the-phasor-diagram-for-an-rlc-circuit-is-shown-in-flgure-24-38-a-if-the-resistance-in-this-circuit-i

Question

The phasor diagram for an RLC circuit is shown in FlGURE $24-38$ . (a) If the resistance in this circuit
is $525 \Omega,$ what is the impedance? (b) If the frequency in this circuit is increased, will the impedance increase, or stay the same? Explain.

João Gabriel Alencar Caribé · Accepted Answer

in the first item. We just have to remember that the co sign off the phase is he goes true. The resistance divided by the impedance and then the impedance is because to the resistance divided by the co sign off the phase, the resistance is 5 to 5 homes. Onda face is 30 degrees, so we have the cool sign off 30 degrees and these is equals 25 25 divided by the square it off three divided by two. These gives approximately 600 seeks owns off impedance. For the second item, we can remember off the following the tangent off the phase is equals two Accel Miners XY divided by the resistance. The phase in these questions is equal to 30 degrees and the tangent off 30 degrees is bigger than zero. Therefore, excel in this circuit is already bigger than exceed. Now remember, the following Excel is equal to the frequency times. They look tense on daxi musicals to a world divided by the frequency times the capacitance. By increasing the frequency, we are increasing excel while decreasing exceed. Therefore, what happens is that the quantity excel miners XY as a wall, you increase then remember that impudence is It goes to the square it off r squared. Nothing happens in the resistance as we mass with the frequency plus Excel miners XY squared. We have seen that by increasing the frequency, we are increasing this term here. Therefore, by increasing the frequency in this particular sirrah quite that particular set up. We are also increasing the impudence.

João Gabriel Alencar Caribé · Answer

for the first item. Remember that the co sign off the phase Is it close to the resistance divided biting Penis, then the impudence. Easy course, too, the resistance divided by the co sign off the face. The resistance is he goes to 25 homes. The co sign off the face is a course to describe it off. Three Divided by two. This is the co sign off 20 degrees, and this is approximately 29 homes for the second item. Remember that impedance is the question that square it off the resistance squared, plus the difference between the capacity the reactant, says squared. Then we can solve this equation before the capacity reactors. To get the following we first square both sides to get to C squared easy course towards Squared plus Excel, my new sexy squared. Then we know this to get Z squared, minds are squared. He&#x27;s equals two Excel miners XY squared, then the square it off both sides to get pleasure minus the square it off. The Z squared minus R squared is he goes to excel minus X e finally exceeds the capacity reactors is equals. Two Excel plus or minus squared off Z Squared Minds Arctic Squared Dan, we can calculate using the data given in the problem. Exhale is he goes to two pi times the frequency times 160 times 10 to the minus three, which is the doctors, plus or minus the square it off Z squared. So to keep the press even, let&#x27;s do like this 25 divided the way the square root off. Three divided way too squared, which is named P squared minus 25. Squared them. We get the reactive capacitance off approximately 69 point 7 to 6 homes. War 40 point 858 hose. Then we have to choose one off those values. How can he do that? Well, not that the circuit is such that the voltage is leading the current, therefore disease an inductive circuit. Then we must choose. There&#x27;s more capacity reactors. So we go with these value for the capacity reactors. Then we can finally complete One is the capacitance off that circuit. So remember that the capacity reactors is it goes to one divided by two pi times the frequency times the capacitance, then the capacitance is equals to one divided by two pi times the frequency times, the capacity reactors, the reform We get the capacitance off one divided by two pi times 55 times 40.858 And these is approximately 71 me grew for its now for the last item We have to analyze what happens to the impedance when we decrease the capacitance. True knows that, Z because he caused to the square root r squared plus Excel My news XY squared No, that has decreased the capacitance. What happens when we decrease the capacitance? XY is he goes to one If I don&#x27;t bite to pi times the frequency times the capacitance By decreasing the capacitance, we will increase the capacity reacting lt&#x27;s under four. By increasing the capacity reactions thes difference as a wound, we&#x27;ll decrease. Then the impedance will also decrease if we decrease the capacitance.

João Gabriel Alencar Caribé · Answer

for the first item. Remember that the co sign off the phase is it goes to the resistance divided by the impedance, then the resistance. Is he close to be those times they call Sign off the face and we know both. Impedance is authority to 337 and the co signed off the phase is the co sign off 30 degrees, which is the square root of tree divided by truth. And this is approximately 200 and 92 rooms for the second item. It is quite straightforward to see that this record is not working at resonance. And why, in saying that he&#x27;s quite that it is quite straightforward because of the following the tangent off the fees is equal to Excel mine Oh, sexy, divided by the resistance when the circuit is working at residence. What happens is that both react. Ince&#x27;s are equal and the face is the cost of zero. And these is not the case. Our faces bigger than zero. It z Costa 30 degrees, then it&#x27;s either bigger than the resonant frequency or smaller than the resonant frequency. How can we check for that? Well, very easy. Excel is given by the frequency times they looked in a while. Zeke? Yeah. CSI Easy goes to one divided by the frequency. Times like a pastimes. Note this following. We have an unknown face angle that is bigger than zero. It means that exhale Is it bigger than XY? In order for that circuit to go to the resonance frequency, we have to lower excel while increasing exceed. And the only way to do that by massive me the frequency is to make the frequency smaller. Because my making the frequencies Moeller, we make excels more while increasing Maxie that a four toe achieve the residence. We have to lower our frequency. Therefore, the frequency off the circuit is bigger than the resonant frequency.

João Gabriel Alencar Caribé · Answer

the first item. We remember that the resonant frequency is F because too one divided by two pi times the square it off. L time see So the resonant frequency itself do not depend on the resistance. So it doesn&#x27;t change by doing the resistance. And these is there. Sort off the first item for the maximum current. We&#x27;ve gotta remember the following the are a master voltage that is furnished by the source. Is it close to the R. M s current times the impudence on the circuit through Let&#x27;s take a look at Howell. Impedance is related to the resistance. Impedance is the cost of the square root off the resistance is squared plus the difference between the reactant squared now Not that by increasing the resistance, we are increasing the impudence found they are a mass current is given by the voltage divided by the impedance. So by increasing the impudence, we are decreasing the current and remember the maximum current as equals two the R. M s current times the square root off to then decreasing the army&#x27;s current means that we are also decreasing the maximum current and finally the current will decrease if we increase the resistance because the increase in the resistance will cause an increase in the Penis

João Gabriel Alencar Caribé · Answer

the restaurant frequency in on our little scene, sir, Quit is getting by the falling relation. The frequency is equals to one divided by the look tense times the capacitors Now remember the following by adding a new capacitor in sceneries with the existing one, we will get a new equivalent capacitance that is a smaller than the previous one. So what happened with the frequency is that as we decrees the capacitance, the frequency will increase So the resonant frequency will increase when we add in a capacitor in Siri&#x27;s with the existing one. And the best explanation before that&#x27;s phenomenal is turned one.

João Gabriel Alencar Caribé · Answer

in the first item. We just have to note that the voltage leads the current by a reasonable amount. Then the circuit is dominated by a look tense and therefore we have that the inductive reactors is bigger than the capacity reactors. For the second. Like him, we have to remember to expressions expression for the conductive reactions We cheese equals two amiga times. They booked us on expression for the capacity react in some cheesy goes to one divided by oiga times the capacitance. Now, when the circuit is that resonance, what happens is that x l Z equals two XY And what we have here is a situation where excel is bigger than exceed. Then we have to increase excel while decrease exceed is starting from the residence. We can do that by increasing the frequency so increasing the frequency XY decreases. Why you exhale increases, which is our situation. Then we conclude that, uh, the frequency of the source omega is bigger than they really want frequency. Omega&#x27;s Europe

Problem

Figure $24-38$ shows the phasor diagram for an $R…

Problem 83 Medium Difficulty

The phasor diagram for an RLC circuit is shown in FlGURE $24-38$ . (a) If the resistance in this circuit
is $525 \Omega,$ what is the impedance? (b) If the frequency in this circuit is increased, will the impedance increase, or stay the same? Explain.

Answer

a) 606 ohms
b) see explanation

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a) 606 ohmsb) see explanation

Physics

Liev B.

Marshall S.

Farnaz M.

Zachary M.

Electric Charge

The Electric Force

James S. WalkerPhysics

Liev B.

Marshall S.

Farnaz M.

Zachary M.

a) 606 ohms
b) see explanation

James S. Walker

Physics