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

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Multiple Choice

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

Explanation:
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.

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