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  4. A series LCR circuit containing 5.0 H inductor, 80 μ F capacitor and 40 Ω resistor is connected to 230 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:

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Q. A series LCR circuit containing $5.0\, H$ inductor, $80\, \mu F$ capacitor and $40\, \Omega$ resistor is connected to $230\, V$ 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:

NEETNEET 2021Alternating Current

Solution:

$\begin{array}{l} Q =\frac{\omega}{\Delta \omega}=\frac{\omega L }{ R } \\ \Rightarrow \Delta \omega= R / L =\frac{50}{4}=8 rad / sec \\ \omega_0=\frac{1}{\sqrt{ LC }}=\frac{1}{\sqrt{5 \times 80 \times 10^{-6}}}=50 rad / sec \\ \omega_{\min }=\omega_0-\frac{\Delta \omega}{2}=46 rad / sec \\ \omega_{\max }=\omega_0-\frac{\Delta \omega}{2}=54 rad / sec \end{array}$