What is the resonance condition for a series RLC circuit and the impedance at resonance?

What is the resonance condition for a series RLC circuit and the impedance at resonance?

• A. ω0 = 1/√(LC); Z = R (real)
• B. ω0 = √(LC); Z = 0
• C. ω0 = 1/(LC); Z = jX
• D. ω0 = 1/√(LC); Z = ∞

Answer: (A)

In a series RLC circuit, resonance happens when the inductive and capacitive reactances cancel each other out. The impedance is Z = R + j(ωL − 1/(ωC)). At resonance the imaginary part must be zero, so ωL = 1/(ωC). Solving gives ω0^2 = 1/(LC), hence ω0 = 1/√(LC). With the reactive parts canceled, the impedance becomes purely real and equals Z = R. So the resonance condition is ω0 = 1/√(LC), and the impedance at resonance is R, not zero or infinite.

In a series RLC circuit, resonance happens when the inductive and capacitive reactances cancel each other out. The impedance is Z = R + j(ωL − 1/(ωC)). At resonance the imaginary part must be zero, so ωL = 1/(ωC). Solving gives ω0^2 = 1/(LC), hence ω0 = 1/√(LC). With the reactive parts canceled, the impedance becomes purely real and equals Z = R. So the resonance condition is ω0 = 1/√(LC), and the impedance at resonance is R, not zero or infinite.