Which expression gives the Q factor for a series RLC circuit in terms of L, C, and R (without using ω0)?

Which expression gives the Q factor for a series RLC circuit in terms of L, C, and R (without using ω0)?

• A. Q = ω0 L / R
• B. Q = R / (ω0 C)
• C. Q = (1/R) √(L/C)
• D. Q = ω0 C / R

Answer: (C)

Quality factor measures how underdamped and selective a series resonant circuit is. For a series RLC at resonance, the reactive energy stored in the inductor and capacitor dominates the circulating energy, while the resistance dissipates energy each cycle. The standard way to quantify this is Q = ω0 L / R, which compares the energy storage in the reactive element to the energy lost in resistance per cycle. To express Q without using the resonant frequency ω0, use ω0 = 1/√(LC). Substituting gives Q = (1/R) √(L/C). This form uses only L, C, and R, and it shows how increasing L or decreasing C raises Q, while increasing R lowers it. Other expressions that include ω0 are equivalent only if you keep ω0, but the requested form eliminates ω0 entirely.

Quality factor measures how underdamped and selective a series resonant circuit is. For a series RLC at resonance, the reactive energy stored in the inductor and capacitor dominates the circulating energy, while the resistance dissipates energy each cycle. The standard way to quantify this is Q = ω0 L / R, which compares the energy storage in the reactive element to the energy lost in resistance per cycle.

To express Q without using the resonant frequency ω0, use ω0 = 1/√(LC). Substituting gives Q = (1/R) √(L/C). This form uses only L, C, and R, and it shows how increasing L or decreasing C raises Q, while increasing R lowers it.

Other expressions that include ω0 are equivalent only if you keep ω0, but the requested form eliminates ω0 entirely.