A choke coil of inductance Land series resistance R is shunted by a capacitor C. The dynamic impedance of the resonant circuit would be

Dynamic impedance

It is an impedance offered by the network to the source under resonance conditions.

The input admittance is given by:

\(Y=j\omega C\space +\space {1\over R+j\omega L}\)

\(Y=j\omega C\space +\space ({1\over R+j\omega L}\times {R-j\omega L\over R-j\omega L} )\)

\(Y=j\omega C\space +\space {R-j\omega L\over R^2+(\omega L)^2}\)

\(Y={R\over R^2+(\omega L)^2}+j({\omega C-{\omega L\over R^2+(\omega L)^2}})\).........(i)

At resonance, the imaginary part is zero.

\({\omega C={\omega L\over R^2+(\omega L)^2}}\)

\({\omega L={\omega C (R^2+(\omega L)^2}})\)...........(ii)

Putting the value of equation (ii) in equation (i), we get:

\(Y={RC\over L}\)

\(Z={1\over Y}\)

\(Z=\rm \frac{L}{RC}\)