Correct Option: D

Given circuit

i L (0–) = i L (0+) =	15	where R eq = 25 || (10 + 20)
	Req

		25 × 30	=	25 × 30	Ω
		25 + 30		55

or i L (0–) =	15 × 55	= 1.1 amp.
	25 × 30

Calculation for i _L (∞):
Circuit becomes here the current through the inductor
I_L (∞)=I₁ + I₂

I1 =	VA – 0
	20

=		15 × 10 / 10 + 10 (- 0)	=	150	=	3
		20		20 x 20		8

and I2 =		15	=	3
		25		8

IL =		3	+	3	=	24 + 15	=	39	1 amp.
		5		8		40		40

As we know that the general equation for the current

i (t) = [i (0_–) – i (∞)] e ^–t + i (∞) .....(i)
Calculation for the time constant ():

=		L	=	1 / 2
		Req		[(10 || 100 + 20) || 25]

=		1	=	1
		2(25 / 2)		25

Now, on putting these values in equation (i), we get.
i (t) = [1.1 – 1] e ^{– t / 1/25} + 1