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For an L-C-R A.C. circuit the resonance frequency is 500 Hz and the frequencies at the half-power points are 450 Hz and 550 Hz. What will be the Q-factor?

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

• (1) 5
• (2) 1/5
• (3) 6
• (4) 1/6

Step-by-step solution

Why the other options are wrong

• (2) 1/5=(100)/(500) is bandwidth over resonant frequency, the ratio upside down. The Q-factor is (f₀)/(f₂-f₁), which is large for a sharp resonance.
• (3) No single slip gives 6 from these numbers. Sanity check: the bandwidth is 550-450=100 Hz, and (500)/(100)=5.
• (4) No single slip gives 1/6 from these numbers; it is not even the inverse of the true value. Sanity check: Q=(500)/(100)=5.

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