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MHT CET 2026 (20 May, Shift 1) · Resonance, Bandwidth & Q Factor

Resonance, Bandwidth & Q Factor question from MHT CET 2026 (20 May, Shift 1)

Q16MHT CET 2026 · 20 MAY · SHIFT 1Medium

Resonance, Bandwidth & Q Factor

A resistor of 200 Ω200\ \Omega, an inductor of self inductance (2π2)\left(\frac{2}{\pi^2}\right) H and a capacitor of unknown capacity are connected in series to an a.c. source of 100100 V and 5050 Hz. When the current and voltage are in phase the capacitance and the power dissipated is

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Answer: (c)

  1. Current and voltage in phase means resonance: C=1ω2LC = \frac{1}{\omega^2 L}, ω=100π\omega = 100\pi.
  2. C=1(100π)2⋅2π2=12×104=5×10−5C = \frac{1}{(100\pi)^2\cdot\frac{2}{\pi^2}} = \frac{1}{2\times10^{4}} = 5\times10^{-5} F
  3. At resonance Z=RZ = R: P=V2R=1002200=50P = \frac{V^2}{R} = \frac{100^2}{200} = 50 W
  4. So the answer is (c) 5×10−55\times10^{-5} F, 50 W.
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