A time varying voltage V= 2t (Volt) is applied across and ideal inductor of inductance L =2H as shown in Fig. Then (assume current to be zero at t =0)

Options

A. current versus time graph is a parabola
B. energy stored in magnetic field at t = 2 s is 4 J
C. potential energy at time t = 1 s in magnetic field is increasing at a rate of `1Js^(-1)`
D. energy stored in magnetic field is zero all the time.

Answer

A, B, C

Explanation

(a, b, c) We have, V = 2t
`therefore" "V=L.(di)/(dt)=2t or 2.(di)/(dt)=2t or (di)/(dt)=t`
or `(di)=t(dt)`
On integrating, we get `i=(t^(2))/(2)`
i.e., i-t graph is a parabola.
At t = 2 s, `i`= 2 A
`therefore` Potential energy, `U=(1)/(2)Li^(2)=(1)/(2)xx2xx4=4J`
`(dU)/(dt)=Li((di)/(dt))=(2)((r^(2))/(2))(t)=t^(3)`
At t = 1
Potential energy, `(dU)/(dt)= 1Js^(-1)`