A series LCR circuit driven by 300   V at a frequency of 50   Hz contains a resistance R = 3 &#160…

A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R=3 kΩ, an inductor of inductive reactance XL=250π Ω and an unknown capacitor. The value of capacitance to maximise the average power should be:
take π2=10
  1. 400 μF
  2. 4 μF
  3. 40 μF
  4. 25 μF

Solution

Angular frequency, ω=2πf=2π×50=100π rad s-1

At resonance,

XC=XL⇒1ωC=ωL⇒1ωC=250π⇒C=1100π×250π F=4 μF

Asked in: JEE Main 2021 (26 Aug Shift 1)

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