sheh Lit Chang · Answer

in this question we have on our see syriza kit. Okay, so are lfc serious? A kids, he went by the are is 2.5 own and then the hour is our 100 micro Henry capacitance is 80 micro ferret t. So they apply parts in this question. Um, had they want to find us, sir? Kids impudence. It&#x27;s 120 hoods. Okay, so given that f is 120 hertz, okay, so we can calculate to buy f is 140 pie, right? And then impedance. The formula for impedance is equal to our square plus XL minus x c square. Then take the square it. Okay, so, uh, because we calculate XL minus x e so XL minus X is two pi f l finance. Wanna work toe by FC? Mhm. So you have 40 pie hangs 100. My cruel Henry minus one over. Um, too high. 2040 pie. Okay, Thanks. 80 micro. Okay. All right. Yeah. So if you calculate this number, you get negative. 16.5 homes. Okay. So you can calculate the impedance Z is equal to our square place XL minus X c square. Okay, Okay. clear. You get 2.5 square plus 16.5 square square roots. You get 16.7 homes. Okay, so this is the answer for part a, then in part B, we want to find Serkis impudence at five kilohertz. Okay, so basically, repeat the steps. That part, eh? So five kilohertz. You know, to buy f iss, um, tend to the fall pie. Okay, so again we find XL minus X Aetius. So 10 to the four. It just rewrite the formula again. Kato by f l minus. Wanna work toe by FC? Okay, so this is attended for high times 100 times ended. Uh, negative six. I&#x27;m sorry. Induct INTs and then one over and to the fall pie 80 times 10 to the 26. Okay. And company days, you get 2.74 rooms. So we calculate this, um, calculate the impedance Z is going to be our square plus x l minus x c square, square it and then 2.5 square plus 2.74 square square It he gets 3.71 rooms. Okay, so this is the answer for part B and then in part C We wants to find a ah I rms at each frequency. Okay, so since we calculated the impedance Okay, so the i r message Just the RMS divide by the impedance. Okay, so at he goes 220 hertz i r m s goes through we rms by Z. Okay. And this is 5.6. Divide by 16.7, get 0.335 MPs and then it goes to five kilohertz. I i r m s if you go to be RMS by Z, which is 5.6 divided by 3.71 Calculated to get 1.51 and gives he Hey, Dan in part, Stevie wants to find a resident frequency. Okay, So resonant frequency. It has a formula. Is he going to run over two pi square root? I&#x27;ll see. Okay, So put the numbers for L. A. C. So you have 80 100 times 10 to the negative six and then the sea is 80 times 10 to the negative six. Okay. And concrete days you get 1780 puts. Okay, this is the answer for party then part e. Want to find I rms at residence. Okay, so at residence Excel goes to XY, and so the impedance is equal to our, which is 2.5 homes. Okay, so the i r m s u p uh, we are m s by our, which is 5.6. Divide by 2.5 couple days. You get 2.24 Yes. Okay, So this is the answer for pretty, and that&#x27;s all for the whole question.

Problem

A $0.22-\mu \mathrm{H}$ inductor is connected to …

Problem 38 Medium Difficulty

An rms voltage of 22.2 V with a frequency
of 1.00 kHz is applied to a 0.290-mH inductor. (a) What is the rms
current in this circuit? (b) By what factor does the current change
if the frequency of the voltage is doubled? (c) Calculate the current for a frequency of 2.00 kHz.

Answer

a) 12.2 $\mathrm{A}$
b) 0.500
c) 6.09 $\mathrm{A}$

Related Courses

Physics

Related Topics

Discussion

Top Physics 102 Electricity and Magnetism Educators

Elyse G.

Christina K.

Aspen F.

Jared E.

Physics 102 Electricity and Magnetism Courses

Electric Charge

The Electric Force

Recommended Videos

Watch More Solved Questions in Chapter 24

Video Transcript

James S. Walker

Physics

Elyse G.

Christina K.

Aspen F.

Jared E.

Electric Charge

The Electric Force

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

a) 12.2 $\mathrm{A}$b) 0.500c) 6.09 $\mathrm{A}$

Physics

Elyse G.

Christina K.

Aspen F.

Jared E.

Electric Charge

The Electric Force

James S. WalkerPhysics

Elyse G.

Christina K.

Aspen F.

Jared E.

a) 12.2 $\mathrm{A}$
b) 0.500
c) 6.09 $\mathrm{A}$

James S. Walker

Physics