Average Power Calculation in RLC Circuit at 402 Hz?

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SUMMARY

The average power calculation for an RLC circuit at 402 Hz involves using the given rms voltage of 149 V, resistance of 298 Ω, capacitance of 4.1 μF, and inductance of 0.23 H. The correct formula for average power is P = Vrms * Irms * cos(φ), where Vrms is derived from the maximum voltage. The phase angle was determined to be 58.4 degrees, leading to the final average power calculation. The user successfully resolved their confusion regarding the rms voltage and completed the calculation correctly.

PREREQUISITES
  • Understanding of RLC circuit components: resistance, capacitance, and inductance.
  • Knowledge of rms voltage and its relationship to maximum voltage.
  • Familiarity with trigonometric functions, particularly cosine for phase angle calculations.
  • Proficiency in using Ohm's Law and power formulas in AC circuits.
NEXT STEPS
  • Study the derivation of the average power formula in AC circuits.
  • Learn about the impact of phase angle on power calculations in RLC circuits.
  • Explore the use of complex impedance in RLC circuit analysis.
  • Investigate the effects of frequency changes on circuit behavior and power consumption.
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing RLC circuits and power calculations in AC systems.

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Homework Statement



If the rms voltage across the generator is 149 V, calculate the average power P(at 402 Hz) being used by the circuit.

R = 298 Ω, a capacitance C = 4.1 μF, inductance of L = 0.23 H

https://tycho-s.physics.wisc.edu/cgi/courses/shell/common/showme.pl?courses/phys104/spring09/homework/07/rclseries/ex2s92p4.gif


Homework Equations



V=IR
Avg power=Vrms*Irms(cos phase angle)
vrms=vmax/(sqrt 2)
Irms=Imax/(sqrt 2)

The Attempt at a Solution



Vrms=IrmsR
149/(sqrt 2)=Irms*298 I think that the 149 V given in the problem needs to be divided by 2 to get Vrms? is rms voltage across generator same as max voltage? I'm not exactly sure about that part...anyways I got:
Irms=.35355
Avg power= (.35355)(149/sqrt 2) cos (phase angle)
i solved for XL (581) and XC (96.6), which were both correct. so I got the phase angle to be 58.4 degrees
Avg power= (.35355)(149/sqrt 2) cos (58.4)

I'm not getting the right answer, so maybe my approach was wrong? Any help is appreciated.
 
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nevermind, got it
 

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