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The capacitive reactance in an RLC circuit is determined to be 45$\Omega$ when the inductive reactance is 65$\Omega .$ (a) Is the generator frequency $\omega$ higher or lower than the natu-ral frequency $\omega_{0} ?$ (b) Is the phase angle $\phi$ positive or negative?(c) Calculate the phase angle $\phi$ if $R=33 \Omega .$

a) the generator frequency $\omega$ must be greater than that of the natural frequency $\omega_{0}$ .b) positive.c) $31^{\circ}$

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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before restoring this question. Note that the question is referring to the angular frequency omega and not to the frequency off, which is given by two pi times the angular frequency. So you warned about it. Now for the first item, we have to determine if the resonant frequency is bigger than the frequency right now in that circuit. Let us do that. We begin this question by remembering their following relations for the react. Ince's The capacity of reactors is equals to one divided by the frequency times. The capacitance wild inductive reactions is given by the frequencies times they looked at us. No note the following the resonant frequency. It's such that the reactor's is out of the same. So they are equal a newness situation given by the problem. They are not the same, so the circuit is not running at residence. In orderto achieve residents, we have to lower the inductive reactions while you're increasing the capacity of reactors. And to do that by looking at these equations in these equation, we conclude that we don't have to lowered the frequency of the circuit because by lowering the frequents off the circuit, we are increasing the capacity reactors while decreasing inductive reactors. Then we conclude that the frequency of the circuit omega is bigger than the resonant frequency off that circuit for the second night. And we have to remember that detainment off the face angle is given by the difference between the nuclear reactors and the capacity reactions divided by the resistance of that circuit, and now knows that the resistance is obviously bigger than zero. So the only thing that can be smaller than zero is the difference between the react, Ince's and disease. What that reminds the side. No off the face. So this is what that their minds if the fate is bigger than zero or smaller than zero and note that in the current situation we have Excel will cost you 6 to 5 on that, C goes to 45 and these is it goes to 20 and 20 is bigger than zero, then the tangent off the phase is bigger than zero, and because of that, we conclude that the angle's off. The phase is bigger than 02 in the final light, and we have to evaluate the faith's angle for a given value off the resistance. So for our equals to 23 year olds. What is the value off that face angle? So we just have to use this relation that we had analyzed in the last item. Then it goes as follows. The tangent off the figs angle is it goes to 20 which which we had already done. The calculation divided by 33 and this yell DS and facing Lou that is given by the inverse tangent. So the tension my nose one off 20 divided by 33 needs is approximately 31 degrees.

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