For a series LCR circuit, the impedance is R + jX at angular frequency ω₁ and R - jX at angular frequency ω₂. Which relation is exactly correct?
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Question

For a series LCR circuit, the impedance is R + jX at angular frequency ω₁ and R − jX at angular frequency ω₂. Which relation is exactly correct?

G1 Physics · Accepted Answer

Equal and opposite net reactances satisfy Lω₁ − 1/(Cω₁) = −[Lω₂ − 1/(Cω₂)]. Rearranging gives ω₁ω₂ = 1/(LC) = ω₀².