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Resonant angular frequency for an L-C-R A.C. series circuit is ω₀ = ______.

Asked in GSEB Board July 2015 · Resonance condition and tuning

• (1) 1/(√LC)
• (2) (2π)/(√LC)
• (3) √LC
• (4) 1/(2π√LC)

Step-by-step solution

Why the other options are wrong

• (2) Multiplies the correct value by 2π. The factor 2π turns a frequency in hertz into an angular frequency (ω = 2π f); 1/(√LC) is already ω₀, so multiplying again counts it twice.
• (3) The reciprocal of the correct value. √LC has the unit of time (seconds), so it cannot be an angular frequency.
• (4) This is f₀, the resonant frequency in hertz. The angular frequency is 2π times larger: ω₀ = 2π f₀ = 1/(√LC).

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