Solve RLC Circuit: Find Capacitor, Voltage, Power

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Discussion Overview

The discussion revolves around solving a problem related to a series RLC circuit, specifically focusing on determining the unknown capacitor value, voltage across the inductor, and total power consumed when energized by a sinusoidal supply. The context includes homework-related queries and technical reasoning about circuit behavior.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The initial post provides calculations for the capacitor value, voltage across the inductor, and total power consumed based on given circuit parameters.
  • Some participants confirm that the results appear correct, indicating no immediate issues with the calculations presented.
  • One participant questions the impedance of the circuit, suggesting that if the current and voltage are in phase, the impedance should equal the resistor value, yet finds the calculated impedance to be less than the resistor value.
  • Another participant agrees with the doubt raised about the impedance and suggests that the problem statement may contain inaccuracies, such as a possible typo or changes to the values that could affect the question's validity.

Areas of Agreement / Disagreement

There is no consensus on the accuracy of the problem statement, with some participants agreeing that the impedance should match the resistor value if the current and voltage are in phase, while others accept the calculations without addressing the impedance concern.

Contextual Notes

The discussion highlights potential limitations in the problem statement, including assumptions about phase relationships and the implications for impedance calculations, which remain unresolved.

cool_stuff_lol
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Homework Statement



A series RLC circuit consists of resistor of 200Ω, an inductor of 0.214H and a capacitor of unknown value. When this circuit is energized by 240∠0°, 50Hz sinusoidal supply, the current was found to be 2.6∠0° amperes. Determine:

(i) Value of capacitor in microfarad
(ii) Voltage across the inductor
(iii) Total power consumed

Homework Equations





The Attempt at a Solution



(i) arctan 0°=(χL-χC)/R
χC=χL
χC=2*pi*50*0.214=67.23Ω

C=1/(2*pi*50*0.214)=47.3μF

(ii) V=2.6*67.23=174.8V

(iii) Power= 200*(2.6)^2=1.35kW
 
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Did you have a question about your solution? The results look fine.
 
I had a doubt regarding the impedance of the circuit. If the current and voltage are in phase with each other shouldn't the impedance equal the value of the resistor? However, the impedance is less than the value of the resistor using Z=V/I.
 
cool_stuff_lol said:
I had a doubt regarding the impedance of the circuit. If the current and voltage are in phase with each other shouldn't the impedance equal the value of the resistor? However, the impedance is less than the value of the resistor using Z=V/I.

True. We'll have to conclude that the problem statement is not accurate. Perhaps there's a typo or someone changed the values at some point to make a "new" question.

But your approach is correct if the voltage and current are in phase.
 

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