GATE 2025 IN – Question 62
A series RLC circuit resonates at 7500 rad/s for inductance L = 20 mH and resistance R = 10 Ω. The uncertainties in the measurement of L and R are 0.8 mH and 0.3 Ω, respectively. The percentage uncertainty in the measurement of quality factor is _________% (rounded off to one decimal place).
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Correct answer: 4.5 to 5.5
Explanation
With resonance frequency treated as specified, Q=ω0L/R.
First-order worst-case relative uncertainty is ΔL/L+ΔR/R=0.8/20+0.3/10=0.04+0.03=0.07.
However when Q=√(L/C)/R and C is fixed, frequency changes with L and the L contribution is halved: 0.5×4%+3%=**5.0%**, the official convention.