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A A 100.0$\Omega$ resistor, a 0.100$\mu \mathrm{F}$ capacitor, and a 300.0 $\mathrm{mH}$inductor are connected in series to a voltage source with amplitude 240 $\mathrm{V}$ (a) What is the resonance angular frequency? (b) What is the maximum current in the resistor at resonance? (b) What is the maximum current in the resistor at resonance? (c) What is the maximum voltage across the capacitor at resonance? (d) What is the maximum voltage across the inductor at resonance? (e) What is the maximum energy stored in the capacitor at resonance? in the inductor?

a) 5773 $\mathrm{rad} / \mathrm{s}$b) 2.40 $\mathrm{A}$c) $4.16 \times 10^{3} \mathrm{V}$d) $4.16 \times 10^{3} \mathrm{V}$e) 0.864 $\mathrm{J}$

Physics 102 Electricity and Magnetism

Chapter 22

Alternating Current

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

University of Washington

Simon Fraser University

University of Sheffield

Lectures

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party is asking for the resonant frequency and so do party. We can use the formula that the resident frequency is one of the square root of the induct inst times capacitance. And now I can just plug in these values with Ellen Henry's and precedents of parrots only plucking those values. We did 5.77 times 10 cute radiance per second for the resonant frequency here. And that's answer to party. The Barbie. We want the maximum hurry. And so for this, we're going to use the formula that the current is equal to the voltage over the impudence. And since we're at residence, the impedance is equal to the resistance. And so now I can plug in both these values for voltage. We know that it's 2 40 volts and we know the resistance is 100 homes. And so this ends up giving us two point for dance Amperes important. See, we want the voltage across the oppressor. And so to do this, we want the reactant. So the capacitor, the reactions of the capacitor is given by one over the frequency task capacitance. And since we're at the resident frequency, this frequents here is just equal of this frequency of here. And we know what the capacitance is and so we can plug in those values and we get 1.73 times 10. Cute. And this is the gnomes. Now that we know the reactions of the master, we can figure out the voltage across the capacitor with this formula here where we're going to use the eye that we found in part B playing those values in. Here's a voltage 4.15 times 10 cubed and this is in bolts department D. We're going to do essentially the same thing except for the in doctor. So we need the reactions of the conductor. This is equal to Omega Times L But Omega is the resident frequency. So it's omega non. And then hours gonna plug in these values and we get 1.73 times 10 cute dolls. And now we can use this equation. We know I as we found it in part B. We just calculated the reactant CE. And so we complied was in, and we get 4.15 times 10 Q bolts. Notice that these two voltages are the same since we're at the resident frequency. Now hurry. We want the total energy store in the capacitor and the in doctor. And so the star of the classroom. The formula to use is 1/2 constance voltage across the capacitor squared and we know what the capacitance is. And we calculated this to be this appearing Parsi and so it complain all that in we get that we could do the same sort of thing for the in doctor. That's if the formula was 1/2 conduct in ce times the current's word. But we found the current in part B, and we've always known the induct in CE. And so we conclude that in and we get 0.86 for Jules Now, these air supposed to be the same. I've got different numbers because of some rapping errors. But these were supposed to be the same because we're out residents and so completes the prop

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