The switch has been in position a for a long time. All transients have died out. At t $=0,$ the switch moves instantaneously to position b$.$

a$.$ At t$=0($the last instant that the switch is in position a$),$ what is the current through the capacitor?

b$.$ At t$=0($the last instant that the switch is in position a$),$ what is the voltage across the capacitor?

c$.$ At t$=0+($the f