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NEET AIPMT SOLVED PAPER 2001

  • question_answer
                      In an inductor of self-inductance \[L=2\,mH\], current changes with time according to relation \[i={{t}^{2}}{{e}^{-t}}\,.\] At what time emf is zero?                                                                                                                                       

    A)                 4 s                          

    B)                 3 s                          

    C)                 2 s          

    D)                 1 s

    Correct Answer: C

    Solution :

                              Key Idea: The emf is given by the relation \[e=-L\frac{dt}{dt}.\]                 It is given that emf is zero i.e.,                 \[e=-L\,\frac{di}{dt}=0\] \[orL\,\frac{di}{dt}=0\] \[or\frac{d}{dt}({{t}^{2}}{{e}^{-t}})=0\] \[or2t\times {{e}^{-t}}+{{t}^{2}}+(-1)\,{{e}^{-t}}=0\] \[ort{{e}^{-t}}(2-t)=0\] \[ort=2\,s\,(\because \,t{{e}^{-t}}\ne 0)\]


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