Find Resonant Freq, Q, Power Diss pwr Half Pwr Freq in RLC Circuit

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SUMMARY

The discussion focuses on calculating key parameters of a parallel RLC circuit driven by a variable frequency 10-A source with resistance R=500Ω, inductance L=0.5mH, and capacitance C=20μF. The resonant frequency (ω₀) is determined to be 10,000 rad/sec, the quality factor (Q) is calculated as 100, and the bandwidth (BW) is 100 rad/sec. The half-power frequencies are identified as ωₕ = 1005.01 rad/sec and ωₗ = 995.01 rad/sec. The average power dissipated at resonant frequency and half-power frequencies was initially unclear but was resolved as straightforward calculations.

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  • Understanding of parallel RLC circuit theory
  • Familiarity with resonant frequency calculations
  • Knowledge of quality factor (Q) and bandwidth (BW) concepts
  • Basic principles of power dissipation in electrical circuits
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  • Explore the effects of component values on resonant frequency
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Electrical engineers, circuit designers, and students studying RLC circuits who seek to deepen their understanding of resonant frequency, quality factor, and power dissipation in parallel circuits.

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Question:
A parallel RLC circuit, which is driven by a variable frequency 10-A source, has the following parameters:
[tex]R=500\Omega[/tex]
[tex]L=0.5mH[/tex]
[tex]C=20\muF[/tex]

Find the resonant frequency, the [itex]Q[/itex], the average power dissipated at resonant frequency, the [itex]BW[/itex], and the average power dissipated at the half-power frequencies.

Answer:
[itex]Q[/itex], [itex]\omega_0[/itex], and [itex]BW[/itex] are all straightfoward calculations.

[tex]Q = 100 [/itex]<br /> [tex]BW = 100 \frac{rad}{sec}[/tex]<br /> [tex]\omega_0 = 10000\frac{rad}{sec}[/tex]<br /> <br /> The half power frequencies are:<br /> [tex]\omega_{hi} = 1005.01[/tex]<br /> [tex]\omega_{lo} = 995.01 [/itex]<br /> <br /> I don't understand how to calculate the average power dissapated at resonant frequency, OR at the half power frequencies. If someone could give me a push in the right direction, that would be swell <img src="https://www.physicsforums.com/styles/physicsforums/xenforo/smilies/oldschool/redface.gif" class="smilie" loading="lazy" alt=":redface:" title="Red Face :redface:" data-shortname=":redface:" />[/tex][/tex]
 
Last edited:
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:smile: nm, figured it out. That was embarrassingly easy.
 

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