The figure shows current varying with time. The magnitude of constant direct current for a particular time which would produce same heat in an identical resistance as produced by given time varying current in three seconds is

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Heat = ∫ i 2 R d t ​ = ∫ 0 1 ​ ( t 2 ) R d t + ∫ 1 2 ​ 1 2 R d t + ∫ 2 3 ​ ( 3 − t ) 2 R d t = 3 1 ​ R + R + 3 R ​ = 3 5 R ​ ​ ​ ​ I 2 R × 3 = 3 5 R ​ ⇒ I 2 = 9 5 ​ ⇒ I = 3 5 ​ ​ A I 2 R × 15 = 3 5 R ​ ⇒ I = 3 1 ​ A

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JEE Advanced (2028)