Question

For a coil having L=2 mh, current flow through it is I=t2e−t then the time at which emf become zero :-

Answer 1

Question: 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) 4s

(b) 3s

(c) 2s

(d) 1s

Answer : Option B

Answer 2

The time is 2 sec.

Explanation:

Given that,

Equation of current

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

Inductance = 2 mh

emf = 0

We need to calculate the time

Using formula of emf

$|emf|=L\dfrac{dI}{dt}$

$\dfrac{dI}{dt}=0$

Given equation of current

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

On differentiating

$\dfrac{dI}{dt}=2te^{-t}-t^2e^{-t}$

Put the value of $\dfrac{dI}{dt}$

$2te^{-t}-t^2e^{-t}=0$

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

$2t=t^2$

$t=2\ sec$

Hence, The time is 2 sec.

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Topic : Inductance

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