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COMEDK2018PhysicsAlternating Current

For a series L-C-R circuit at resonance, the statement which is not true ?

Options

  1. APeak energy stored by a capacitor = peak energy stored by an inductor
  2. BAverage power = Apparent power
  3. CWattless current is zero.
  4. DPower factor is zero.

Correct answer

D. Power factor is zero.

Step-by-step solution

In series L-C-R circuit, aligned X_ L &=X_ C & Z= R²+ (X_ L -X_ C )² aligned aligned &= R²+0² Z &=R Power factor &= &= R Z = R R =1 aligned Hence, power factor is not zero. Therefore option (d) is not correct. In L-C-R series resonance circuit, peak energy stored by a capacitor is equal to peak energy stored by an inductor. Average power, P_ avg =V_ rms I_ rms 0^ aligned &=V_ rms I_ rms &= apparent power aligned L-C-R series resonance circuit is purely resistive because X_ L =X_ C , hence no wattless current exists

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