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$\bullet$ In a series $R-L-C$ circuit, the phase angle is $40.0^{\circ},$ with the source voltage leading the current. The reactance of the capacitor is $400 \Omega,$ and the resistance of the resistor is 200$\Omega .$ The average power delivered by the source is 150 $\mathrm{W}$ . Find (a) the reactance of the inductor, (b) the rms current, (c) the rms voltage of the source.

a) 567.8$\Omega$b) 0.866 $\mathrm{A}$c) 226 $\mathrm{V}$

Physics 102 Electricity and Magnetism

Chapter 22

Alternating Current

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

McMaster University

Lectures

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so here for party. The phase angle tangent of Fei is equaling the inductive reactant Sinus. The capacity of reactive is divided by the resistance are we can solve for the inductive reactions. This would simply be equal two 400 homes, which would be the capacitive, reactant CE plus 200 homes. The resistance of the resistor multiplied by tangent of the phase angle tangent of 40 degrees. And so the inductive reactant is 567 0.8 arms, four part to be. We can see that the average power is equaling. The root means squared current quantity squared, multiply, literate by the resistance are the root means. Squared. Current is then equaling to the square root of the average power divided by the resistance of their sister are This is equaling to the square root of 150 watts, divided by 200 homes, and we find that the root means squared. Current is equaling 2.866 amps and four part C. To find the root means Where voltages would be, the root means squared current multiplied by other impotence. This would be the root means squared current multiplied by the square root of the resistance of the resistor, plus the difference between the difference of the capacitive reactant ce from the inductive reactant ce so acceptable minus except see quantity squared and we find that the root means squared voltages equaling 0.866 amps multiplied by the square root of 200 bums. Quantity squared plus 200 homes plus 567 0.8 arms minus 400 arms quantity squared extend the square root and the root means squared. Voltage is equal to 226 votes. This would be our final answer for part C. That is the end of the solution. Thank you for watching.

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