How does the impedance of a resonant circuit depend on frequency?

The impedance of a resonant circuit depends on frequency in a predictable way.

As the frequency of an AC source applied to a resonant circuit changes, the impedance of the circuit also changes. At the resonant frequency, the impedance of the circuit is at its minimum value, which is equal to the resistance of the circuit. This is because at the resonant frequency, the capacitive and inductive reactances cancel each other out, leaving only the resistance.

At frequencies above and below the resonant frequency, the impedance of the circuit increases due to the increasing reactance of either the capacitor or the inductor. This increase in impedance can be modelled using the impedance equation for a series resonant circuit, which is Z = R + j(XL - XC), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.

At frequencies far above or below the resonant frequency, the impedance of the circuit is dominated by either the inductor or the capacitor, resulting in a large reactance and a high impedance. This can be seen in the impedance vs frequency graph for a resonant circuit, which shows a sharp dip in impedance at the resonant frequency and high impedance values on either side of the dip.

In summary, the impedance of a resonant circuit depends on frequency due to the changing reactance of the inductor and capacitor, resulting in a minimum impedance at the resonant frequency and high impedance values at frequencies above and below the resonant frequency.