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JEE MainPhysicsAlternating Current

An AC source of RMS voltage 100 V is connected across a series combination of a resistor of 3 and an inductor of reactance 4 . The magnitude of the wattless component of the RMS current in the circuit is:

Options

  1. A12 A
  2. B16 A
  3. C20 A
  4. D15 A

Correct answer

B. 16 A

Step-by-step solution

The total impedance of the RL series circuit is given by Z = R^2 + X_L^2 . Substituting the given values: Z = 3^2 + 4^2 = 9 + 16 = 5 . The total RMS current in the circuit is: I_ rms = V_ rms Z = 100 5 = 20 A . The current in an AC circuit can be resolved into two components: the active (wattful) component I_ rms and the reactive (wattless) component I_ rms . From the impedance triangle, = X_L Z = 4 5 . The magnitude of the wattless component of the current is: I_ wattless = I_ rms = 20 4 5 = 16 A . Answer: 16 A

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