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 :
- A \( \frac{1}{\sqrt{5}} \)
- B \( \frac{1}{\sqrt{7}} \)
- C \( \frac{1}{\sqrt{3}} \)
- D \( \frac{1}{\sqrt{13}} \)
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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