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JEE MainPhysicsAlternating Current

A direct current of 3 A flows through a resistance of 4 . An alternating current flows through a resistance of 2 . If both the currents produce the same amount of heat in the two resistances in the same interval of time, the peak value of the alternating current is :

Options

  1. A3 2 A
  2. B3 A
  3. C12 A
  4. D6 A

Correct answer

D. 6 A

Step-by-step solution

Heat produced by the direct current in time t is H_ dc = I_ dc ^2 R₁ t H_ dc = (3)^2 4 t = 36t Heat produced by the alternating current in time t is H_ ac = I_ rms ^2 R₂ t = ( I₀ 2 )^2 R₂ t H_ ac = I₀^2 2 2 t = I₀^2 t Since the heat produced is the same, H_ dc = H_ ac 36t = I₀^2 t I₀^2 = 36 I₀ = 6 A Answer: 6 A

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