$2.$ The switch in the circuit has been in the left position for a long time. At $\backslash ($ t$=0\backslash )$ it moves to the right position and stays there.

a$)$ Find the initial voltage drop across the capacitor.

b$)$ Find the initial energy stored by the capacitor.

c$)$ Find the time constant of this circuit for $\backslash ($ t$>0\backslash ).$

d$)$ Write the expression for the capacitor voltage $\backslash ($ v$($t$)\backslash )$ for $\backslash ($ t $\backslash$geq $0\backslash ).$