Resonance in LC(R) parallel circuit

[guest1234]

Homework Statement

I did an experiment as followed

Given following circuit

I measured voltage across capacitor and reciprocal frequency of the generator. espilon, L, C, R, and R_E were given.

In one configuration, R was shorted.

I have to calculate relative frequencies (gamma) (easy - resonance frequency divided by frequency) and relative impedances (zeta); q factors and (absolute and relative) bandwidths. I also have to find a relation between U_C and gamma.

I have no idea whether I did this experiment right - is voltage across capacitor even relevant in this case? What information is possible to extract from this data? What should graphs I vs gamma; U vs gamma; zeta vs gamma look like?

Homework Equations

In my lecture notes, there's this formula

[itex]M(\gamma)=\frac{Z}{Z*}=\frac{1}{\sqrt{1+Q^2(\gamma-\frac{1}{\gamma})^2}}[/itex]

where gamma is relative frequency, Z is impedance, Z* is probably impedance at resonance frequency and Q is ... Q factor.

[itex]I_C=\omega\epsilon{C}[/itex]

where I_C is current in capacitor.

And there's also this thing

[itex]Z=\frac{L}{C}\frac{1}{\sqrt{R^2+(\omega{L}-\frac{1}{\omega{C}})^2}}[/itex]

The Attempt at a Solution

I think the last equation is not complete, so I added R_E and experimented with this value. It gave me silly numbers for Q (it clearly didn't match with plot).

I also plotted {U_C, I_C, Z, zeta} vs {frequency, gamma} (all combinations imaginable) and they all looked like typical resonance curves. Not sure about that whether it's a good sign or not..

I fiddled around with my data and found this relation

[itex]U_C=\frac{U_{C,RESONANCE}}{\sqrt{1+Q^2(\omega-\frac{1}{\omega})^2}}[/itex]

If more information is needed (e.g. graphs, example data), I'll provide it.

 

[anathema]

Hello, thank you for sharing your experiment and data with us. From your post, it seems like you have a good understanding of the equations and concepts involved in this experiment. However, to answer your questions, I would need to see your data and graphs to better understand your results.

In general, measuring the voltage across the capacitor can be relevant in this experiment as it can give you information about the current in the capacitor, which is related to the impedance and resonance frequency. It's important to make sure your measurements are accurate and consistent, and that you are using the correct equations for your specific circuit.

From your equations, it looks like you are trying to calculate the Q factor, relative frequency, and impedance at resonance. To do this, you will need to use your measured values for epsilon, L, C, R, and R_E. It's possible that your data may not match the expected results due to experimental errors or incorrect measurements. I would recommend reviewing your data and equations to see if there are any discrepancies.

As for the graphs, they should show a resonance curve, with the peak representing the resonance frequency and the bandwidth representing the range of frequencies where the circuit is resonant. The relative impedance should also show a similar curve, with the peak corresponding to the resonance frequency. The relative frequency and relative impedance should have a linear relationship, as shown in your first equation.

In summary, it seems like you have a good understanding of the concepts involved in this experiment, but it's important to review your data and equations to ensure accuracy. If you need further assistance, please provide more information and I would be happy to help.