Question 346: Electromagnetic Induction

Question

For a coil having L = 2 mH, current flow through it is $$I = {t^2}{e^{ - t}}$$ then, the time at which emf become zero

Accepted Answer

Given, $$I = {t^2}{e^{ - t}}$$
So, $${{dI} \over {dt}} = 2t{e^{ - t}} - {t^2}{e^{ - t}}$$
$$\left| \varepsilon  ight| = L{{dI} \over {dt}}$$
here emf is zero when $${{dI} \over {dt}}$$ = 0
$$ 	herefore $$ $$2t{e^{ - t}} - {t^2}{e^{ - t}}$$ = 0
$$ \Rightarrow $$ $$2t{e^{ - t}} = {t^2}{e^{ - t}}$$
$$ \Rightarrow $$ $$t{e^{ - t}}\left( {t - 2} ight)$$ = 0
As t $$ 
e $$ $$\infty $$, t $$ 
e $$ 0
$$ 	herefore $$ t = 2 sec

Answer

2 sec

Answer

1 sec

Answer

4 sec

Answer

3 sec

Electromagnetic Induction

For a coil having L = 2 mH, current flow through it is $I = {t^2}{e^{ - t}}$ then, the time at which emf become zero

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