GATE Electrical Engineering (EE) 2021 Solved Papers

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Question : 65 of 65

Marks: +1, -0

In the circuit, switch '

{S}

' is in the closed position for a very long time. If the switch is opened at time

{t}

,

=0

, then

{i}_{ {L}}( {t})

in amperes, for

{t} ≥ 0

is:

$8 {e}^{-10 {t}}$
$8+2 {e}^{-10 {t}}$
$10$
$10(1- {e}^{-2 {t}})$

Solution:

At

{t}=0^{-}

{i}_{ {L}}(0^{-})=\;{10}/{1}=10 {A}

At

{t}=∞

i_{L}(∞)=\;{40}/{5}=8 {A}

Time constant

τ=\;{L}/{R}

τ=\;{0.5}/{5}=\;{1}/{10} {sec}

For Ist order

{R}- {L}

circuit,

{i}_{ {L}}( {t})= {i}_{ {L}}(∞)-[ {i}_{ {L}}(∞)- {i}_{ {L}}(0^{+})] {e}^{- {t}} {/} τ

=8-[8-10] {e}^{-10 {t}}

=8+2 {e}^{-10 {t}} {A}

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