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JEE MainPhysicsAlternating Current

A series LCR circuit is connected to an AC voltage source given by V(t) = 200 (1000t) V. The circuit has a resistance R = 50 , and a capacitance C = 50 , F . If the resultant current in the circuit lags the applied voltage by a phase angle of 45^ , the value of the inductance L is

Options

  1. A30 mH
  2. B50 mH
  3. C70 mH
  4. D20 mH

Correct answer

C. 70 mH

Step-by-step solution

From the given voltage equation V(t) = 200 (1000t) , the angular frequency is = 1000 rad/s . The capacitive reactance is: X_C = 1 C = 1 1000 50 10⁻⁶ = 1 0.05 = 20 , Since the current lags the voltage, the circuit is inductive in nature, which means X_L > X_C . The phase difference is given by: = X_L - X_C R Given = 45^ , we have 45^ = 1 . Substituting the known values: 1 = X_L - 20 50 X_L - 20 = 50 X_L = 70 , The inductance L is then: L = X_L = 70 1000 = 0.07 H = 70 mH Answer: 70 mH

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