The current in the circuit is, I(t)=I(∞)−[I(∞)−I(0)]e−t∕τ‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I) The time constant, τ=‌
L
R
=‌
5
10
=0.5s At t→∞, inductor behaves as short circuit hence circuit will be
I(∞)=‌
15
10
=1.5A‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(II) At t→0, inductor behaves as open circuit, I(0)=0 I(t)=1.5−[1.5−0]e‌
−t
(1∕2t)
At t=1 sec I(1)=1.5(1−e−2t)‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(III) From equation (II) and (III), ‌