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JEE Main20265 April 2026Morning ShiftPhysicsAlternating CurrentActual

An a.c. source of angular frequency is connected across a resistor R and a capacitor C in series. The current is observed as I . Now the frequency of the source is changed to /4 , (keeping the voltage unchanged) the current is found to be I/3 . The ratio of resistance to reactance at frequency is

Options

  1. A6 7
  2. B3 5
  3. C7 8
  4. D3 4

Correct answer

C. 7 8

Step-by-step solution

The current in the RC circuit at frequency is given by I = V R^2 + X_C^2 where X_C = 1 C is the capacitive reactance. When the frequency is changed to /4 , the new reactance becomes X_C' = 1 ( /4)C = 4X_C . The new current is given as I/3 , so I 3 = V R^2 + (4X_C)^2 Substituting the expression for I , we get V 3 R^2 + X_C^2 = V R^2 + 16X_C^2 Squaring both sides, we obtain 1 9(R^2 + X_C^2) = 1 R^2 + 16X_C^2 9R^2 + 9X_C^2 = R^2 + 16X_C^2 8R^2 = 7X_C^2 R^2 X_C^2 = 7 8 R X_C = 7 8 Answer: 7 8

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