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CMC Medical CMC-Medical VELLORE Solved Paper-2009

  • 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)  3 s                                         

    B)  4 s

    C)  1 s                                         

    D)  2 s

    Correct Answer: D

    Solution :

                     Emf across an inductor is given by \[emf=L\frac{di}{dt}\] \[=L\frac{d}{dt}({{t}^{2}}{{e}^{-t}})=0\] \[\Rightarrow \]                               \[\frac{d}{dt}({{t}^{2}}{{e}^{-t}})=0\] \[\Rightarrow \]               \[{{e}^{-t}}\times 2t+{{t}^{2}}\times (-1)\,{{e}^{-t}}=0\] \[\Rightarrow \]                               \[t{{e}^{-t}}(2-t)=0\] \[\Rightarrow \]                               \[2-t=0\] \[\Rightarrow \]                               \[t=2\,s\]


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