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MHT CET 2024 (4 May, Shift 1) · Resonance, Bandwidth & Q Factor

Resonance, Bandwidth & Q Factor question from MHT CET 2024 (4 May, Shift 1)

Q38MHT CET 2024 · 4 MAY · SHIFT 1Easy

Resonance, Bandwidth & Q Factor

An inductor of inductance 2 μH2\ \mu\text{H} is connected in series with a resistance, a variable capacitor and an a.c. source of frequency 5 kHz. The value of capacitance for which maximum current is drawn into the circuit is 1x F\frac{1}{x}\text{ F}, where the value of ' xx ' is (Take π2=10\pi^2 = 10)

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Answer: (c)

  1. Maximum current means resonance: C=14π2f2LC = \dfrac{1}{4\pi^2 f^2 L}
  2. 4π2f2L=4(10)(5×103)2(2×10−6)=40×25×106×2×10−6=20004\pi^2 f^2 L = 4(10)(5\times10^3)^2(2\times10^{-6}) = 40 \times 25\times10^{6} \times 2\times10^{-6} = 2000
  3. C=12000 FC = \frac{1}{2000}\text{ F}, so x=2000x = 2000.
  4. So the answer is (c) 2000.
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