ExamBro
ExamBro
NEET · Physics · STD 12 -7. Alternating current

A series \(LCR\) circuit containing \(5.0\, \mathrm{H}\) inductor, \(80\, \mu \mathrm{F}\) capacitor and \(40\, \Omega\) resistor is connected to \(230 \,\mathrm{~V}\) variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be :

  1. A \(25\, \mathrm{rad} / \mathrm{s}\) and \(75 \,\mathrm{rad} / \mathrm{s}\)
  2. B \(50 \,\mathrm{rad} / \mathrm{s}\) and \(25 \,\mathrm{rad} / \mathrm{s}\)
  3. C \(46\, \mathrm{rad} / \mathrm{s}\) and \(54 \,\mathrm{rad} / \mathrm{s}\)
  4. D \(42 \,\mathrm{rad} / \mathrm{s}\) and \(58 \,\mathrm{rad} / \mathrm{s}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(46\, \mathrm{rad} / \mathrm{s}\) and \(54 \,\mathrm{rad} / \mathrm{s}\)

Step-by-step Solution

Detailed explanation

\(\mathrm{Q}=\frac{\omega}{\Delta \omega}=\frac{\omega \mathrm{L}}{\mathrm{R}} \Rightarrow \Delta \omega=\mathrm{R} / \mathrm{L}=\frac{50}{4}=8\, \mathrm{rad} / \mathrm{sec}\) \(\omega_{0}=\frac{1}{\sqrt{\mathrm{LC}}}=\frac{1}{\sqrt{5 \times 80 \times 10^{-6}}}=50\, \mathrm{rad} / \mathrm{sec}\)
Same subject
Explore more questions on app
From NEET
Explore more questions on app