Q Factor in Series-Parallel Shunt Circuits

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phantomvommand
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Screenshot 2024-11-27 at 11.10.51 PM.png

Screenshot 2024-11-27 at 11.11.11 PM.png


The above content discusses the conversion of RL (in series) to RL (in parallel). Importantly, the context is that the RL (in series) was in parallel with a capacitor.

I am interested to know the following:

Q1. Why is ##\frac {\omega L} {R} = Q## true for this circuit, given that this formula was derived for the pure series RLC circuit (and is not applicable to this RL||C circuit unless we are assuming R-L-C is approximately equal to R-L||C)?

Q2. Notably, the conversion between RL to R||L is not technically true, since it takes ##R_L >> R## and therefore ignores R. Is there a physical interpretation for the technical impossibility of converting from RL to R||L? Related to this, what is the physical meaning of a circuit in a situation where ##R_L## is not much larger than R, and therefore cannot be converted from series to parallel?
 
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