Derive an expression for the current in the circuit depicted in Figure $3\mathrm{.}1.$ Assume that the current through the inductor is initially $10$A at $\backslash (\backslash$mathrm$\{$t$\}=0\backslash ).$

Figure $3\mathrm{.}1$

The voltage source in Figure $3\mathrm{.}1$ is replaced with a voltage source of the form

$\backslash [$

v$($t$)=$e$^\{-$t$\}$

$\backslash ]$

for all $\backslash ($ t$>0\backslash ).$ Derive an expression for the current in the circuit depicted in

Figure $3\mathrm{.}1.$ Again assume that the current through the inductor is initially $10$ A