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

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 $$on and VC $$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?