Given that $E=14\mathrm{.}0V,R=1\mathrm{.}50M$ and $C=1\mathrm{.}60F.$

We charge the initially empty capacitor by putting the switch in position $a$ at time $t=0$; so the initial condition is $q(0)=q_0=0$

$($a$)$ What are the time constant $$ and the half life $T?$

$($b$)$ What is the maximum value of the charge $Q$ on and $V_C$ the voltage across the capacitor after a long time $)=($

$($c$)$ What is the maximum value of the current in the circuit? When does it occur? $($hint: it's either $t=0$ or $t=)$

$($d$)$ What is the charge on the capacitor after three time constants?

$($e$)$ How long does it take for the charge $q$ to reach $90\%$ of its maximum?