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JEE MainPhysicsAlternating Current

A circuit carries a current that has both a direct current (DC) component and a sinusoidal alternating current (AC) component. If the total current is given by I = I₁ + I₂ t , the effective (r.m.s.) value of the current is

Options

  1. AI₁^2+I₂^2 2
  2. BI₁^2+ I₂^2 2
  3. CI₁+I₂ 2
  4. DI₁^2+I₂^2

Correct answer

B. I₁^2+ I₂^2 2

Step-by-step solution

The r.m.s. current is the square root of the mean of the squared current over a complete cycle. The instantaneous current is I = I₁ + I₂ t . Squaring the current yields: I^2 = I₁^2 + I₂^2 ^2 t + 2 I₁ I₂ t Taking the time average over one full cycle: I^2 = I₁^2 + I₂^2 ^2 t + 2 I₁ I₂ t Since the average value of t over a full cycle is 0 and the average value of ^2 t is 1 2 : I^2 = I₁^2 + I₂^2 2 + 0 The r.m.s. current is: I_ rms = I^2 = I₁^2 + I₂^2 2 Answer: I₁^2+ I₂^2 2

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