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NEETPhysicsAlternating Current

An alternating current has a frequency of 50 Hz. What is the shortest time it takes for the current to reach its root mean square (RMS) value, starting from zero?

Options

  1. A1 200 s
  2. B1 400 s
  3. C1 600 s
  4. D1 100 s

Correct answer

B. 1 400 s

Step-by-step solution

The instantaneous value of an alternating current is given by I = I₀ (2 f t) . The RMS value of the current is I_ rms = I₀ 2 . To find the time taken to reach the RMS value from zero, we set I = I_ rms : I₀ (2 f t) = I₀ 2 (2 f t) = 1 2 The shortest time corresponds to the smallest positive phase angle, which is 4 radians. 2 f t = 4 t = 1 8f Given f = 50 Hz: t = 1 8 50 = 1 400 s. Answer: 1 400 s

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