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For an L-C-R A.C. circuit the resonance frequency is 5000 Hz and the frequencies at the half-power points are 4950 Hz and 5050 Hz. The Q-factor is ______.

Asked in GUJCET 2016 · Power and bandwidth at resonance

• (1) 50
• (2) 0.02
• (3) 100
• (4) 0.01

Step-by-step solution

Why the other options are wrong

• (2) The ratio taken upside down: (f₂ - f₁)/(f₀) = (100)/(5000) = 0.02. A sharp resonance has a large Q, so Q is f₀ divided by the bandwidth.
• (3) Divides by half the bandwidth: (f₀)/(f₂ - f₀) = (5000)/(50) = 100. The bandwidth is the full gap between the two half-power points, 100 Hz.
• (4) No single slip gives 0.01; it combines both errors above, half the bandwidth and the ratio inverted: (50)/(5000) = 0.01. Q is (5000)/(100) = 50.

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