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$\bullet$ In a series $R-L-C$ circuit, the components have the following values: $L=20.0 \mathrm{mH}, C=140 \mathrm{nF},$ and $R=350 \Omega$ . The generator has an rms voltage of 120 $\mathrm{V}$ and a frequency of 1.25 kHz. Determine (a) the power supplied by the generator; and (b) the power dissipated in the resistor.

a) $P=7.31 \mathrm{W}$b) $=7.31 \mathrm{W}$

Physics 102 Electricity and Magnetism

Chapter 22

Alternating Current

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Cornell University

University of Michigan - Ann Arbor

University of Sheffield

McMaster University

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have some givens. We have the induct insa 20 Miller Henry's or 20 times 10 to the negative. Third Henry's capacitance at 140. Nano Affair. It's a 140 times 10 to the negative ninth Ferrets. We have the resistance at 350 arms and the R. M s voltage at 120 volts and the frequency at 1.25 kilohertz I have converted to simply to hurt. So 1250 hertz We can find the implants in circuit. However, First we must find the reactive, the inductive reactant CE, which would be equal to Omega, multiplied by out. In this case, this would be to pi multiplied by the frequency multiplied by al where again omega. Here is the angular frequency of the circuit. This would be equaling to two pi multiplied by 1250 Hertz multiplied by the inductive of 20 times 10 to the negative Third Henry's and we find that the inductive react Ince's equaling 157 homes. The capacitive reactor Ince's equaling one over Omega Psi. This was equaling one over to pie times one my apologies. One over two pi times 1250 Hertz multiplied by 140 times 10 to the negative Ninth Farage's And we find that the capacitive reactor since is equally 909.45 homes. So we can say that the Impotence Z is gonna be equal to the square root of R squared Plus except l'm honest, except see quantity squared and plugging in. We have 350 homes, quantity squared plus 909 point knowing Two minus 157 Quantity squared. I'm squared. Extend the square root and we have our impotence is equaling. 830 comes now The R. M s current is equaling than the arms voltage divided by the impotence Izzy. This would be 120 volts, divided by 830 homes. And this is giving us 0.1445 amps. The power factor co sign co sign If I equaling the resistance in the resistor divided by Z the impotence this would be equaling 2 350 ums divided by 830 homes. And this is giving us 0.4217 So for part A, the powers supplied by the generator P would be equal in the arm s voltage multiplied by the arm s current multiplied by co sign of Fei or the power factor. And so this would be equaling two, 120 volts multiplied by 0.144 five amps multiplied by 0.4 217 And we have that The power supplied by the generator is 7.31 watts. Four part to be the voltage across the resistor. We can say that first, the voltage across the resistor would be the arm s voltages to be equal to the army's current multiplied by the resistance. This is equaling 2.1445 amps. This would be multiplied by 350 homes and this is giving us 50 0.6 votes. So the power dissipated in the resister. We can say piece of our This would be equaling to the R. M s voltage multiplied by the R. M s current multiplied by co sign of five power factor. And so the power dissipated in the resistor would be in 50 0.59 volts multiplied by 0.1445 amps multiplied by one. And this is giving us seven point 31 wants since the average power dissipated. And in the induct er's and the capacitors zero, uh, so whole power. So the entire power is dissipated, Uh, in the resistor. That is the end of the solution. Thank you for watching.

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