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Figure $24-38$ shows the phasor diagram for an $R L C$ circuit in which the impedance is $337 \Omega$. (a) What is the resistance, $R$, in this circuit? (b) Is this circuit driven at a frequency that is greater than, less than, or equal to the resonance frequency of the circuit? Explain.

a) 2920 $\mathrm{hms}$b) greater than

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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for the first item. Remember that the co sign off the phase is it goes to the resistance divided by the impedance, then the resistance. Is he close to be those times they call Sign off the face and we know both. Impedance is authority to 337 and the co signed off the phase is the co sign off 30 degrees, which is the square root of tree divided by truth. And this is approximately 200 and 92 rooms for the second item. It is quite straightforward to see that this record is not working at resonance. And why, in saying that he's quite that it is quite straightforward because of the following the tangent off the fees is equal to Excel mine Oh, sexy, divided by the resistance when the circuit is working at residence. What happens is that both react. Ince's are equal and the face is the cost of zero. And these is not the case. Our faces bigger than zero. It z Costa 30 degrees, then it's either bigger than the resonant frequency or smaller than the resonant frequency. How can we check for that? Well, very easy. Excel is given by the frequency times they looked in a while. Zeke? Yeah. CSI Easy goes to one divided by the frequency. Times like a pastimes. Note this following. We have an unknown face angle that is bigger than zero. It means that exhale Is it bigger than XY? In order for that circuit to go to the resonance frequency, we have to lower excel while increasing exceed. And the only way to do that by massive me the frequency is to make the frequency smaller. Because my making the frequencies Moeller, we make excels more while increasing Maxie that a four toe achieve the residence. We have to lower our frequency. Therefore, the frequency off the circuit is bigger than the resonant frequency.

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