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In the circuit shown the switch is opened at t = 0 after having been closed for a long time. Current through the inductor for t > 0 is given by:

In the circuit shown the switch is opened at t = 0 after having been closed for a long time. Current through the inductor for t > 0 is given by: Correct Answer 4 e<sup>-120t</sup>

CONCEPT:

At t = 0, inductor is O.C. and capacitor is S.C.

AT t = ∞ inductor is S.C. and capacitor is O.C.

Inductor opposes sudden change of current, IL (0+) = IL (0-)

Instantaneous value, I(t)  = I(∞) + e -t/ τ .........(1)

EXPLANATION:

At t = 0-

IL(0-) = IL(0+) = 100 / 25 = 4 A

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At t = 0+(at  the instant of switching)

Voltage source is S.C. and inductor is O.C.

[ alt="F1 Harish Madhuri 21.05.2021 D13" src="//storage.googleapis.com/tb-img/production/21/05/F1_Harish_Madhuri_21.05.2021_D13.png" style="height: 141px; width: 233px;">

Rth = 20 + 15 + 25 = 60 Ω 

Τ = L / R = 0.5 / 60 = 1 / 120 sec

At t > 0 or t = ∞ 

[ alt="F1 Harish Madhuri 21.05.2021 D14" src="//storage.googleapis.com/tb-img/production/21/05/F1_Harish_Madhuri_21.05.2021_D14.png" style="height: 137px; width: 187px;">

IL (∞) = 0

From equation (1),

IL (t) = IR (t) = 0 + (4 - 0) e -120 t = 4 e -120 t A

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