Question

Mention the factors on which the resonant frequency of a series LCR circuit depends. Plot a graph showing variation of impedance of a series LCR circuit with the frequency of the applied a.c. source.

Answer 1

The resonance frequency of a series LCR circuit is given by

`omega_r = 2pif_r = 1/sqrt(LC)`

or `f_r =1/(2pisqrt(LC))`

So, it depends upon the values of inductance and capacitance of the circuit.

Now `Z = sqrt(R^2 + (X_L - X_C)^2)`

⇒ `Z = sqrt(R^2 + (2pifL - 1/(2pifC))^2)`

At f = f_r ⇒ X_L = X_C