A $\backslash (2\mathrm{.}40\backslash$mathrm$\{$M$\}\backslash$Omega $\backslash )$ resistor and a $\backslash (1\mathrm{.}40\backslash$mu $\backslash$mathrm$\{$~F$\}\backslash )$ capacitor are connected in series with an ideal battery of emf $\backslash (\backslash$mathscr$\{$E$\}=5\mathrm{.}00\backslash$mathrm$\{$~V$\}\backslash ).$ At $2\mathrm{.}22$ s after the connection is made, what is the rate at which $($a$)$ the charge of the capacitor is increasing, $($b$)$ energy is being stored in the capacitor, $($c$)$ thermal energy is appearing in the resistor, and $($d$)$ energy is being delivered by the battery?