Resonance of a Parallel LCR network

[nathangrand]

Why does the resonance peak of a parallel LCR network (capacitor in parallel with in-series inductor and resisitor) get smaller in amplitude with increasing resistance? I have impedance/DC resistance plotted against frequency.


I'm really not sure about how to go about showing this, preferably mathematically. At resonance is the reactance 0, implying the impedance is just the resistance?

Also, what is the correct expression for the resonant frequency of this circuit? I get w$$^{2}$$ = w0$$^{2}$$ - y$$^{2}$$ when y=R/2L and w0= 1/ $$\sqrt{LC}$$ but I've seen different expressions, such as under other configurations here http://en.wikipedia.org/wiki/RLC_circuit

Any help would be massively appreciated!

 

[ehild]

Write up the impedance of the LRC circuit. Resonance is usually defined as the frequency where the magnitude of impedance is maximum(parallel circuit) or minimum (series circuit). But sometimes it is defined as the frequency where the impedance is real, the imaginary part being zero. Are you familiar with complex numbers?

ehild

 

[nathangrand]

Yeah I'm familiar with complex numbers. I can show the various how to get some of the resonance frequency equations - its the first part of my question I'm more stuck with

 

[ehild]

If you define resonance when the imaginary part is zero, w^2=1/(LC) holds for the resonant angular frequency. What is the resonant impedance then?

ehild