$(10$ points$)$ Consider the circuit shown.

$($a$)$ Find the combined resistance and capacitance $($symb$.)$

$($b$)$ What's the time constant $$ and the half life $T_{\text{h}\text{a}\text{l}\text{f}\text{?}}?($symb$.)$

$($c$)$ What are $$ and $T_{\text{h}\text{a}\text{l}\text{f}}$ for the special case $R_1=R_2=R$ and $C_1=C_2=C?$

$($d$)$ Sinnose $R=8\mathrm{.}80k$ and $C=14\mathrm{.}0F.$ What are $$ and the half life $\text{'}1$ half! $($mum$.)$

e$)$ What is the current when $t=3,$ assuming the switch is closed al $E=20V?$