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NEETPhysicsAlternating Current

A capacitor is connected to a 200 V , 50 Hz AC source. If the peak value of the current in the circuit is 2 2 A , the capacitance of the capacitor is:

Options

  1. A100 2 F
  2. B100 F
  3. C200 F
  4. D25 F

Correct answer

B. 100 F

Step-by-step solution

The rms current in the circuit is related to the peak current by: I_ rms = I₀ 2 = 2 2 2 = 2 A The capacitive reactance X_C is given by: X_C = V_ rms I_ rms = 200 2 = 100 We also know that X_C = 1 2 f C . Rearranging for capacitance C : C = 1 2 f X_C C = 1 2 50 100 = 1 10000 F Converting to microfarads ( F ): C = 1 10000 10^6 F = 100 F Answer: 100 F

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