A series LCR circuit containing 5.0 H inductor, 80 μF capacitor and 40Ω resistor is connected to 230 V variable frequency ac source.
A series LCR circuit containing 5.0 H inductor, 80 μF capacitor and 40Ω 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 :
(1) 25 rad/s and 75 rad/s
(2) 50 rad/s and 25 rad/s
(3) 46 rad/s and 54 rad/s
(4) 42 rad/s and 58 rad/s
Correct answer: (3) 46 rad/s and 54 rad/s
Explanation:
Q = \(\frac{\omega}{\Delta \omega}\) = \(\frac{\omega L}{R}\)
⇒ Δω = R/L = \(\frac{50}{4}\) = 8 rad/sec
ω_{0 }= \(\frac{1}{\sqrt{LC}}\) = \(\frac{1}{\sqrt{5 \times 80 \times 10^{6}}}\)
= 50 rad/s
ω_{min }= ω_{0 } \(\frac{\Delta \omega}{2}\) = 46 rad/s
ω_{max }= ω_{0 } \(\frac{\Delta \omega}{2}\) = 54 rad/s

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