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An ac generator supplies an rms voltage of 5.00 V to an RL circuit. At a frequency of 20.0 $\mathrm{kHz}$ the rms current in the circuit is $45.0 \mathrm{mA} ;$ at a frequency of 25.0 $\mathrm{kHz}$ the rms current is 40.0 $\mathrm{mA}$ . What are the values of $R$ and $L$ in this circuit?

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Physics 102 Electricity and Magnetism

Chapter 24

Alternating-Current Circuits

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Alternating Current

University of Michigan - Ann Arbor

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to solve this question, we have to analyze the impudence in each of those situations in situation. One in situation too. Situation one we can complete impedance by using homes. Law v. R a. Mass is the coast. Why every mess times the impedance in situation one which leads to an impedance off Vieri, Mass. Divided by IRA mess. Then the first situation The impudence is equals 25 divided by 45 times, 10 to the minus street, on the other hand, on the second situation. Similarly, in credence, he's given by five divided by 40 times 10 minus street. Now remember the following the impudence The situation is equal to the square root off R squared plus Excel squared. Now we can use Z one z two to complete. Both are on Excel How to do that as follows. First Z one is opposed to the square root off R squared clothes to pi times the frequency number one times being booked us on disease squared We already know the value off one Then we solve this equation for l to get the following z one square is equals two R squared plus too pious one times l squared then too pious One times l is equal to the square root off Z one squared minds are squared Finally l A is equal to the square root off 01 squared miners R squared, divided by to pi times F one Then keep these results we now use it to. And so busy too for the resistance Ze truth is equal to the square root off R squared Plus to buy I have two times l and Disease all squared No, no to that Z two squared These equals two r squared plus two pi times at two times l squared and then r squared, which is what we have to know is equals two z two squared minus to pie F two times l squared. Now we substitute these value off r squared these equations for the doctors to get the following The doctor's is equals two the square root off See one's weird minus R squared which is? It goes to Z two squared Plus because there is a minus minus true pi times two times l squared and these eggs all divided by to five times f one No, we can solve these equations for inducting we get to pie F one l He's in close to the square root office. You one squared minus Z chu squared plus two pi f two will squared squaring both sides We get to pie F one hell squared is equal to Z one squared minus z two squared plus two pi f to l squared. We can now but this term on the other side to get to pie F 10 squared my nose to pie F two times l squared is equal to Z one squared minus z two squared Then we can factor out these l to get l squared times too pious one squared minus too pious two squared Is it close to ze world squared minus the two squared And finally the doctors is the course too The square root off z one squared my Z True squared divided by to pipe F one squared minus two by as two squared by plugging the values that we have completed for Z one z two and the vials that were given by the problem for F one And after we got the following square root off Z one, which is egos 25 divided by 45 times, 10 to the minus three. So five divided by 45 times 10 to the minus three squared minus Zi Chu, which is five, divided by 40 times, 10 to the minus three squared. Invited by to pi times F one F one is 20 times 10 to the third squared minus two ply times after you. True was 25. Time Stand to the turd when these is squared and this gives us an in doctors off approximately 608 Me crow Harry's. Now we can go back to the expression we had obtained for the resistance squared, which is there's one plugging the values that we have right now and get the value for the resistance. So the resistance squared. He's equals two. Zi chu squared z True, he was five, divided by 40 times, 10 to the minus tree squared minus to pie times F two times l to pie. Time left to F too is equals two 25 Time Stand to the third diamonds L, which is equals two seeks your wait time. Stand to the mind of six squared So the resistance them because to the square root of this thing, which gives us approximately 81 homes

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