a$)$ The switch in the circuit in Fig. P$7\mathrm{.}52$ has been in position a for a long time. At $\backslash ($ t$=0\backslash ),$ the switch moves instantaneously to position b and stays there. Find the initial and final values of the capacitor voltage, the time constant for $\backslash ($ t $\backslash$geq $0\backslash ),$ and the expression for the capacitor voltage for $\backslash ($ t $\backslash$geq $0\backslash ).$

b$)$ Now suppose the switch in the circuit in Fig. P$7\mathrm{.}52$ has been in position b for a long time. At $\backslash ($ t$=0\backslash ),$ the switch moves instantaneously to position a and stays there. Find the initial and final values of the capacitor voltage, the time constant for $\backslash ($ t $\backslash$geq $0\backslash ),$ and the expression for the capacitor voltage for $\backslash ($ t $\backslash$geq $0\backslash ).$

Figure P$7\mathrm{.}52$