Consider the below circuit with a constant current source.

The parameter values are $i_s=1,R_1=2,R_2=1,$ and $C=1.($Neglect units in this question.$)$ The switch has been in position a for a long time. At $t=0,$ the switch moves to position $b.$ Answer parts $($a$)-($f$)$ below.

$($a$)(3$ pts$)$ Find the voltage across the capacitor at $t=0,v_C(0).($b$)(2pts)$ Find the current through the capacitor at $t=0,i_C(0).($c$)(5$ pts$)$ Find the voltage across the capacitor as a function of time, $v_C(t),$ for $t0.($d$)(3pts)$ Find the current through the capacitor as a function of time, $i_C(t),$ for $t0.($e$)(2$ pts$)$ Find the steady state voltage across the capacitor as $t.($f$)(3$ pts$)$ Mandatory for honors students, extra credit for all others. Find the energy dissipated by the resistor $R_2$ over the time interval tin$[0,).$

Consider the below circuit with a constant current source.

The parameter values are $i_s=1,R_1=2,R_2=1,$ and $C=1.($Neglect units in this question.$)$ The switch has been in position a for a long time. At $t=0,$ the switch moves to position $b.$ Answer parts $($a$)-($f$)$ below.

$($a$)(3pts)$ Find the voltage across the capacitor at $t=0,v_C(0).$