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KCET2013PhysicsAlternating Current

A series combination of resistor (R) , capacitor (C) is connected to an A.C. source of angular frequency . Keeping the voltage same, if the frequency is changed to / 3 , the current becomes half of the original current. Then the ratio of the capacitive reactance and resistance at the former frequency is

Options

  1. A0.6
  2. B3
  3. C2
  4. D6

Correct answer

A. 0.6

Step-by-step solution

The impedance of the circuit, Z= R²+X_ C ² When angular frequency of source is reduced to 1 3 , the capacitor reactance is increased by 3 times. Z^ = R²+ (3 X_ C )² = R²+9 X_ C ² As current becomes half Z^ =2 Z array ll & 2 Z= R²+9 X_ C ² & 2 R²+X_ C ² = R²+9 X_ C ² & 4 (R²+X_ C ² )=R²+9 X_ C ² & 3 R²=5 X_ C ² or & X_ C R = 3 5 = 0.6 array

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