a-115-omega-resistor-a-676-mh-inductor-and-a-189-mu-f-capacitor-are-connected-in-series-to-an-ac-gen

Name: a 115 omega resistor a 676 mh inductor and a 189 mu f capacitor are connected in series to an ac gen
Uploaded: 2020-02-18
Duration: 3 min 1 s
Channel: Numerade
Description: A $115-\Omega$ resistor, a 67.6 -mH inductor, and a $189-\mu$ F capacitor are connected in series to an ac generator. (a) At what frequency will the current in the circuit be a maximum? (b) At what frequency will the impedance of the circuit be a minimum?

Question

A $115-\Omega$ resistor, a 67.6 -mH inductor, and a $189-\mu$ F capacitor are connected in series to an ac generator. (a) At what frequency will the current in the circuit be a maximum? (b) At what frequency will the impedance of the circuit be a minimum?

João Gabriel Alencar Caribé · Accepted Answer

for the first time thing, you have to remember the following. So there is a relation between the Ari mass voltage and current in the circuit. And this relation is as follows. There are events of alterations. It goes to the R. M s current times. They see this then the hairy mess current is he goes to the harem as voltage divided by an impedance. Now remember the following this is the vocation of alters depends only on the stores and not on anything else. No, The only thing that we can change anything that circuit he&#x27;s impedance. So to get the maximum current ever we have to couple it. What is the minimum impedance ever. So we have a minimum Impedance, you have the maximum possible are a masquerade. Now remember that the impudence is equal to the square it off r squared, plus the difference between the two react Ince&#x27;s So it&#x27;s very easy to see that when this turns is it goes to zero, we have the minimal impedance. Then, because of that, we conclude the following through the biggest ever current that can run for the circuit. Who happened when the reactant is on the same. And when this happens, the circuit is running out residence. And we already know that the resonant frequency of that, sir quite is equals to one divide it by two pi times the square it off the inducted its times the capacitance playing in the values that are given by the problem we get the following resonant frequency one divided by to pi times the square id off 67.6 Time stand to the minor street because off the mili perfect here for us clothes No sorry times 189 times 10 to the minus six Because of the my group prefix here and this is all under a square it then this is approximately 44.5 hertz on the next item we have to calculate what is the frequency that makes the imperials minimum Now, Lord, that in the rest item we had a ready analyzer impedance and concluded that wending attendance is minimal. The current is the maximum and we have further calculated that if the resonant frequency is the one that makes the emptiness minimum, as we had already think when doing the last item and therefore the frequency that minimizes the impudence is the resonant frequency, as we had just seen in the last item. Then the frequency that makes the impudence minimal is approximately 44.5 hertz, which is the resonant frequency That&#x27;s so great.

Luis Mendoza · Answer

so pretty scrolling were considering on our Lissy circuit on the circuit House resist or we tend homes. Resistance Capacitance, off 12 0.0 Total Ferrets conductors off syrup ones who are 17. Hendry&#x27;s on all the story elements are collectively Siri&#x27;s do on a senior writer with 100 55 bolts on first winning to find what is the frequency. Because, I said the current said his maximum on the grand halls of silicate. Well, I was gonna be this maximum when the generator has the frequency that if the circuits restaurant pregnancy, I always need to find that rested and frequency, which is the invited standard equation. One over to buy the courtroom healthy. Well, any numbers between a resonant frequency of 352 hertz don&#x27;t remember. By definition of the resonant frequency, it means that the capacity reactions and inducted reactors cancel each other out so the impotence is equal to the resistance, so C equals R. Then the current in the circuit is simply even by the voltage of the generator, divided by parties resistance, which is keeps us. Our Karenna off 15.5 appears

Averell Hause · Answer

party, the impotence Z of the parallel combination. We can say that one over the impotence Izzy would be equaling to the square root of one over R squared plus omega psi minus one over llega al quantity squared. And here, when Z equals are the impotence of the parallel residents reaches its maximum, which would mean that the inductive, capacitance or rather, omega psi, equals one over. We&#x27;ll make it out, and so we know that weaken. Let&#x27;s change the notation of omega because we&#x27;re at residence. So we&#x27;ll say that omega, not as the maximum resonance frequency and then solving for Omega, not this, would be equaling 21 over the square root of the induct insult part by the capacitance. And so, for part A, we have the resident&#x27;s frequency is equaling one over the square root. Ah, 8.50 times 10 to the negative Sixth Farage&#x27;s multiplied by 11.2 times 10 to the negative Third Henry&#x27;s, and this is giving us 3.24 times 10 to the third radiance for a second. And then we can say for part B will one over. The impotence is equal in the square root of one over R squared and again we can see that Z equals R or Z is equal in 125 homes. That is the end of the solution. Thank you for watching.

João Gabriel Alencar Caribé · Answer

we begin the first item by calculating the impudence of the circuit. The Penis is given by the square root off the resistance squared. Plus they took the reactant squared. They looked Reactors is given by to pi times the frequency times in doctors. Then the impudence is he goes to the square it off r squared plus to buy times the frequency times they looked at us squared finally putting the value was given in the problem We get the following value for the impudence Z is he calls to 1.15. Don&#x27;t forget about this kilo here Time stand to the turn squared Plus to buy times 1250 times they&#x27;re five 05 times 10 to the minus street Because there is a feeling here squared And these is approximately four one to mine 0.62 homes And now we can calculate the current that flows from that circuit. Remember, Holmes? Well, we are Romance is a costa Why are a mass times impedance? Therefore I r a mass is equals two busy Ramesses divided by the impedance. From then, we can just plug in the value of impudence. We have just calculated and the value of the voltage. That was even money problem to get 14.2 divided by 4129.62 to get a value off approximately 3.44. Really Mm years on the second item. We want to include a capacitor in Siri&#x27;s lifting brokered such that the new current Hi are a mass is he goes to have off the old current No, don&#x27;t achieve this result. We know that the only thing we have to do if this capacitor is get a new impedance z prime that is he close to two times the old impudence. So we want to double the value off impedance. Then we begin to solve the question and you impudence! Is it close to the square root off r squared? Plus the difference between the react Ince&#x27;s squared? No, we have a capacitor and these must be question to times square it off r squared plus exhale squared then with solve this equation for XY and this is as follows squaring both sides. We have power squared plus XY minus x l squared is equals 24 r squared plus exile squared Dan, move. These are to the other side and we got X l x c minus x l squared He&#x27;s equals True for R squared minus R squared plus four eggs l squared them. That next step is to move these exponents to the other side of the square root and then we got accede mines. Excel is equal to the square it off three R squared plus four eggs Ill squared Damn! We move Excel to the other side XY is equal to the square root off three R squared bliss for that was that was squared plus excel There is an important detail your had music which is the following when they move exponents to the other side and think this square it We have to consider both values So plus or minus the square root then exceed musicals to plus or minus to the square root plus excel Now we can plug in the values that were given by the problem So we got XY easy cause too excel how much he&#x27;s excel You&#x27;re a tease This expression to pipe times the frequency times they booked us time Stand to the ministry because there is Emilie in look tense plus or minus the square root off tree times The resistance is 1.15 kilo warms so there is a 10 to the turn here squared plus four times again eggs ill which is to pie times 1 to 50 times 55 Thanks. 10 to the minus three squared. Finally, we get the following results. For the capacity of reactions, it will be equals. True, 12 063 point servant 85 or my news for 131 point to six free. Well, the reactor&#x27;s can&#x27;t negative. So we just throw the solution or wait, then these is capacity. Reactor&#x27;s off the new capacity we have two, including the circuit. But then this is not the whole story. We have now to remember that capacity reactant is equals two word divided by two pipe the frequency times the capacitance. So Indians for the capacitance we get that past tense. Is it close to one? Divided by two pi times the frequency times the reactors Damn, we get that the capacitance is ICO stoop to pi times 1 to 5 old times ones is true. 063 0.785 under one and finally leaving approximately 10 0.5 Nano fire. It&#x27;s

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.

Ryan Hood · Answer

party is asking for the resonant frequency and so do party. We can use the formula that the resident frequency is one of the square root of the induct inst times capacitance. And now I can just plug in these values with Ellen Henry&#x27;s and precedents of parrots only plucking those values. We did 5.77 times 10 cute radiance per second for the resonant frequency here. And that&#x27;s answer to party. The Barbie. We want the maximum hurry. And so for this, we&#x27;re going to use the formula that the current is equal to the voltage over the impudence. And since we&#x27;re at residence, the impedance is equal to the resistance. And so now I can plug in both these values for voltage. We know that it&#x27;s 2 40 volts and we know the resistance is 100 homes. And so this ends up giving us two point for dance Amperes important. See, we want the voltage across the oppressor. And so to do this, we want the reactant. So the capacitor, the reactions of the capacitor is given by one over the frequency task capacitance. And since we&#x27;re at the resident frequency, this frequents here is just equal of this frequency of here. And we know what the capacitance is and so we can plug in those values and we get 1.73 times 10. Cute. And this is the gnomes. Now that we know the reactions of the master, we can figure out the voltage across the capacitor with this formula here where we&#x27;re going to use the eye that we found in part B playing those values in. Here&#x27;s a voltage 4.15 times 10 cubed and this is in bolts department D. We&#x27;re going to do essentially the same thing except for the in doctor. So we need the reactions of the conductor. This is equal to Omega Times L But Omega is the resident frequency. So it&#x27;s omega non. And then hours gonna plug in these values and we get 1.73 times 10 cute dolls. And now we can use this equation. We know I as we found it in part B. We just calculated the reactant CE. And so we complied was in, and we get 4.15 times 10 Q bolts. Notice that these two voltages are the same since we&#x27;re at the resident frequency. Now hurry. We want the total energy store in the capacitor and the in doctor. And so the star of the classroom. The formula to use is 1/2 constance voltage across the capacitor squared and we know what the capacitance is. And we calculated this to be this appearing Parsi and so it complain all that in we get that we could do the same sort of thing for the in doctor. That&#x27;s if the formula was 1/2 conduct in ce times the current&#x27;s word. But we found the current in part B, and we&#x27;ve always known the induct in CE. And so we conclude that in and we get 0.86 for Jules Now, these air supposed to be the same. I&#x27;ve got different numbers because of some rapping errors. But these were supposed to be the same because we&#x27;re out residents and so completes the prop

Problem

(a) Find the frequency at which an 18 -\muF capac…

Problem 65 Medium Difficulty

A $115-\Omega$ resistor, a 67.6 -mH inductor, and a $189-\mu$ F capacitor are connected in series to an ac generator. (a) At what frequency will the current in the circuit be a maximum? (b) At what frequency will the impedance of the circuit be a minimum?

Answer

a) see work
b) 44.5 $\mathrm{Hz}$

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a) see workb) 44.5 $\mathrm{Hz}$

Physics

Elyse G.

Christina K.

Marshall S.

Zachary M.

Electric Charge

The Electric Force

James S. WalkerPhysics

Elyse G.

Christina K.

Marshall S.

Zachary M.

a) see work
b) 44.5 $\mathrm{Hz}$

James S. Walker

Physics