The resonant frequency of a parallel tuned circuit is given by

A capacitor and coil or LC circuit in parallel resonant circuit is called a tuned or tank circuit.

They are used in tuner circuit to generate signals of a particular frequency or picking up signals of a particular frequency.

At Resonance:

X_c = X_L

\(\frac{1}{2\pi fC}=2\pi fL\)

The resonant frequency of a parallel tuned circuit is given by:

\(f=\frac{1}{2π\sqrt{{L}{C}}} \)

If an LC tank circuit consists of an ideal capacitor C connected in parallel with a coil of inductance L having an internal resistance R.

The resonant frequency of the tank circuit is

\(f= \frac{1}{{2{\rm{π }}\sqrt {{\rm{LC}}} }}\sqrt {1 - {{\rm{R}}^2}\frac{{\rm{C}}}{{\rm{L}}}}\)