For a series RLC circuit, what is the resonant frequency f0?

For a series RLC circuit, what is the resonant frequency f0?

• A. f0 = 1/(2π√(LC))
• B. f0 = 1/(2πLC)
• C. f0 = √(LC)/(2π)
• D. f0 = 2π√(LC)

Answer: (A)

In a series RLC circuit, resonance occurs when the inductive and capacitive reactances cancel each other, so the impedance is purely resistive. That happens when ωL equals 1/(ωC), leading to ω0 = 1/√(LC). Converting to frequency in hertz gives f0 = ω0/(2π) = 1/(2π√(LC)). The other forms don’t match frequency units or the correct relationship: 1/(2πLC) has wrong dimensions, √(LC)/(2π) has units of time, and 2π√(LC) also comes out in time units, not cycles per second.

In a series RLC circuit, resonance occurs when the inductive and capacitive reactances cancel each other, so the impedance is purely resistive. That happens when ωL equals 1/(ωC), leading to ω0 = 1/√(LC). Converting to frequency in hertz gives f0 = ω0/(2π) = 1/(2π√(LC)). The other forms don’t match frequency units or the correct relationship: 1/(2πLC) has wrong dimensions, √(LC)/(2π) has units of time, and 2π√(LC) also comes out in time units, not cycles per second.