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- Derive Q of R in parallel with tank circuit

I've been experimenting with an LC tank circuit in series with a resistance R, and I've noted that the Q seems to increase with R. I've tried to derive this result via phasor analysis, but I'm not sure if my expression is correct.

To make things clear, I'm talking about the circuit with impedance ##Z=R+jX_L || X_C=R+j(\dfrac{\omega L}{1-\omega^2 LC}) ##

The only thing I've found via google is this:

https://electronics.stackexchange.com/questions/108788/voltage-output-from-a-tank-circuit

where the first answer suggests that ##Q=R\sqrt{\dfrac{C}{L}}## which at least agrees with my measured results. I've found however that ##Q=R\sqrt{\dfrac{C}{L+4R^2C}}##

So which result, if either, is right? I note that mine approximates the quoted result if ##L \gg 4R^2C##.

To make things clear, I'm talking about the circuit with impedance ##Z=R+jX_L || X_C=R+j(\dfrac{\omega L}{1-\omega^2 LC}) ##

The only thing I've found via google is this:

https://electronics.stackexchange.com/questions/108788/voltage-output-from-a-tank-circuit

where the first answer suggests that ##Q=R\sqrt{\dfrac{C}{L}}## which at least agrees with my measured results. I've found however that ##Q=R\sqrt{\dfrac{C}{L+4R^2C}}##

So which result, if either, is right? I note that mine approximates the quoted result if ##L \gg 4R^2C##.