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NEET 2020
Exam
NEET
Year
2020
Subject
Physics
Chapter
Alternating Current

NEET 2020 · Physics · Alternating Current

A series LCR circuit is connected to an ac voltage source. When L...

A seriesLCRLCR circuit is connected to an ac voltage source. When LL is removed from the circuit, the phase difference between current and voltage is π3\dfrac{\pi}{3}. If instead CC is removed from the circuit, the phase difference is again π3\dfrac{\pi}{3} between current and voltage. The power factor of the circuit is:

Options

  1. A0.50.5
  2. B1.01.0
  3. C–1.0– 1.0
  4. Dzero

Correct answer

B. 1.01.0

Step-by-step solution

As phase angle contribution by capacitor and inductor are equal in magnitude, so \begin{gathered}\mathrm{X}_{\mathrm{L}}=\mathrm{X}_{\mathrm{c}}\\ \Rightarrow \omega \mathrm{L}=\frac{1}{\omega \mathrm{C}} \end{gathered}ItmeansthattheRLCcircuitisinresonancecondition.So,impedanceatresonance,(Z=R2+(XL−XC)2=R2+(XL−XL)2=R2=R)Thus,powerfactor,(cos⁡ϕ=RZ=RR=1)It means that the RLC circuit is in resonance condition. So, impedance at resonance, (Z=\sqrt{R^2+\left(X_L-X_C\right)^2}=\sqrt{R^2+\left(X_L-X_L\right)^2}=\sqrt{R^2}=R) Thus, power factor, (\cos \phi=\frac{R}{Z}=\frac{R}{R}=1)
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