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An ac generator with a frequency of 1.55 kHz and an rms voltage of 20.8 $\mathrm{V}$ is connected in series with a 2.00 -k\Omega resistor and a$292-\mathrm{mH}$ inductor. (a) What is the power factor for this circuit?(b) What is the average power consumed by this circuit?

a) 0.575b) 71.6 $\mathrm{mW}$

Physics 102 Electricity and Magnetism

Chapter 24

Alternating-Current Circuits

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Alternating Current

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in the first item. We have to evaluate the power factor of the circuit. So we have to evaluate the co sign other fees and the music goes to the resistance divided by BNP. This and in this case, the impudence has two contributions, one coming from the resistance and another one coming from they looked at us. So the feelings is it goes to the square it off squares plus the inductive reactors. Where'd they looked? Reactant is given by two quiet times the frequency times, the induct ins. No, we can plug in the values given by the problem in this equation and get the power factor. We choose the square root off two times, stand to the turns. There is a kilo there squared plus to pi times 1.55 Again there is a kilo times 292 merely squared. This is old under the resistance reaches two times 10 to return and these things approximately 0.5 seven 52 which we can for the approximate to 0.575 in the next item we have to complete. What is the average power consumers by that stir Great the average power is given by the are a mess voltage times the arguments current times the power factor. Now remember that there is a relation between the aromas voltage on the Aramis current and that relation is the following. The remans voltage is of course, to ari mass current. Multiply it biting Peters, then solving for the R. M s current, we get that the Aramis current is equals two The aromatase voltage divided by eating peanuts. No, the average power is then the remans voltage squared divided by they impede us and multiply it by the power factor and disease equals truth. A square root off the resistance is squared. Plus to buy f l squared under a square root under the aromatics voltage squared times the power factor This is just impedance which we have already calculated here. So we know just have to put in their values given by the problem on the power factor that we have completed before To get the following square root off two times 10 to the third squared plus to five times 1.55 time stand to deterred times 292 times 10 to the minus tree squared This is all under 20 points. Eight squared times the power factor, which is 0.575 and disease approximately 0.715 five, which we can write as 71.6. Really, What?

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