A series L - C - R circuit containing 5 . 0 H inductor, 80 μ F capacitor and 40 Ω resistor is connected to…

A series L-C-R 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:
  1. 25 rad s-1 and 75 rad s-1
  2. 50 rad s-1 and 25 rad s-1
  3. 46 rad s-1 and 54 rad s-1
  4. 42 rad s-1 and 58 rad s-1

Solution

L=5H,C=80μF,R=40ω; V=230 V

Resonance angular frequency =ω0=1LC=15×80×10-6=50 rad s-1

Half power angular frequency =ω0±R2L=50±402×5=50±4=54 or 46

We get,

ω1=46 rad s-1

And ω2=54 rad s-1

Asked in: NEET 2021

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