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CUET · PHYSICS · PYQ PAPER 2023

The power factor of an RL circuit is \( \frac{1}{2} \). If the frequency of a.c. is doubled, the power factor will be :

  1. A \( \frac{1}{\sqrt{5}} \)
  2. B \( \frac{1}{\sqrt{7}} \)
  3. C \( \frac{1}{\sqrt{3}} \)
  4. D \( \frac{1}{\sqrt{13}} \)
Verified Solution

Answer & Solution

Correct Answer

(D) \( \frac{1}{\sqrt{13}} \)

Step-by-step Solution

Detailed explanation

\( \cos \phi_1 = \frac{R}{\sqrt{R^2+X_{L1}^2}} = \frac{1}{2} \) \( 4R^2 = R^2+X_{L1}^2 \implies X_{L1}^2 = 3R^2 \implies X_{L1} = \sqrt{3}R \) \( f_2 = 2f_1 \implies X_{L2} = 2X_{L1} = 2\sqrt{3}R \)…
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