Problem $1$a: Capacitors and Resistors

Consider the circuit shown below. Suppose that the switch $($S$)$ has been CLOSED for a really really really long time. The

battery provides a voltage epsi$=1\mathrm{.}0$ Volts $($which does not change as a function of time$).$ The resistances are given by R$1=$

$2$Omega,R$2=1$Omega and the capacitor has a capacitance C$=1$mu F$.$ Suddenly at time t$=0,$ you OPEN the switch.

$($i$)$ Right after time t$=0($instantaneously after the switch is OPEN$),$ what is the current flowing through each

resistor and the battery?

$($ii$)$ The switch is OPEN for a really really really long time. What is the current through each resistor and the

battery?

$($iii$)$ The switch is OPEN for t$=1$ microsecond, such that the capacitor is not fully charged. At this time, what is the

current flowing through each resistor and the battery?