For the R-L circuit shown in the figure, the input voltage `V_(i)(t)=u(t)`. Find the current i(t) for `t=1/2` sec.

Options

A. `0.316`
B. `0.613`
C. `0.216`
D. `0.136`

Answer

A

Explanation

`tau=(L)/(R)=1/2 `
`I_(0)=(E)/(R)=1/2==0.5A`
`I=I_(0)(1-e^(-t//tau))" "because" "(-t)/(tau)=(-1//2)/(1//2)=-1`
`I=I_(0)(1-e^(-1))=1/2(1-0.368)=0.316`