For an RLC circuit driven with voltage of amplitude Vm and frequency ω0=1LC√ the current exhibits resonance the quality factor, Q is given by

The quality factor, Q, for a resonant RLC circuit is given by the formula:

Q = ω0L / R

where:

• ω0 is the resonant frequency, given by ω0 = 1/√(LC)
• L is the inductance of the inductor in the circuit
• R is the resistance of the resistor in the circuit

The quality factor, Q, is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It represents the energy loss per cycle in a resonating system. A high Q indicates a low rate of energy loss and the oscillations die out more slowly. A low Q indicates a high rate of energy loss and the oscillations die out more quickly.

In the context of the RLC circuit, the quality factor, Q, can be interpreted as the ratio of the reactance of the inductor to the resistance of the resistor. This means that the higher the Q, the higher the voltage across the inductor compared to the voltage across the resistor at resonance.