The potential difference across a 2-H inductor as a function of time is shown in Fig. At time t = 0, current is zero.

The variation of current versus time is

Options

A. a straight line
B. a parabola
C. a hyperbola
D. expotential

Answer

B

Explanation

For `t le 1s`
`V_(L)=8t`
`Ldi=V_(L)dt`
`int Ldi = int 8t dt`
`Li =(8t^(2))/(2) = 4t^(2)`
`i=2t^(2)`
so current versus time graph is a parabola
For `1s le t le 2s` ltbtgt `V_(L) = 16 -8t`
`int Ldi=int (16-8t)dt`
`Li = 16t-(8t^(2))/(2)`
`i=8t - 2t^(2)`
so i-t graph in a parabola.
so, for entire time shown, i-t graph in a parabola.