Electro Magnetic Induction And Alternating Currents Question 488

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

Options:

A) 4s

B) 3s

C) 2s

D) Is

Show Answer

Answer:

Correct Answer: C

Solution:

  • $ L=2mH $ ,

    $ i=t^{2}{{e}^{-t}} $

    $ E=-L\frac{di}{dt}=-L[-t^{2}{{e}^{-t}}+2t{{e}^{-t}}] $

    when $ E=0,-{{e}^{-t}}t^{2}+2t{{e}^{-t}}=0 $

    or, $2t,{{e}^{-t}}={{e}^{-t}},t^{2}\Rightarrow t=2,\sec $ .



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