The impedance of a resonant circuit exhibits a predictable relationship with frequency.

As the frequency of an alternating current (AC) source applied to a resonant circuit varies, the circuit’s impedance changes correspondingly. At the resonant frequency, the impedance reaches its minimum value, which is equal to the circuit’s resistance. This occurs because, at resonance, the capacitive reactance and inductive reactance effectively cancel each other out, leaving only the resistance to influence the impedance.

For frequencies that are either above or below the resonant frequency, the impedance of the circuit increases. This increase is due to the rising reactance of either the capacitor or the inductor. The impedance for a series resonant circuit can be modeled using the equation:

where $R$ represents the resistance, $X_L$ is the inductive reactance, and $X_C$ is the capacitive reactance.

At frequencies significantly above or below the resonant frequency, the impedance is predominantly determined by either the inductor or the capacitor, leading to high reactance and, consequently, high impedance. This behavior is illustrated in the impedance versus frequency graph for a resonant circuit, which reveals a sharp dip in impedance at the resonant frequency, accompanied by elevated impedance values on either side of this dip.

In summary, the impedance of a resonant circuit is frequency-dependent due to the variations in reactance of the inductor and capacitor. This results in a minimum impedance occurring at the resonant frequency, while high impedance values are observed at frequencies both above and below this point.