# Resonance in LC(R) parallel circuit

1. Nov 20, 2012

### guest1234

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

In my lecture notes, there's this formula

$M(\gamma)=\frac{Z}{Z*}=\frac{1}{\sqrt{1+Q^2(\gamma-\frac{1}{\gamma})^2}}$

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

$I_C=\omega\epsilon{C}$

where I_C is current in capacitor.

And there's also this thing

$Z=\frac{L}{C}\frac{1}{\sqrt{R^2+(\omega{L}-\frac{1}{\omega{C}})^2}}$

3. 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

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

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