In a series RLC circuit, which option correctly gives the resonance frequency and Q factor relationship?

• A. f0 = 1/(2π√(RC)); Q = ω0L/R
• B. f0 = 1/(2π√(LC)); Q = L/(RC)
• C. f0 = 1/(2π√(LC)); Q = R/ω0L
• D. f0 = 1/(2π√(LC)); Q = ω0L/R

Answer: (D)

In a series RLC circuit, resonance occurs when the inductive and capacitive reactances cancel each other: ω0L = 1/(ω0C). This gives ω0^2 = 1/(LC), so the resonance frequency is f0 = ω0/(2π) = 1/(2π√(LC)).

The Q factor for a series RLC is defined by how much energy is stored versus dissipated per cycle, which at resonance is Q = ω0L / R. Using ω0 = 1/√(LC), this can also be written as Q = (1/R)√(L/C). This describes how sharp the resonance is.

Why the other forms don’t fit: using RC under the square root would incorrectly place the resonance on R rather than L and C, which isn’t how a series LC tank behaves. Writing Q as R/(ω0L) or L/(RC) is simply not the correct relationship for a series circuit. The correct pair is f0 = 1/(2π√(LC)) and Q = ω0L / R.