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$\bullet$ In a series $R-L-C$ circuit, $R=400 \Omega, L=0.350 \mathrm{H},$ and $C=0.0120 \mu \mathrm{F}$ (a) What is the resonance angular frequency of the circuit? (b) The capacitor can withstand a peak voltage of 550 $\mathrm{V}$ . If the voltage source operates at the resonance frequency, what maximum voltage amplitude can it have if the maximum capacitor voltage is not exceeded?

$a ) w=1.54 .10^{4} r a d / s$$b ) V=40.7 V$

Physics 102 Electricity and Magnetism

Chapter 22

Alternating Current

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Hope College

University of Winnipeg

McMaster University

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let's write down some relevant formulas for this problem. The resident frequency can be found in terms of the induct inside the capacitance. By this formula, we know that the voltage across the faster is equal to the current times. They're reacting. So the capacitor and we know the voltage throughout the entire circuit is equal to the current times. The impudence we also know at residence nor out residents. The impedance is just equal to the resistance. And so now let's start with party and party. We want to figure out what the resident frequency is. So we're going to use this formula here, except I'm going deploy in the values for lnc for l. We have 0.350 Henry's. And for the capacitance, we have 0.1 to 0 times 10 to the natives experience. And so I'm doing this calculator gives us 1.54 times 10 to the fourth radiance for second. That's the resident frequency for Part B. We want to figure out what he is by this formula. We know V is equal to Isay or Z is the impedance to figure out what I is. We're going to use this form here. And so I is also equal to the voltage across the faster over the reactions of the past year times the impedance. All I did was substitute what? I was based on this guy here and now we need the reactions of the pastor. The reactions of the capacitor is equal to one over Omega time. See? And so we can play. What see is that we complying in what Omegas omega we found here? All right, we're at resident frequency, so I should put not there. And so whenever I played this and I get it 5.41 times 10. Cute. That's an old. And so now I can plug in everything here. And so when I do that, I get that he is equal to 40.7 volts. And that's answer we're looking for

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