The quality factor, often denoted as Q, for an R-L-C (resistor-inductor-capacitor) circuit can be given by the following formula:
Q = ω₀L / R
Where:
- Q is the quality factor.
- ω₀ is the angular frequency of the circuit, given by ω₀ = 1/√(LC).
- L is the inductance of the circuit.
- R is the resistance of the circuit.
The quality factor describes the sharpness or selectivity of the resonance in the circuit. A higher quality factor indicates a narrower resonance bandwidth and a sharper peak in the current response.
In an R-L-C circuit, the quality factor Q represents the ratio of energy stored in the inductor and capacitor to the energy dissipated in the resistor per cycle of oscillation. It characterizes the efficiency of the energy transfer within the circuit. A higher Q value implies less energy loss and a more efficient transfer of energy.
Note that the quality factor can also be expressed in terms of the bandwidth (Δf) and the resonant frequency (f₀) as follows:
Q = f₀ / Δf
where Δf is the bandwidth of the resonance.
In summary, the quality factor Q for an R-L-C circuit driven with voltage of amplitude Vm and frequency ω₀ = 1/√(LC) is given by Q = ω₀L / R.