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For an L-C-R A.C. circuit the resonance frequency is 600 Hz and the frequencies at the half-power points are 550 Hz and 650 Hz. What will be the Q-factor?

Asked in GSEB Board March 2018 · Power and bandwidth at resonance

• (1) 1/6
• (2) 1/3
• (3) 6
• (4) 3

Step-by-step solution

Why the other options are wrong

• (1) 1/6=(100)/(600) is the ratio upside down: bandwidth over resonant frequency. The Q-factor is resonant frequency over bandwidth, so a narrow band gives a large Q.
• (2) No single slip gives 1/3; it needs the ratio inverted and the bandwidth doubled, (200)/(600). Sanity check: Q=(f₀)/(f₂-f₁)=(600)/(100)=6.
• (4) 3=(600)/(200) comes from Q=(f₀)/(2Δ f) with the full width 100 Hz used as Δ f. In that form Δ f is the half-width, 50 Hz, which gives 6 again.

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