Resonance of a Parallel LCR network

AI Thread Summary
The discussion centers on the behavior of resonance in a parallel LCR network, specifically how increasing resistance diminishes the amplitude of the resonance peak. At resonance, the reactance is zero, leading to the conclusion that the impedance equals the resistance. The correct expression for the resonant frequency is debated, with references to w0 = 1/√(LC) and variations depending on circuit configuration. Participants seek mathematical clarification and a deeper understanding of the relationship between resistance and resonance amplitude. The conversation highlights the complexity of LCR circuits and the need for precise formulas in analyzing their behavior.
nathangrand
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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!
 
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