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For an L-C-R A.C. circuit the resonant 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 July 2015 · 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) The ratio upside down: (f₂-f₁)/(f₀)=(100)/(600)=1/6 is the fractional bandwidth, which equals 1/Q, not Q.
• (2) Needs two slips at once, the ratio inverted and the bandwidth doubled: (2×100)/(600)=1/3. A resonance this sharp has Q>1.
• (4) Comes from putting the full width f₂-f₁=100 Hz into Q=(f₀)/(2Δ f), where Δ f is only the half-width. That doubles the bandwidth: (600)/(200)=3.

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