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WB JEE Medical WB JEE Medical Solved Paper-2010

  • question_answer
    The current through a coil of self-inductance \[L=2mH\] is given by \[i={{t}^{2}}{{e}^{-t}}\]at time t. How long it will take to make the emf zero?

    A)  1s             

    B)  2s

    C)  3s             

    D)  4 s

    Correct Answer: B

    Solution :

                     The current is given by the relation \[i={{t}^{2}}{{e}^{-t}}.\] Hence the emf would be equal to \[e=-L\frac{di}{dt}=-2\times {{10}^{-3}}\times (2t{{e}^{-t}}-{{t}^{2}}{{e}^{-t}})\] If the emf is zero, \[e=0,\]hence \[2t{{e}^{-t}}={{t}^{2}}{{e}^{-t}}\Rightarrow t=2s\]


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