For the circuit above:

$($a$)$ What is the time constant for the circuit when the switch is in position $1?$

$($b$)$ What is the time constant for the circuit when the switch is in position $2?$

$($c$)$ Assume the circuit reaches steady state at position $1.$ What is the voltage across the capacitor?

$($d$)$ Assume the circuit reaches steady state at position $2.$ What is the voltage across the capacitor?

$($e$)$ Before $\backslash (\backslash$mathrm$\{$t$\}=0\backslash ),$ the circuit is at steady state. The switch moves to position $2$ at $\backslash (\backslash$mathrm$\{$t$\}=0\backslash ).$ The switch then moves back to position $1$ at $\backslash (\backslash$mathrm$\{$t$\}=4\backslash$mathrm$\{$~ms$\}\backslash ).$ Plot the voltage across the capacitor as a function of time, $\backslash ($ v$\_\{\backslash$mathrm$\{$c$\}\}(\backslash$mathrm$\{$t$\})\backslash ),$ in the plot below. Clearly label the time constant, and minimum$/$maximum voltage values, and any steady state voltage value for each transient change.