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NEET 2012
Exam
NEET
Year
2012
Subject
Physics
Chapter
Alternating Current

NEET 2012 · Physics · Alternating Current

In an electrical circuit R, L, C and an AC voltage source are all...

In an electrical circuit R,L,CR, L, C and an AC\mathrm{AC} voltage source are all connected in series. When LL is removed from the circuit, the phase difference between the voltage and the current in the circuit is π/3\pi / 3. If instead, CC is removed from the circuit, the phase difference is again π/3\pi / 3. The power factor of the circuit is

Options

  1. A1/21 / 2
  2. B1/21 / \sqrt{2}
  3. C1
  4. D3/2\sqrt{3} / 2

Correct answer

C. 1

Step-by-step solution

Here, phase difference tan⁡ϕ=XL−XCRtan⁡π3=XL−XCR\begin{aligned} \tan \phi & =\frac{X_L-X_C}{R} \\ \tan \frac{\pi}{3} & =\frac{X_L-X_C}{R} \end{aligned} When, LL is removed 3=XCRXC=3R\begin{aligned} & \sqrt{3}=\frac{X_C}{R} \\ & X_C=\sqrt{3} R \end{aligned} When CC is removed tan⁡π3=3=XLRXL=R3\begin{gathered} \tan \frac{\pi}{3}=\sqrt{3}=\frac{X_L}{R} \\ X_L=R \sqrt{3} \end{gathered} Hence, in resonant circuit tan⁡ϕ=3R−3RR=0ϕ=0\begin{aligned} \tan \phi & =\frac{\sqrt{3} R-\sqrt{3} R}{R}=0 \\ \phi & =0 \end{aligned}\thereforePowerfactorPower factor\cos \phi=1ItistheconditionofresonancethereforephasedifferencebetweenvoltageandcurrentiszeroandpowerfactorisIt is the condition of resonance therefore phase difference between voltage and current is zero and power factor is\cos \phi=1$.
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