$($Difficulty: $**)$

In the circuit shown below the switch has been open for a long time and there is no charge on the capacitor.

Assume $R_1=2,R_2=4,C=2F.$

a$)$ The switch $S$ is now closed. Find all the currents just after the switch is closed.

b$)$ Find all the currents after the switch has been closed for a very long time.

c$)$ After the switch has been closed for a very long time it is reopened. Calculate an equation for the

current $i_2(t)$ passing through $R_2$ as a function of time. What is the direction of the current $?$