How does the presence of inductance and capacitance affect the impedance of an RLC circuit at resonance?

Inductance (L):

Inductance is the property of a circuit element (inductor) that opposes changes in current. At resonance, the inductive reactance (XL) of the inductor cancels out the capacitive reactance (XC) of the capacitor, resulting in a purely resistive impedance. The inductive reactance and capacitive reactance have equal magnitudes but opposite phases.

Capacitance (C):

Capacitance is the property of a circuit element (capacitor) that opposes changes in voltage. Like the inductor, the capacitive reactance (XC) at resonance cancels out the inductive reactance (XL), leading to a purely resistive impedance.

At resonance, the impedance of the RLC circuit is at its minimum value. This occurs when the inductive and capacitive reactances are equal and opposite. The impedance of the RLC circuit at resonance is given by the resistance (R) alone, and this minimum impedance is known as the resonance impedance.

The resonance frequency (f_res) is the frequency at which resonance occurs and can be calculated as:

f_res = 1 / (2π√(LC))

Where:

f_res is the resonance frequency in Hertz (Hz).

L is the inductance of the inductor in Henrys (H).

C is the capacitance of the capacitor in Farads (F).

At frequencies above or below resonance, the reactances do not cancel out, and the impedance of the RLC circuit will have both a resistive and a reactive component.

To summarize, at resonance, the presence of inductance and capacitance in an RLC circuit results in a minimum impedance (purely resistive) due to the cancelation of inductive and capacitive reactances. The circuit is said to be "tuned" or "resonating" at this frequency.