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JEE MainPhysicsAlternating Current

Which of the following pairs of voltage and current equations represents a circuit where the current is entirely wattless?

Options

  1. AV = V₀ t and I = I₀ t
  2. BV = V₀ t and I = I₀ t
  3. CV = V₀ t and I = I₀ ( t + 4 )
  4. DV = V₀ t and I = -I₀ t

Correct answer

A. V = V₀ t and I = I₀ t

Step-by-step solution

Wattless current flows when the average power dissipated over a complete cycle is zero. The average power is given by P_ avg = V_ rms I_ rms . For P_ avg = 0 , the power factor must be zero, which implies that the phase difference between the voltage and the current must be 2 (or 90^ ). In the pair V = V₀ t and I = I₀ t , the current can be rewritten as I = I₀ ( t + 2 ) . The phase difference between voltage and current is exactly 2 , making the power factor zero and the current entirely wattless. Answer: V = V₀ t

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