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KVPY Sample Paper KVPY Stream-SX Model Paper-30

  • question_answer
    The magnetic flux \[\phi \] through a metal ring varies with time t according to: \[\phi =3\,\,(a{{t}^{3}}-b{{t}^{2}})T{{m}^{2}},\] with \[a=2{{s}^{-3}}\] and \[b=6{{s}^{-2}}\]. The resistance of the ring is \[3\Omega .\]. The maximum current induced in the ring during the interval t = 0 to t = 2s, is:

    A) 1 A

    B) 2 A

    C) 3 A      

    D) 6 A

    Correct Answer: D

    Solution :

    \[i\,(t)=-\frac{1}{R}\frac{d\phi }{dt}=2bt-3a{{t}^{2}}\]
    i is maximum when \[\frac{di}{dt}=0\]
    or \[t=\frac{2b}{6a}\]
    Using values, at t=1 s,
     i maximum its value =\[12-6=6A\]                       


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