Define quality factor Q for a series RLC circuit using R, L, C. Which expression is correct?

Define quality factor Q for a series RLC circuit using R, L, C. Which expression is correct?

• A. Q = R / (ω0 L)
• B. Q = ω0 C / R
• C. Q = ω0 L / R
• D. Q = ω0 / (R C)

Answer: (C)

Quality factor Q tells us how sharp the resonance is in a series resonant circuit and how little the signal is damped by the resistor. At resonance, the circuit behaves like a purely real impedance, but how quickly the response falls off away from resonance depends on how much energy can be stored in the reactive parts (L and C) versus how much is lost in R. For a series RLC, the standard way to express this balance is Q = ω0 L / R. This captures the idea that larger inductive reactance at the resonant frequency (ω0 L) relative to the loss R yields a higher Q, i.e., a narrower bandwidth. You can also write it as Q = 1 / (ω0 R C) because ω0 = 1/√(LC); both forms describe the same relationship between energy storage and dissipation. A handy intuition is to think of the bandwidth Δω of the resonance being roughly Δω ≈ R / L for a series circuit. Then Q = ω0 / Δω gives Q ≈ ω0 L / R, tying the concept directly to how the circuit stores energy versus how it loses energy.

Quality factor Q tells us how sharp the resonance is in a series resonant circuit and how little the signal is damped by the resistor. At resonance, the circuit behaves like a purely real impedance, but how quickly the response falls off away from resonance depends on how much energy can be stored in the reactive parts (L and C) versus how much is lost in R.

For a series RLC, the standard way to express this balance is Q = ω0 L / R. This captures the idea that larger inductive reactance at the resonant frequency (ω0 L) relative to the loss R yields a higher Q, i.e., a narrower bandwidth. You can also write it as Q = 1 / (ω0 R C) because ω0 = 1/√(LC); both forms describe the same relationship between energy storage and dissipation.

A handy intuition is to think of the bandwidth Δω of the resonance being roughly Δω ≈ R / L for a series circuit. Then Q = ω0 / Δω gives Q ≈ ω0 L / R, tying the concept directly to how the circuit stores energy versus how it loses energy.