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A series LR circuit is connected to an ac source of frequency and the inductive reactance is equal to 2 R . A capacitance of capacitive reactance equal to R is added in series with L and R . The ratio of the new power factor to the old one is :

Options

  1. A2 3
  2. B2 5
  3. C3 2
  4. D5 2

Correct answer

D. 5 2

Step-by-step solution

Power factor _ (old) = R R ^2+ X _ L ^2 = R R ^2+(2 R )^2 = R 5 R Power factor _ (new) = R R ^2+ (X_L-X_C )^2 = R R^2+(2 R-R)^2 = R 2 R New power factor Old power factor = R 2 R R 5 R = 5 2

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