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 :
- A \(25\, \mathrm{rad} / \mathrm{s}\) and \(75 \,\mathrm{rad} / \mathrm{s}\)
- B \(50 \,\mathrm{rad} / \mathrm{s}\) and \(25 \,\mathrm{rad} / \mathrm{s}\)
- C \(46\, \mathrm{rad} / \mathrm{s}\) and \(54 \,\mathrm{rad} / \mathrm{s}\)
- D \(42 \,\mathrm{rad} / \mathrm{s}\) and \(58 \,\mathrm{rad} / \mathrm{s}\)
Answer & Solution
Correct Answer
(C) \(46\, \mathrm{rad} / \mathrm{s}\) and \(54 \,\mathrm{rad} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{Q}=\frac{\omega}{\Delta \omega}=\frac{\omega \mathrm{L}}{\mathrm{R}} \Rightarrow \Delta \omega=\mathrm{R} / \mathrm{L}=\frac{50}{4}=8\, \mathrm{rad} / \mathrm{sec}\) \(\omega_{0}=\frac{1}{\sqrt{\mathrm{LC}}}=\frac{1}{\sqrt{5 \times 80 \times 10^{-6}}}=50\, \mathrm{rad} / \mathrm{sec}\)
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