Consider inductor with air gap and solid metal core made from material with relative magnetic permeability 1 regardless of temperature (such as copper or aluminium).

There is Air gap between coil and metal core.

Please also consider Eddy currents in the solid metal core.



The inductor is connected with capacitor in:

1. Series LC circuit
2. Parallel LC circuit

Is it possible under certain values of frequency and capacitance to obtain LC resonance with high Q factor?

 

Probably Not, because the conductive core will greatly reduce the energy return because of the circulating current losses. That is why tuning a resonant circuit with a conductive core will always result in a lower "Q" factor.

 

If we increase frequency so the inductive reactance (Xl= 2*Pi*f*L) will increase and hence perhaps it is possible to achieve high Q ?
In case there is air gap between coil and solid metal core (as shown in the picture)