In the circuit shown the capacitor is initially uncharged. The switch is closed at time $t=0s.$ Is given that: $R=1\mathrm{.}0M,C=3\mathrm{.}6F$ and $=20V$

$($a$)$ Calculate the time constant of the circuit $(4$p$)$

$($b$)$ What is the current value immediately after the switch is closed? $(4$p$)$

$($c$)$ Calculate the current after the switch has been closed for $0\mathrm{.}8$ seconds. $(6$p$)$

$($d$)$ Calculate the charge on the capacitor when it is fully charged. $(3$p$)$

$($e$)$ What is the value of the current when the capacitor is fully charged? $(3$p$)$