$1.$ The switch has been in the a position for a long time. At $\backslash ($ t$=0\backslash )$ the switch is thrown from position a to position b$.$

a$)$ Determine the initial current in the inductor.

b$)$ Determine the time constant of the circuit for $\backslash ($ t$>0\backslash ).$

c$)$ Find $\backslash (\backslash$mathrm$\{$i$\},\backslash$mathrm$\{$v$\}1\backslash )$ and v $2$ for $\backslash (\backslash$mathrm$\{$t$\}\backslash$geq $0\backslash ).$