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MHT CET 2024 (16 May, Shift 2) · Resonance, Bandwidth & Q Factor

Resonance, Bandwidth & Q Factor question from MHT CET 2024 (16 May, Shift 2)

Q47MHT CET 2024 · 16 MAY · SHIFT 2Medium

Resonance, Bandwidth & Q Factor

An inductance of 2 mH, a condenser of 20 μF20\ \mu\text{F} and a resistance of 50 Ω50\ \Omega are connected in series to an a.c. source. The reactance of inductor and condenser are same. The reactance of either of them will be

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Answer: (d)

  1. XL=XCX_L = X_C means resonance: ω=1LC\omega = \frac{1}{\sqrt{LC}}.
  2. ω=12×10−3×20×10−6=12×10−4=5000\omega = \frac{1}{\sqrt{2\times10^{-3}\times20\times10^{-6}}} = \frac{1}{2\times10^{-4}} = 5000 rad/s
  3. XL=ωL=5000×2×10−3=10 ΩX_L = \omega L = 5000\times2\times10^{-3} = 10\ \Omega
  4. So the answer is (d) 10 Ω10\ \Omega.
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