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An $R L$ circuit consists of a 40.0$\Omega$ resistor and a 3.00 $\mathrm{mH}$ inductor. (a) Find its impedance $Z$ at 60.0 $\mathrm{Hz}$ and 10.0 $\mathrm{kHz}$ . (b) Compare these values of $Z$ with those found in Example 23.12 in which there was also a capacitor.

refer solution

Physics 102 Electricity and Magnetism

Chapter 23

Electromagnetic Induction, AC Circuits, and Electrical Technologies

Electromagnetic Induction

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

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so here for part A. We know that there's no capacitor, so the, uh, the reactive capacitance is equaling. Zero. The react, the inductive react Ince's equaling two pi times the frequency times the induct in CE And you know that here this would be equaling two pi times. And for the first case, 60 Hertz, then three. Miller Henry's so three times 10 to the negative Third Henry's and we find that the inductive reactant is equal in 1.131 comes. We know that then, for the impotence, this would be equaling r squared the resistance squared plus the difference between the inductive um react. It's minus the capacitive reactor Is quantity squared all raised And this some rather is all raised to the 1/2 power. We know that this value is zero because there isn't any capacitor and so solving this would be equaling 40 arms Ah squared plus 1.131 comes squared, all raised to the 1/2 power and we find that the incidence for 60 hertz is 40.2 thumbs. This would be one answer for party. Second answer for part A, um would simply be the impotence see equaling again 40 arms and then squared, plus two pi times the frequency here being 10 kilohertz or 10 1000 hertz multiplied by again. Three. Miller Henry's three times 10 The negative Third Henry's This entire term would be squared and this sum would be raised to the 1/2 power. And we find that Z, the impotence at 10 kilohertz would be equaling 192.7 thumbs. So this would be our answer for the frequency being 10 kilohertz and so four part B simply asking us to compare these values. And we know that then, at a frequency equaling 60 hertz and a capacitive reactant ce um, of equal in 531 comes the value of impotence Z would be 13 times as high as without the capacitor. So we can say loaf at at low frequencies. Uh, the capacitor makes a large difference, and four part be continuing for part B, but at frequency equaling 10 kilohertz, we know that in the capacitive reactor s equaling 531 comes. Um, the value of impotence is the same, so we can say at high frequencies the capacitor because they the capacitors effect, um, is much lower were much smaller. That is the end of the solution. Thank you for watching.

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