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The current through a coil self inductan...

The current through a coil self inductance L = 2 mH is given by `I=t^(2)e^(-1)` at time t. How long it will take to make the e.m.f. zero ?

A

1 s

B

2 s

C

3 s

D

4 s

Text Solution

Verified by Experts

The correct Answer is:
B
`I=t^(2)e^(-t)`
`therefore (dl)/(dt)=2te^(-t)-t^(2)e^(-t)=te^(-t)(2-t)`
The induced emf is `epsilon = -L(dI)/(dt)`
According to given problem, `epsilon = 0`
`rArr (dI)/(dt)=0 " "` (Since `L ne 0`)
or `e^(-t)t(2-t)=0`. Either t = 0 or t = 2 s
t = 2 matches with the option (b).
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