A plot of the current $i(t)$ through a $100$ mH inductor is shown.

${?}^a$ a$.$ Estimate the time constant of the exponential decay of $i(t).$

$v(t)=L\frac{di}{dt}$

$t=2$ from?

l b$.$ Find an expression for $i(t)$ for $t>0.$

${\displaystyle \underset{0}{\overset{t}{}}}k{e}^{-3t}$

$i(t)=I_l()+k_e^{-R_t\frac{t}{L}}$

$1$

c$.$ Find an expression for the voltage across the inductor for $t>0.$

$v(t)=L\frac{di}{dt}$

$100mH\frac{{\displaystyle \underset{0}{\overset{2}{}}}}{3}t{\displaystyle \underset{d}{\overset{d}{}}}$

$3$ d$.$ Estimate the energy stored in the inductor at $t=0\mathrm{.}5sec.$

$E=\frac{1}{2}L{i}^2$

$=\frac{1}{2}(100mH)x^2$readi$(5)$ from $g^{\text{r}\text{a}\text{p}\text{h}}$

$=5{10}^{5}J$