a-generator-connected-to-an-rlc-circuit-has-an-rms-voltage-of150-mathrmv-and-an-rms-current-of-39-ma

Question

A generator connected to an RLC circuit has an rms voltage of150 $\mathrm{V}$ and an rms current of 39 $\mathrm{mA}$ . If the resistance in the circuit
is 3.3 $\mathrm{k} \Omega$ and the capacitive reactance is $6.6 \mathrm{k} \Omega,$ what is the inductive reactance of the circuit?

João Gabriel Alencar Caribé · Accepted Answer

to some of this question, we have to remember two things. One is the relation between the Aramis Voltage on the R. M s current. Which of these wines and the 2nd 1 is how to calculate impedance, which is known in the following way. Then we have to do the following. So we have both the voltage on the current. Then we concoct anything Peters Pete does. Is he close to default ish, provided by the current and using their value is giving you the problem. We get that impedance is equals to 150 divided by 39 times 10 to the minus treat. Then we can plug in these value these equations to get 150 divided by 39 times 10 to the minus three. His equals to the square root off. No lugging these value for the resistance here. 3.3 times Stand to the turn squared plus excel which we don&#x27;t know miners exceed reach wasn&#x27;t even 6.6 times 10 deterred square. And then we just have to solve this equation for excel. Then we do it as follows. So squaring both sides. We got 3.3 time stand to the turn squared plus Excel Mind 6.6 times 10 to the third squared equals to 150 divided by 39 times, 10 to the minus tree squared. Then we move these terms to the other side to get Excel minus 6.6 times. Tend to deterred. Squared being Equals two, 150 divided by 39 times, 10 to the minus. Street squared miners 3.3 times 10 to the third. It&#x27;s queer. No, we can take the square root off both sides. So taking the square root, we get eggs. L minus 6.6 times 10 to occurred being you close to plus or minus the square root off 150 divided by 39 times, 10 to the minus. Street squared minus 3.3 Time stent littered squared. And finally we move these terms with the other side to get excel. Is it close to 6.6 time? Stand to deterred flows or miles. The square root off. 150 divided by 39 times 10 to the minus. Tree squared minus 3.3 times 10 to the third squared and disease approximately 8.6. The won&#x27;s or 4.6 warms. Both solutions are good.

Luis Mendoza · Answer

So this problem were considered on RLC circuit and serious general social conservative issues. Capacitor assistance on Dr Will connect any serious to the same alternate during generator is shown to Samish right here. So we have to the ballot. Your resistance is 275 homes. The resistive inducting excel due to doctor A 648 on under system capacitance due to the laboratory here exceeds 415 homes. I thought that the current that flows through a circuit he start off 0.23 Tree and pierce are finding goldfish of the generator. So what does The generator is related directly to the current times. Ditto impotence of the circuit. See into funding because of the security we used expression, expression terrace final on your textbook. His eye is the square root off r squared plus X l inductive reckons minus d. Okay, that sitting practice. So our quarter close exile mind sexy both times square and squared. With that so useful in our numbers, we have a value for the current. We have other for our excellent exceed. You know, if this gives us a bowl. Tisch of 83.9 volts

João Gabriel Alencar Caribé · Answer

we begin this question by calculating the impudence off the circuit so we can couple of impudence by using and adapted for off homes low. Which is the r a mass is he goes to Why we mass times p this so I didn&#x27;t do this. These equals two V hurry mass divided by I are a mess which using the information given in the problem. Zico Stoop 36 divided by 0.28. And now we remember that the students is given by the square root off the resistance squared plus and the reactor squared where the reactant is given by one divided by two pie factory frequency times the capacitors squared so we can solve for the capacitance To get Z squared, he&#x27;s equals towards squared Plus to buy FC under one squared. No, we have one Divided by two pi embassy is equal to the square. Root off these words. Minds are squared Then to buy F seat is equals to one divided by the square root off Z squared minus R squared And finally the capacitance is given by to pi times the frequency times the square it off the squared minds are squared this is all under one and now blinking all the values even by the problem on our impudence, we get that the capacitance is the question to pie times 180 times the square root off 36 divided by 0.28 squared, minus 54 squired. This is all in the war, then, is approximately 7.6 times 10 to the minus six for us and 10 for the minor. Six was on my crew then the capacitance is approximately 7.6 me crow forest.

Breanna Kloczkowski · Answer

Okay, guys. So I already wrote out all the information you were given in the problem on the screen. So to solve this, we are just going to start off with the egregious we&#x27;re gonna use. So solving it&#x27;s from our first gonna use except out equals two pi f o. And then, um What? When I saw that for l, we get That&#x27;s so now what we wanna do issues the equation. Sorry, x seven l equals the RMS over I, IRA, Miss and substitute got into the equation that we just your down so wanted You don&#x27;t really get Ellie whose The RMS over I or of us all over two pi f And so when we do that, we&#x27;ll be able to simple by it and get this equation. And so now I want to Europe this we can just substitute in you numbers that we were given in the question and we wanna use this room hurts and no, it, um kilohertz just because that&#x27;s what the But there&#x27;s the units at this equation and requires us to use. So just make sure that you&#x27;re not messing up by feeling to convert that, and then all we have to do is soft our problem and this is the answer

João Gabriel Alencar Caribé · Answer

to complete the resistance in the circuit. We begin by calculating the impedance off the circuit so we can complete the impudence by using the adopted version off as well. So v are a mess. He&#x27;s equals two. Why are a mass times the impudence? So thank you. This is equals two V. All right. Mass divided by right. I remember plugging the value is given by their problem, these one in these one we got 95 divided by 0.722 And now we remember that impedance is given by the square root off the resistance squared plus the reactant squared. The reactant is one divided by two pi times the frequency times they could pass down squared. Then from these equation we get, that is this word is equals two R squared plus to buy See under one squared. Now we can solve for the resistance to get our is equal to the square. Root off these weird minus to buy F C under one squared, then plugging the value we have calculated for the peters and the order values given by the problem, we get that the resistance is equals to the square root off 95 divided by 0.72 squared miners to PI times 150 times 13 meat group. All right, and this is all under one and squared. Finally, By solving the equation, we&#x27;ll get that the resistance is approximately 103.6 to serve them homes.

João Gabriel Alencar Caribé · Answer

in these questions, we have to complete the impedance off that R L C circuit. So to complicate the impedance, we have to complete both reactors first. And we begin by copulating the capacity reactors, which is given by one divided by two pi times the frequency times, the capacitance and blinking in the values given by the problem. We have two pi times 60 times 22.8 times 10 to the minus six, and this is all under one. And this is approximately 116 goals. Now we complete the inductive reactors, which, even by two why times the frequency times they looked at us and its Sequels to two pi times 16 times 135 times 10 to the minus three and disease approximately 50.9 homes. Now we are in position to copulate impudence, which, given by the square root off the resistance squared, plus the difference between the reactor NCIS squared and these these equals to the square root off 1.5 understand to the third squared plus 116 minus 51 9 squared and usually is approximately 15 Who won owns, which can be further approximated to 1.5. Keeler warms

Problem

A manufacturing plant uses 2.22 kW of electric po…

Problem 56 Medium Difficulty

A generator connected to an RLC circuit has an rms voltage of150 $\mathrm{V}$ and an rms current of 39 $\mathrm{mA}$ . If the resistance in the circuit
is 3.3 $\mathrm{k} \Omega$ and the capacitive reactance is $6.6 \mathrm{k} \Omega,$ what is the inductive reactance of the circuit?

Answer

8.60 $\mathrm{k} \Omega$

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