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Question

# A series LCR circuit containing 5.0 H inductor, 80 μF 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 -

A
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B
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C
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D
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Solution

## The correct option is D 46 rad/s and 54 rad/sThe resonance frequency of LCR series circuit is given as, ω0=1√LC=1√5×80×10−6=50 rad/s Now, half power frequencies are given as, ω=ω0±R2L So, ωL=50−402×5=46 rad/s ωH=50+402×5=54 rad/s Hence, option (D) is the correct answer.

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