In this circuit, the switch has been open for a very long time. At t $=0$ the switch closes. Vs $=6$ volts, R$1=7$ ohms, R$2=14$ ohms, R$3=6$ ohms. After the switch closes, $($a$)$ what is the initial voltage in the capacitor, in volts? $($b$)$ What is the final value of the voltage in the capacitor, in volts? $($c$)$ What is the time constant of the capacitor voltage decay, in seconds? $($d$)$ How long do you have to wait for the capacitor voltage to reach its final value on engineering standards, in seconds? $($e$)$ At what time, in seconds, has the voltage decayed to half its initial value? The polarity of reference for voltage in the capacitor is plus at the top, minus at the bottom.