Consider the circuit below. $($a$)$ What is the initial current through resistor $R_2$ when the switch is closed? $($b$)$ What is the current through resistor $R_2$ when the capacitor is fully charged, long after the switch is closed? $($c$)$ What happens if the switch is opened after it has been closed for some time? $($d$)$ If the switch has been closed for a time period long enough for the capacitor to become fully charged, and then the switch is opened, how long before the current through resistor $R_1$ reaches half of its initial value?