$7\mathrm{.}35$ The switch in the circuit shown in Figure P$7\mathrm{.}35$ has been closed for a long time before it is opened at $\backslash ($ t$=0\backslash ).$

Figure P$7\mathrm{.}35$

a$.$ Find the initial current $\backslash ($ i$(0)=$I$\_\{0\}\backslash )$ through the inductor at $\backslash ($ t$=0\backslash ).$

b$.$ After switch is opened, find the resistance seen from the inductor.

c$.$ Find time constant $\backslash (\backslash$tau $\backslash ).$