A $2\mathrm{.}90$ resistor and a $0\mathrm{.}810$F capacitor are connected in series with an ideal battery of emf $85\mathrm{.}00$ V$.$ At $0\mathrm{.}796$ 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?