Resonant RLC circuit and in inductance

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SUMMARY

A resonant RLC circuit can function as an amplifier for specific frequency bands, particularly at 200Hz and 4000Hz, with a gain of 0.5. The circuit consists of a series configuration with an 8.0Ω resistor, and the relationship between the inductor (L) and capacitor (C) is critical for achieving resonance. At resonance, the inductive reactance (Xl) equals the capacitive reactance (Xc), and the resonant frequency is given by the formula W0=1/(L*C). To solve for the required inductance, both the output/input voltage ratio and the resonant frequency equations must be utilized.

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  • Understanding of resonant RLC circuits
  • Knowledge of AC voltage sources and their behavior
  • Familiarity with the concepts of inductive and capacitive reactance
  • Ability to manipulate algebraic equations involving frequency and impedance
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  • Study the relationship between frequency and impedance in RLC circuits
  • Learn how to derive the resonant frequency formula for RLC circuits
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  • Investigate the effects of varying resistance, inductance, and capacitance on circuit behavior
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Worme
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1. A resonant RLC circuit can be used as an amplifier for a certain band of frequencies around the resonant frequency. Consider a series RLC circuit as an audio band amplifier with an AC voltage source as the input, and the voltage across the 8.0Ω resistor as the output. The amplifier should have a gain (=output/input ) of 0.5 at 200Hz and 4000Hz . What is the required value of the inductor in Henry?ata

Homework Equations

3. At resonance Xl=Xc and W0=1/(L*C).
Could you explain me how to do?
Thanks.
 
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Hi W,
Is your problem statement complete ? C isn't mentioneed ?
The section "relevant equations" sure isn't. What have you got that you can use there ?
Make a darwing and post your attempt at solution. Good luck !
 
Yes C is not mentioneed and so is L. But i know that at resonance a RLC circuit has a frequency 1/(2*pi*sqrt(L*C)). So i know f and R.
 
No you don't, because you don't know L and C. You only know R.
What you do know: at the two given frequencies ouput/input voltage has to be 0.5. Write down an expression for this ratio in terms of R, L and C. With two frequencies you have two equations with two unknowns. The rest is math.
 
Ok but what is the relation between frequencies and output/input?
 
Look under: 2. equations. Oops, empty :rolleyes: ! So what do you have in your notes or in your textbook that can help you out here ? It's not that I am playing hide and seek, it's just that I'm not supposed to just hand over the answer, so you'll have to make an effort.

With DC and two resistances it would be easy, right ? Well, what do we have as an equivalent instead of resistance when we are dealing with alternating currents ?
 

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