The potential difference across a `10H` inductor as a function of time is shown in the figure. At `t=0` current is zero. Then

Options

A. The current in the inductor at `t=6` is 3 amp
B. The current in the inductor at `t=1` sec is `1//4` amp
C. The current in the inductor at `t=4` is `5//2` amp.
D. The variation of current versus time parabola.

Answer

A, B, C, D

Explanation

`V_(L)=L (di)/(dt)impliesLdi=V_(L)dt`
`L int di=int V_(L)d=1/2 . 6 . 10=30`
`L(i_(f)-i_(i))=30` Amp
`i_(f)=30/10=3` amp
for `tlt2`
`V_(L)=10/2t=5t`
`int_(0)^(i) Ldi=intV_(L) dt =5 int_(0)^(1) tdt`
`L(i-0)=5/2`
`impliesi=1//4`
For `tge2`
`V_(L)=(15-5/2t)`
`int_(1)^(i)Ldi=int_(2)^(4)(15-5/2t)dt`
`impliesi=5//2` amp