Problem

A large air conditioner has a resistance of 7.0$\…

01:58

Problem 41 Medium Difficulty

(a) Sketch the phasor diagram for an ac circuit with a $105-\Omega$
resistor in series with a 22.5 -mH inductor. The frequency of the
generator is 60.0 $\mathrm{Hz}$ (b) If the rms voltage of the generator is 120 $\mathrm{V}$ ,
what is the average power consumed by the circuit?

Answer

a) $=4.65^{\circ}$
b) $\therefore P_{a v}=136 \mathrm{W}$

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Physics 102 Electricity and Magnetism

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Watch More Solved Questions in Chapter 24

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Video Transcript

in the first item off this problem, we have to do a sketch off the phaser diagram for that circuit. We begin by remembering that the co sign off the face and go these equals to the resistance divided by the impudence. And for this case, the evidence is given by the resistance squared. Plus, they looked reactive, squared, so they co signed off the fees. Is he goes to are invited by Thank you. This No. Remember that being looked? Reactions Easy. Close to two pi times the frequency times looked us. Then the co sign off the phases, plugging the values the problem gave to us 105 you guided by the square root off 105 squared plus to pie times 60 times 22.5 Time stand to the minor street There's a nearly perfect squared and this is approximately zero point 99 seven. Then the phase These egos too. The universe co signed off zero point 997 which is approximately 4.4 degrees. Then our phaser diagram is as follows we have to access and three phasers. One of them say these one representative voltage across the resistor. And that footage. Easy clothes, too. Hi, Max. Times the resistance. We have another phaser representing the voltage across the doctor. And that voltage is in close to the current times they left the reactors. And finally 1/3 Lecter representing the average voltage across the world. Sir. Quit. We just give them by the current times. Thank you, James. And these angle is he close to 4.4 degrees in the second item, we have to accomplish the average power that is consumed by the circuit. The average power he's given by Vieira Mass times You're a mess. Times the co sign off the face. The problem tells us that the are a mess is equals to 120 votes. Now, remember that Vieri Mass? His ego's too. I re mass times. You see this? Therefore, the R. M s current is the coast to the harem. As voters divided by the impedance them. The average power is because too the remans voltage squared, divided by the impudence times they come sign. Oh, fight. All we have to do now is used values given by the problem. I'll solve this equation. So what impede us. We have this square it off. 105 squared, plus to pi times 60 times, 22.5 times 10 to the minus tree squared. And this is whole under 120 squared times 0.997 Finally, disease approximately 136. What?

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