Fit P(w) to determine Q,w, and R (Series RLC AC circuit)

In summary, the homework assignment involves fitting P(w) to determine Q and w_0, as well as calculating R. The known constant Vrms is used in the calculations. The lab involves taking measurements of Vrms over a range of frequencies and using known values for R_load, L, C, and V_in_rms. The goal is to determine unknown values of the circuit and compare them to theory. The specific question is unclear, but it may involve plotting P(w) and determining Q from the plot using the FWHM method.
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Homework Statement



Fit P(w) to determine Q, and w_0, and R. You should put in Vrms as a known constant.

Homework Equations



[tex]P(\omega)={\frac{V_{rms}^{2}}{R(1+Q^2(\frac{\omega}{\omega_0}-\frac{\omega_0}{\omega})^2)}[/tex]

[tex]Q=\frac{\omega_0}{\Delta\omega}[/tex]

[tex]R=R_load+r[/tex]



The Attempt at a Solution



I have 14 data points. They are Vrms over the resistor for a range of 1350-2000Hz in increments of 50Hz.

R_load is the resistance of the resistor. r is the unknown resistance in the inductor.

I am not sure what this question is asking here. In this lab, we took measurements of the Vrms as described above using known values for R_load, L, C, and V_in_rms. The question before this has me plot P(w), mark the FWHM (full width half max) and determine Q from the plot.
I know part of point of this lab is to determine unknown values of the circuit using different methods and compare with theory.

I first thought it was asking me to plot P(w) again, but this doesn't make sense. The first plot is terrible since it is dependent on the graphing software (excel) for the curve (so few points).

Does anyone have interpretations of what it is asking here?
 
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What is the expected outcome? Do I have to fit a curve to the points I have and determine the parameters from that? Thanks!
 

1. What is the purpose of fitting P(w) in a Series RLC AC circuit?

Fitting P(w) in a Series RLC AC circuit helps determine the values of Q, w, and R, which are important parameters in understanding the behavior of the circuit. It allows us to analyze the circuit's response to varying frequencies and calculate factors such as impedance, resonance frequency, and bandwidth.

2. How is P(w) fitted in a Series RLC AC circuit?

P(w) is fitted by performing a frequency sweep analysis on the circuit. This involves varying the input frequency and observing the output response. By analyzing the amplitude and phase shift of the output signal, we can determine the values of Q, w, and R that best fit the data.

3. What is the significance of Q, w, and R in a Series RLC AC circuit?

Q, w, and R are important parameters that describe the behavior of a Series RLC AC circuit. Q, or quality factor, represents the ratio of energy stored to energy dissipated in the circuit. w, or angular frequency, is a measure of the circuit's response to input frequency. R, or resistance, represents the energy dissipated in the circuit due to resistive elements.

4. How does fitting P(w) help in circuit analysis?

Fitting P(w) allows us to determine the values of Q, w, and R, which in turn, help us analyze the behavior of the circuit. By understanding the circuit's response to different frequencies, we can design and optimize it for specific applications. Additionally, fitting P(w) can also help identify any discrepancies or errors in the circuit's components.

5. What are some practical applications of fitting P(w) in a Series RLC AC circuit?

Fitting P(w) is useful in a variety of practical applications such as designing filters, amplifiers, and oscillators. It is also used in power systems to analyze the behavior of transformers and transmission lines. Additionally, fitting P(w) can aid in diagnosing faults and optimizing the performance of electronic devices.

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